Nonparametric Convergence Assessment for MCMC Model Selection

In this paper, we consider 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 which 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. We illustrate our approaches with several practical examples.