Annealed Importance Sampling Reversible Jump MCMC Algorithms

• Published in: Journal of computational and graphical statistics 2013-09, Vol.22 (3), p.623-648
• Main Authors: Karagiannis, Georgios, Andrieu, Christophe
• Format: Article
• Language: English
• Subjects: Algorithms; Approximation; Bayesian analysis; Bayesian model selection/determination; Decision making models; Gaussian mixture models; ICMS Highlights: Advances in MCMC; Markov analysis; Monte Carlo simulation; Poisson change point problem; Pseudo-marginal MCMC; Studies
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1080/10618600.2013.805651

We develop a methodology to efficiently implement the reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithms of Green, applicable for example to model selection inference in a Bayesian framework, which builds on the "dragging fast variables" ideas of Neal. We call such algorithms annealed importance sampling reversible jump (aisRJ). The proposed procedures can be thought of as being exact approximations of idealized RJ algorithms which in a model selection problem would sample the model labels only, but cannot be implemented. Central to the methodology is the idea of bridging different models with fictitious intermediate models, whose role is to introduce smooth intermodel transitions and, as we shall see, improve performance. Efficiency of the resulting algorithms is demonstrated on two standard model selection problems and we show that despite the additional computational effort incurred, the approach can be highly competitive computationally. Supplementary materials for the article are available online.