Approximate Bayesian Computation in Julia

This package contains some approximate Bayesian computation algorithms.

A toy example for each algorithm is also provided in the examples.

Algorithms:

• ABC rejection sampling (ABC-RS)
• ABC Markov chain Monte Carlo (ABC-MCMC)
• ABC population Monte Carlo (ABC-PMC)

Kernels:

• Uniform
• Gaussian

Distance function(s):

• (Weighted) Euclidean distance
• Gaussian kernel distance

Posterior inference checks are also provided see ?quantile_interval and ?loss.

• Documentation: https://samuelwiqvist.github.io/ApproximateBayesianComputation.jl/.

Minimal working example

We will in this minimal working example using the ABC rejection sampling algorithm to learn the mean for a Normal distribution with known standard deviation.

Walk-through

Load packages, and set up the model.

using ApproximateBayesianComputation
using Distributions

μ = 0 # true value for the mean, the parameter that  we want to estimate
σ = 1 # known standard deviation
n = 100 # nbr of observations

y = rand(Normal(μ,σ),100) # generate some data

# the prior is a normal distribution with μ = 0.1, and σ = 1
prior = Normal(0.1, 1)

Define the functions needed for the ABC-RS algorithm.

# function to sample from the prior
sample_from_prior() = rand(prior)

# function to generate data
generate_data(μ) = rand(Normal(μ[1],σ),n)

# the summary statistics are the mean and the standard
# deviation, i.e. the sufficient statistics for the data
calc_summary(y_star,y) = [mean(y_star); std(y_star)]

# distance function
ρ(s_star, s) = euclidean_dist(s_star, s, ones(2))

Set up the ABC-RS problem.

problem = ABCRS(10^6,
                0.01,
                Data(y),
                1,
                cores = 1,
                print_interval = 10^5)

Run ABC-RS.

approx_posterior_samples = sample(problem,
                                  sample_from_prior,
                                  generate_data,
                                  calc_summary,
                                  ρ)

Check posterior quantile interval.

posterior_quantile_interval = quantile_interval(approx_posterior_samples)

Posterior and prior distribution.

How to use this package

This package is not added to METADATA.jl. But, you can still install the package locally by running:

Pkg.clone("https://github.com/SamuelWiqvist/ApproximateBayesianComputation.jl")

To run the examples directly in your browser simply click on the binder link, and then open the Jupyter notebook examples.ipynb. However, launching the binder server might take a while (in some cases up to 20 minutes) since the environment has to be installed on the server.

About this package

This package was originally created for the graduate course Approximate Bayesian Computation at Chalmers University of Technology.