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?