I used coda package's effectiveSize() to find the effective sample size of my MCMC simulation. My effective sample size is greater than the actual sample size, e.g. 9813.626 greater than 9501. I wonder if that makes sense?

My understanding is that the effective sample size cannot be greater than the actual sample size, and will be smaller when there is more autocorrelation.


For a particular definition of autocorrelation, negative autocorrelation can cause $N_{eff} > n$. This answer gives a MWE using coda.


In principle yes, you are right. The sample size should not be larger.

  • One possibility is that the package is using some optimization routine to improve the variance such as VEGAS.

  • As kjetil b halvorsen pointed out, it could be that autocorrelation is negative. But I'm not seeing how.

  • 1
    $\begingroup$ well, in principle, with negative autocorrelations, the effective sample size could be larger than the actual sample size. But I doubt that is likely to happen in practice! But your hard statement that it is impossible is untrue! $\endgroup$ Mar 28 '14 at 19:39
  • $\begingroup$ You are right @kjetilbhalvorsen, I didn't even thought about that. Any sane situation where this would happen? $\endgroup$ Mar 28 '14 at 20:01

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