On the Relationship Between Markov chain Monte Carlo Methods for Model Uncertainty
- 1 June 2001
- journal article
- Published by Taylor & Francis in Journal of Computational and Graphical Statistics
- Vol. 10 (2) , 230-248
- https://doi.org/10.1198/10618600152627924
Abstract
This article considers Markov chain computational methods for incorporating uncertainty about the dimension of a parameter when performing inference within a Bayesian setting. A general class of methods is proposed for performing such computations, based upon a product space representation of the problem which is similar to that of Carlin and Chib. It is shown that all of the existing algorithms for incorporation of model uncertainty into Markov chain Monte Carlo (MCMC) can be derived as special cases of this general class of methods. In particular, we show that the popular reversible jump method is obtained when a special form of Metropolis–Hastings (M–H) algorithm is applied to the product space. Furthermore, the Gibbs sampling method and the variable selection method are shown to derive straightforwardly from the general framework. We believe that these new relationships between methods, which were until now seen as diverse procedures, are an important aid to the understanding of MCMC model selection p...Keywords
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