Tobias Ryden


Title: Reversible jump and birth-and-death MCMC: theoretical
  connections and practical comparisons


Abstract: Green's (1995) reversible jump MCMC has had an enormous
impact on Bayesian analysis of variable-dimension problems. Recently,
Stephens (2000) suggested an alternative approach, birth-and-death
MCMC, in the particular context of Bayesian inference in mixture
models. The question we want to address is: are these approaches
fundamentally different, or are they somehow related? As a theoretical
answer to this question we show that for any BDMCMC algorithm, there
is a sequence of RJMCMC samplers that converge weakly to the BDMCMC
sampler under rescaling of time. This leads us to a generalisation of
BDMCMC that we could denote continuous time MCMC. We also report some
results from a comparison of RJMCMC and CTMCMC algorithms for a
mixture model example.