MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 1.5.0 on Thursday 4 July 2024. Using Julia version 1.10.4.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Search · MCMCDiagnosticTools.jl
+
+
+
+
+
+Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Search · MCMCDiagnosticTools.jl
+
+
+
+
+
+Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Search · MCMCDiagnosticTools.jl
+
+
+
+
+
+Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Search · MCMCDiagnosticTools.jl
+
+
+
+
+
+Settings
This document was generated with Documenter.jl version 0.27.25 on Tuesday 26 September 2023. Using Julia version 1.9.3.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
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Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
)
Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
See also: ESSMethod, FFTESSMethod, BDAESSMethod
sourceThe following methods are supported:
MCMCDiagnosticTools.ESSMethod — TypeESSMethod <: AbstractESSMethod
The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
References
Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMCMCDiagnosticTools.FFTESSMethod — TypeFFTESSMethod <: AbstractESSMethod
The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
sourceMCMCDiagnosticTools.BDAESSMethod — TypeBDAESSMethod <: AbstractESSMethod
The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
References
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMonte Carlo standard error
MCMCDiagnosticTools.mcse — Functionmcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
:bm for batch means [Glynn1991]:imse initial monotone sequence estimator [Geyer1992]:ipse initial positive sequence estimator [Geyer1992]
sourceR⋆ diagnostic
MCMCDiagnosticTools.rstar — Functionrstar(
rng=Random.GLOBAL_RNG,
@@ -23,3 +478,4 @@
true
References
Lambert, B., & Vehtari, A. (2020). $R^*$: A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers.
sourceOther diagnostics
MCMCDiagnosticTools.discretediag — Functiondiscretediag(chains::AbstractArray{<:Real,3}; frac=0.3, method=:weiss, nsim=1_000)
Compute discrete diagnostic where method can be one of :weiss, :hangartner, :DARBOOT, :MCBOOT, :billinsgley, and :billingsleyBOOT.
sourceMCMCDiagnosticTools.gelmandiag — Functiongelmandiag(chains::AbstractArray{<:Real,3}; alpha::Real=0.95)
Compute the Gelman, Rubin and Brooks diagnostics.
sourceMCMCDiagnosticTools.gelmandiag_multivariate — Functiongelmandiag_multivariate(chains::AbstractArray{<:Real,3}; alpha::Real=0.05)
Compute the multivariate Gelman, Rubin and Brooks diagnostics.
sourceMCMCDiagnosticTools.gewekediag — Functiongewekediag(x::AbstractVector{<:Real}; first::Real=0.1, last::Real=0.5, kwargs...)
Compute the Geweke diagnostic from the first and last proportion of samples x.
sourceMCMCDiagnosticTools.heideldiag — Functionheideldiag(
x::AbstractVector{<:Real}; alpha::Real=0.05, eps::Real=0.1, start::Int=1, kwargs...
)
Compute the Heidelberger and Welch diagnostic.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(x::AbstractVector{<:Real}; q, r, s, eps, range)
Compute the Raftery and Lewis diagnostic.
sourceSettings
This document was generated with Documenter.jl version 0.27.3 on Monday 12 July 2021. Using Julia version 1.6.1.
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Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
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Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
)
Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
See also: ESSMethod, FFTESSMethod, BDAESSMethod
sourceThe following methods are supported:
MCMCDiagnosticTools.ESSMethod — TypeESSMethod <: AbstractESSMethod
The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
References
Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMCMCDiagnosticTools.FFTESSMethod — TypeFFTESSMethod <: AbstractESSMethod
The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
sourceMCMCDiagnosticTools.BDAESSMethod — TypeBDAESSMethod <: AbstractESSMethod
The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
References
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMonte Carlo standard error
MCMCDiagnosticTools.mcse — Functionmcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
:bm for batch means [Glynn1991]:imse initial monotone sequence estimator [Geyer1992]:ipse initial positive sequence estimator [Geyer1992]
sourceR⋆ diagnostic
MCMCDiagnosticTools.rstar — Functionrstar(
rng=Random.GLOBAL_RNG,
@@ -25,3 +480,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.3 on Wednesday 22 September 2021. Using Julia version 1.6.2.
