Adaptive thinning for testing distributions

[njtierney]

• The KS test for equivalence of mcmc and iid samples is sensitive specifically to correlation in the MCMC samples, i.e., it assumes that there are n independent samples and the test statistic biases the p-value (because the samples are non-independent).
• An ad hoc way of doing this is just to thin to reduce correlation
• It would be more stable to estimate the amount of correlation and then thin appropriately

[goldingn]

Here's code to find a reasonable thinning rate for an mcmclist object:

# find a thinning rate that sufficiently reduces autocorrelation in the samples
find_thinning <- function(draws, max_thin = 100, autocorr_threshold = 0.01) {
  autocorr_list <- coda::autocorr(draws, lags = seq_len(max_thin))
  autocorrs <- do.call(cbind, autocorr_list)
  mean_autocorr <- rowMeans(autocorrs)
  smallest_thin <- which(mean_autocorr < autocorr_threshold)[1]
  if (is.na(smallest_thin)) {
    smallest_thin <- max_thin
    warning("could not find any thinning value that reduces mean autocorrelation to below the threshold, using the maximum thinning amount",
            call. = FALSE)
  }
  smallest_thin
}

# # example
# x <- normal(0, 1)
# m <- model(x)
# draws <- mcmc(m)
# find_thinning(draws)