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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.
As noted, Geyer and Vehtari suggest using n as the denominator, not n-1. This is also used in Stan's, posterior's, and ArviZ's implementations of ESS. Unless we have a reference with simulations for our choice choice, I propose we instead use n-1 as suggested by these sources.
With #58 and #53, this is the last change needed to make our estimates identical to posterior's and ArviZ's within floating point precision.
The text was updated successfully, but these errors were encountered:
Not sure where the n - 1 originally comes from. Maybe since the FFT implementation does not require any rescaling (assuming they yield identical values, which I think they do)?
In any case, I don't think there's a convincing argument (yet) to deviate from the standard software in the area.
Currently we use the estimate of autocov with denominator
n-1
, which is unbiased for lagk = 0
and biased fork > 1
:MCMCDiagnosticTools.jl/src/ess.jl
Lines 10 to 13 in 57cacc1
As noted, Geyer and Vehtari suggest using
n
as the denominator, notn-1
. This is also used in Stan's, posterior's, and ArviZ's implementations of ESS. Unless we have a reference with simulations for our choice choice, I propose we instead usen-1
as suggested by these sources.With #58 and #53, this is the last change needed to make our estimates identical to posterior's and ArviZ's within floating point precision.
The text was updated successfully, but these errors were encountered: