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. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008.

[1]  H. Haario,et al.  An adaptive Metropolis algorithm , 2001 .

[2]  G. Roberts,et al.  Adaptive Markov Chain Monte Carlo through Regeneration , 1998 .

[3]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[4]  Simon J. Godsill,et al.  A reversible jump sampler for autoregressive time series , 1997, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[5]  M. Stephens.  Bayesian analysis of mixture models with an unknown number of components- an alternative to reversible jump methods , 2000 .

[6]  S. Brooks,et al.  Classical model selection via simulated annealing , 2003, Journal of the Royal Statistical Society: Series B (Statistical Methodology).

[7]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[8]  Heikki Haario,et al.  Adaptive proposal distribution for random walk Metropolis algorithm , 1999, Comput. Stat..

[9]  Anatoly Zhigljavsky,et al.  Self-regenerative Markov chain Monte Carlo with adaptation , 2003 .

[10]  S. Chib,et al.  Bayes inference in regression models with ARMA (p, q) errors , 1994 .

[11]  A. Doucet,et al.  Reversible Jump Markov Chain Monte Carlo Strategies for Bayesian Model Selection in Autoregressive Processes , 2004, Journal of Time Series Analysis.

[12]  Walter R. Gilks,et al.  Adaptive Direction Sampling , 1994 .

[13]  Brian D. Ripley,et al.  Stochastic Simulation , 2005 .

[14]  S. Godsill.  On the Relationship Between Markov chain Monte Carlo Methods for Model Uncertainty , 2001 .

[15]  Bradley P. Carlin,et al.  Structured Markov Chain Monte Carlo , 2000 .

[16]  L Tierney,et al.  Some adaptive monte carlo methods for Bayesian inference. , 1999, Statistics in medicine.

[17]  P. Dellaportas,et al.  Bayesian variable and link determination for generalised linear models , 2003 .

[18]  J. Gåsemyr.  On an adaptive version of the Metropolis-Hastings algorithm with independent proposal distribution , 2003 .

[19]  G. Roberts,et al.  Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions , 2003 .

[20]  Simon J. Godsill,et al.  On the relationship between MCMC model uncertainty methods , 1997 .

[21]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[22]  J. Gåsemyr,et al.  An Application of Adaptive Independent Chain Metropolis–Hastings Algorithms in Bayesian Hazard Rate Estimation , 2004 .

[23]  B. Carlin,et al.  Bayesian Model Choice Via Markov Chain Monte Carlo Methods , 1995 .

[24]  Matthew West,et al.  Priors and component structures in autoregressive time series models , 1999 .