Adaptive Proposal Construction for Reversible Jump MCMC

In this paper, we show how the construction of a trans-dimensional equivalent of the Gibbs sampler can be used to obtain a powerful suite of adaptive algorithms suitable for trans-dimensional MCMC samplers. These algorithms adapt at the local scale, optimizing performance at each iteration in contrast to the globally adaptive scheme proposed by others for the fixeddimensional problem. Our adaptive scheme ensures suitably high acceptance rates for MCMC and RJMCMC proposals without the need for (often prohibitively) time-consuming pilot-tuning exercises. We illustrate our methods using the problem of Bayesian model discrimination for the important class of autoregressive time series models and, through the use of a variety of prior and proposal structures, demonstrate their ability to provide powerful and effective adaptive sampling schemes.