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Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
Authors:GREEN  PETER J
Institution:Department of Mathematics, University of Bristol Bristol BS8 1TW, U.K.
Abstract:Markov chain Monte Carlo methods for Bayesian computation haveuntil recently been restricted to problems where the joint distributionof all variables has a density with respect to some fixed standardunderlying measure. They have therefore not been available forapplication to Bayesian model determination, where the dimensionalityof the parameter vector is typically not fixed. This paper proposesa new framework for the construction of reversible Markov chainsamplers that jump between parameter subspaces of differingdimensionality, which is flexible and entirely constructive.It should therefore have wide applicability in model determinationproblems. The methodology is illustrated with applications tomultiple change-point analysis in one and two dimensions, andto a Bayesian comparison of binomial experiments.
Keywords:Change-point analysis  Image segmentation  Jump diffusion  Markov chain Monte Carlo  Multiple binomial experiments  Multiple shrinkage  Step function  Voronoi tessellation
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