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Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
+Home · MCMCDiagnosticTools.jl
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+MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
)
Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
See also: ESSMethod, FFTESSMethod, BDAESSMethod
sourceThe following methods are supported:
MCMCDiagnosticTools.ESSMethod — TypeESSMethod <: AbstractESSMethod
The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
References
Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMCMCDiagnosticTools.FFTESSMethod — TypeFFTESSMethod <: AbstractESSMethod
The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
sourceMCMCDiagnosticTools.BDAESSMethod — TypeBDAESSMethod <: AbstractESSMethod
The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
References
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMonte Carlo standard error
MCMCDiagnosticTools.mcse — Functionmcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
:bm for batch means [Glynn1991]:imse initial monotone sequence estimator [Geyer1992]:ipse initial positive sequence estimator [Geyer1992]
sourceR⋆ diagnostic
MCMCDiagnosticTools.rstar — Functionrstar(
rng=Random.GLOBAL_RNG,
@@ -25,3 +480,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.3 on Tuesday 23 November 2021. Using Julia version 1.6.4.
Search · MCMCDiagnosticTools.jl Settings
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Search · MCMCDiagnosticTools.jl
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Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
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+MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
)
Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
See also: ESSMethod, FFTESSMethod, BDAESSMethod
sourceThe following methods are supported:
MCMCDiagnosticTools.ESSMethod — TypeESSMethod <: AbstractESSMethod
The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
References
Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMCMCDiagnosticTools.FFTESSMethod — TypeFFTESSMethod <: AbstractESSMethod
The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
sourceMCMCDiagnosticTools.BDAESSMethod — TypeBDAESSMethod <: AbstractESSMethod
The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
References
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMonte Carlo standard error
MCMCDiagnosticTools.mcse — Functionmcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
:bm for batch means [Glynn1991]:imse initial monotone sequence estimator [Geyer1992]:ipse initial positive sequence estimator [Geyer1992]
sourceR⋆ diagnostic
MCMCDiagnosticTools.rstar — Functionrstar(
rng=Random.GLOBAL_RNG,
@@ -25,3 +480,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.10 on Saturday 25 December 2021. Using Julia version 1.7.1.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.10 on Saturday 25 December 2021. Using Julia version 1.7.1.
Search · MCMCDiagnosticTools.jl
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This document was generated with Documenter.jl version 0.27.10 on Saturday 25 December 2021. Using Julia version 1.7.1.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
)
Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
See also: ESSMethod, FFTESSMethod, BDAESSMethod
sourceThe following methods are supported:
MCMCDiagnosticTools.ESSMethod — TypeESSMethod <: AbstractESSMethod
The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
References
Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMCMCDiagnosticTools.FFTESSMethod — TypeFFTESSMethod <: AbstractESSMethod
The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
sourceMCMCDiagnosticTools.BDAESSMethod — TypeBDAESSMethod <: AbstractESSMethod
The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
References
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMonte Carlo standard error
MCMCDiagnosticTools.mcse — Functionmcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
:bm for batch means [Glynn1991]:imse initial monotone sequence estimator [Geyer1992]:ipse initial positive sequence estimator [Geyer1992]
sourceR⋆ diagnostic
MCMCDiagnosticTools.rstar — Functionrstar(
rng=Random.GLOBAL_RNG,
@@ -26,3 +481,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
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Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
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+MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
)
Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
See also: ESSMethod, FFTESSMethod, BDAESSMethod
sourceThe following methods are supported:
MCMCDiagnosticTools.ESSMethod — TypeESSMethod <: AbstractESSMethod
The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
References
Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMCMCDiagnosticTools.FFTESSMethod — TypeFFTESSMethod <: AbstractESSMethod
The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
sourceMCMCDiagnosticTools.BDAESSMethod — TypeBDAESSMethod <: AbstractESSMethod
The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
References
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMonte Carlo standard error
MCMCDiagnosticTools.mcse — Functionmcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
:bm for batch means [Glynn1991]:imse initial monotone sequence estimator [Geyer1992]:ipse initial positive sequence estimator [Geyer1992]
sourceR⋆ diagnostic
MCMCDiagnosticTools.rstar — Functionrstar(
rng=Random.GLOBAL_RNG,
@@ -26,3 +481,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.23 on Friday 11 November 2022. Using Julia version 1.8.2.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.23 on Friday 11 November 2022. Using Julia version 1.8.2.
