Convergence Assessment for Reversible Jump MCMC Simulations

Abstract

In this paper we introduce the problem of assessingconvergence of reversible jump MCMC algorithms on the basisof simulation output. We discuss the various directapproaches which could be employed, together with theirassociated drawbacks. Using the example of fitting agraphical Gaussian model via RJMCMC, we show how thesimulation output for models which can be parameterised sothat parameters of primary interest retain a coherentinterpretation throughout the simulation, can be used toassess convergence. In the context of this example, weextend the work of Gelman and Rubin (1992) and Brooks andGelman (1998), to provide convergence assessment proceduresfor graphical model determination problems, but which maybe applied to any form of model choice problem and, indeed,MCMC simulations more generally.