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I use measures of Gelman and Rubin or Geweke. However, they are not applicable to sampling from multi-modal distribution, say p(x), because a chain can be stuck in a local mode. In such cases, the chain seems to be stationary and the two convergence measures will give a bad result that it is safe to terminate sampling, actually it is not. When I handled toy problems, I set first or second moment of target distributions is known. The distance between the value and its approximation using the corresponding chain was used as a convergence measure, but it is practically not applicable.

Is there any MCMC convergence measure that makes use of target distributions?

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  • $\begingroup$ Could you please add references to the measures you mentioned? $\endgroup$ – juliohm Nov 6 '13 at 23:03
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    $\begingroup$ What do you mean 'makes use of target distributions'? General convergence measures should only use MCMC samples. $\endgroup$ – jaradniemi Mar 26 '15 at 15:12
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    $\begingroup$ Both Gelman-Rubin and Geweke are applicable to multi-model distributions, but they will both give misleading results if all chains are in a single mode. $\endgroup$ – jaradniemi Mar 26 '15 at 15:12
  • $\begingroup$ I answered a similar question [Convergence of MCMC for ill-behaved functions] (stats.stackexchange.com/a/391215/7224). $\endgroup$ – Xi'an Feb 7 at 5:28

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