Nonparametric convergence assessment for MCMC model selection

This article considers the problem of assessing the performance of MCMC model selection algorithms using a variety of nonparametric techniques. We consider a wide range of model selection problems to which MCMC model selection may be applied and propose several distance measures that can be used to quantify the similarity between multiple replications. These measures may be used to assess convergence by examining how "close" these replications of the chain are, since if all chains are at stationarity, then this distance should be small. Finally, we describe an alternative approach based upon the estimation of the convergence rate of the sub-Markov chain represented by the model indicators and finish by illustrating our approaches with several practical examples.