Reversible Jump MCMC Converging to Birth-and-Death MCMC and More General Continuous Time Samplers
Olivier Cappé, Christian P. Robert, Tobias Rydén · RePEc: Research Papers in Economics · 2001
Markov chain Monte Carlo [MCMC] methods for statistical inference, in particular Bayesian inference, have undoubtedly become standard during the past ten years (Cappé and Robert, 2000). For variable dimension problems, often arising through model selection, a popular approach is Green's (1995) reversible jump MCMC [RJMCMC] methodology. Recently however, in the context of mixtures of distributions, Stephens (2000a,b) rekindled interest in a different method based on continuous time birth-and-death processes for estimating the number of components of the mixture, following earlier proposals by Grenander and Miller (1994) and Phillips and Smith (1996). We will call this approach birth-and-death MCMC [BDMCMC]. A main question addressed in the present paper is as follows: is there a fundamental difference between reversible jump and birth-and-death MCMC methodologies, or are these approaches similar? As an answer to this question we show in Section 3 that for any BDMCM...