I have an MCMC sampler with weighted samples and I want to compute effective sample size at every step to determine sample degeneracy. I am using the following formula:

$ESS = \frac{(\sum_{i=1}^N{w_i})^2}{\sum_{i=1}^Nw_i^2}$

I realized that this metric does not measure effective sample size well when MCMC algorithm works badly.

For instance, suppose that all samples degenerate into one bad sample, i.e. $x_1 = x_2 = ... = x_N$. Then, after assigning weights (by likelihood $p(y|x_i)$) all samples will have the same weight thus $ESS$ is equal to $N$ while in fact there is only one sample representing the distribution.

Are there alternative ways to compute $ESS$ for MCMC?

  • $\begingroup$ Your ESS definition seems to be the one from Importance Sampling, and not from MCMC. What are the $w$s? $\endgroup$ – Greenparker Feb 15 at 10:56
  • $\begingroup$ @Greenparker $w_i$s are the weights that are assigned to propagated particles after receiving observation at time $t$, i.e. $p(y_t|x_t)$. $\endgroup$ – KRL Feb 18 at 2:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.