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rstan

effective number

In Gelman book, the effective number is defined in terms of the following;

  1. R hat
  2. between- within MCMC sequence of variance, B and W
  3. the number of MCMC samples, denoted by n
  4. the number of chains, denoted by m

I do not know how the samplig() calculate the between MCMC sequence of variance for the case chains=1. So, I cannot calculate these terms ( B,W,m). I want to implement some algorithm according to the paper:https://arxiv.org/abs/1804.06788.

Roughly speaking, this paper construct some test statistics which is uniformly distributed under the null hypothesis that the MCMC sampling is correct. And if MCMC sampling is not correct, then the histogram of the test statistics become skew shape and this deviation from uniformity tells us the MCMC contains bias. I want to implement but it needs to calculate the above quantities.

In rstan, is there such function to extract the above quantities ? I think the process of calculation of R hat statistics, the above quantities B,W, m are retained in some place in the stanfit S4 object.

I am sorry, I found n_eff, but I do not know the choice of m of the case chains =1.

Solution

  • In the case that only one chain is estimated (which should not be happening anyway), then m = 2 because the post-warmup draws from the single chain are split into the first half and the second half. This splitting method is discussed in the documentation.