Search · MCMCDiagnosticTools.jl
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This document was generated with Documenter.jl version 0.27.23 on Friday 11 November 2022. Using Julia version 1.8.2.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
)
Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, chains, parameters) with the method and a maximum lag of maxlag.
See also: ESSMethod, FFTESSMethod, BDAESSMethod
sourceThe following methods are supported:
MCMCDiagnosticTools.ESSMethod — TypeESSMethod <: AbstractESSMethod
The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
References
Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMCMCDiagnosticTools.FFTESSMethod — TypeFFTESSMethod <: AbstractESSMethod
The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
sourceMCMCDiagnosticTools.BDAESSMethod — TypeBDAESSMethod <: AbstractESSMethod
The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
References
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMonte Carlo standard error
MCMCDiagnosticTools.mcse — Functionmcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
:bm for batch means [Glynn1991]:imse initial monotone sequence estimator [Geyer1992]:ipse initial positive sequence estimator [Geyer1992]
sourceR⋆ diagnostic
MCMCDiagnosticTools.rstar — Functionrstar(
rng::Random.AbstractRNG=Random.default_rng(),
@@ -30,3 +485,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.23 on Monday 12 December 2022. Using Julia version 1.8.3.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.23 on Monday 12 December 2022. Using Julia version 1.8.3.
Search · MCMCDiagnosticTools.jl
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This document was generated with Documenter.jl version 0.27.23 on Monday 12 December 2022. Using Julia version 1.8.3.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and potential scale reduction
The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
)
Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, chains, parameters) with the method and a maximum lag of maxlag.
See also: ESSMethod, FFTESSMethod, BDAESSMethod
sourceThe following methods are supported:
MCMCDiagnosticTools.ESSMethod — TypeESSMethod <: AbstractESSMethod
The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
References
Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMCMCDiagnosticTools.FFTESSMethod — TypeFFTESSMethod <: AbstractESSMethod
The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
Info To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
sourceMCMCDiagnosticTools.BDAESSMethod — TypeBDAESSMethod <: AbstractESSMethod
The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
References
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
sourceMonte Carlo standard error
MCMCDiagnosticTools.mcse — Functionmcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
:bm for batch means [Glynn1991]:imse initial monotone sequence estimator [Geyer1992]:ipse initial positive sequence estimator [Geyer1992]
sourceR⋆ diagnostic
MCMCDiagnosticTools.rstar — Functionrstar(
rng::Random.AbstractRNG=Random.default_rng(),
@@ -32,3 +487,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.23 on Wednesday 14 December 2022. Using Julia version 1.8.3.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.23 on Wednesday 14 December 2022. Using Julia version 1.8.3.
Search · MCMCDiagnosticTools.jl
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This document was generated with Documenter.jl version 0.27.23 on Wednesday 14 December 2022. Using Julia version 1.8.3.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
The effective sample size (ESS) and $\widehat{R}$ can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
The effective sample size (ESS) and $\widehat{R}$ can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
[estimator,]
samples::AbstractArray{<:Union{Missing,Real},3};
method=ESSMethod(),
@@ -36,3 +491,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.23 on Thursday 12 January 2023. Using Julia version 1.8.5.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.23 on Thursday 12 January 2023. Using Julia version 1.8.5.
Search · MCMCDiagnosticTools.jl
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This document was generated with Documenter.jl version 0.27.23 on Thursday 12 January 2023. Using Julia version 1.8.5.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
The effective sample size (ESS) and $\widehat{R}$ can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
+Home · MCMCDiagnosticTools.jl
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+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
The effective sample size (ESS) and $\widehat{R}$ can be estimated with ess_rhat.
MCMCDiagnosticTools.ess_rhat — Functioness_rhat(
[estimator,]
samples::AbstractArray{<:Union{Missing,Real},3};
method=ESSMethod(),
@@ -36,3 +491,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.23 on Thursday 12 January 2023. Using Julia version 1.8.5.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.23 on Thursday 12 January 2023. Using Julia version 1.8.5.
Search · MCMCDiagnosticTools.jl
+
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+
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This document was generated with Documenter.jl version 0.27.23 on Thursday 12 January 2023. Using Julia version 1.8.5.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real},3};
kind=:bulk,
autocov_method=AutocovMethod(),
@@ -55,3 +510,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.24 on Monday 27 February 2023. Using Julia version 1.8.5.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.24 on Monday 27 February 2023. Using Julia version 1.8.5.
Search · MCMCDiagnosticTools.jl
+
+
+
+
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+Settings
This document was generated with Documenter.jl version 0.27.24 on Monday 27 February 2023. Using Julia version 1.8.5.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real},3};
kind=:bulk,
autocov_method=AutocovMethod(),
@@ -55,3 +510,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.24 on Monday 27 February 2023. Using Julia version 1.8.5.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.24 on Monday 27 February 2023. Using Julia version 1.8.5.
Search · MCMCDiagnosticTools.jl
+
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+
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+Settings
This document was generated with Documenter.jl version 0.27.24 on Monday 27 February 2023. Using Julia version 1.8.5.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 1.2.1 on Wednesday 14 February 2024. Using Julia version 1.10.0.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real},3};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.24 on Thursday 4 May 2023. Using Julia version 1.8.5.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.24 on Thursday 4 May 2023. Using Julia version 1.8.5.
Search · MCMCDiagnosticTools.jl
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This document was generated with Documenter.jl version 0.27.24 on Thursday 4 May 2023. Using Julia version 1.8.5.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real},3};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.24 on Monday 22 May 2023. Using Julia version 1.9.0.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.24 on Monday 22 May 2023. Using Julia version 1.9.0.
Search · MCMCDiagnosticTools.jl
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This document was generated with Documenter.jl version 0.27.24 on Monday 22 May 2023. Using Julia version 1.9.0.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.24 on Wednesday 31 May 2023. Using Julia version 1.9.0.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.24 on Wednesday 31 May 2023. Using Julia version 1.9.0.
Search · MCMCDiagnosticTools.jl
+
+
+
+
+
+Settings
This document was generated with Documenter.jl version 0.27.24 on Wednesday 31 May 2023. Using Julia version 1.9.0.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.25 on Thursday 3 August 2023. Using Julia version 1.9.2.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.25 on Thursday 3 August 2023. Using Julia version 1.9.2.
Search · MCMCDiagnosticTools.jl
+
+
+
+
+
+Settings
This document was generated with Documenter.jl version 0.27.25 on Thursday 3 August 2023. Using Julia version 1.9.2.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 0.27.25 on Wednesday 4 October 2023. Using Julia version 1.9.3.
Search · MCMCDiagnosticTools.jl Settings
This document was generated with Documenter.jl version 0.27.25 on Wednesday 4 October 2023. Using Julia version 1.9.3.
Search · MCMCDiagnosticTools.jl
+
+
+
+
+
+Settings
This document was generated with Documenter.jl version 0.27.25 on Wednesday 4 October 2023. Using Julia version 1.9.3.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 1.1.0 on Friday 6 October 2023. Using Julia version 1.9.3.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 1.1.2 on Monday 30 October 2023. Using Julia version 1.9.3.
Home · MCMCDiagnosticTools.jl MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Functioness(
samples::AbstractArray{<:Union{Missing,Real}};
kind=:bulk,
relative::Bool=false,
@@ -56,3 +511,4 @@
)
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
sourceMCMCDiagnosticTools.rafterydiag — Functionrafterydiag(
x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
)
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy. The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
- VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
- BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
- FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence. Handbook of Markov Chain Monte Carlo. pp. 175-97. pdf
- Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72. doi: 10.1007/978-3-642-27440-4_18
- Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
- Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
- Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
- Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
- Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
- Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
- Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
Settings
This document was generated with Documenter.jl version 1.2.1 on Wednesday 14 February 2024. Using Julia version 1.10.0.