Adaptive Proposal Construction for Reversible Jump MCMC

摘要

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 fixed-dimensional 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.