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.


2 Answers 2


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! $\endgroup$ Commented Mar 28, 2014 at 19:39
  • $\begingroup$ You are right @kjetilbhalvorsen, I didn't even thought about that. Any sane situation where this would happen? $\endgroup$ Commented Mar 28, 2014 at 20:01

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