Variable Dimension Models and Reversible Jump Algorithms
While the previous chapters have presented a general class of MCMC algorithms, there exist settings where they are not general enough. A particular case of such settings is that of variable dimension models. There, the parameter (and simulation) space is not well defined, being a finite or denumerable collection of unrelated subspaces. To have an MCMC algorithm moving within this collection of spaces requires more advanced tools, if only because of the associated measure theoretic subtleties. Section 11.1 motivates the use of variable dimension models in the setup of Bayesian model choice and model comparison, while Section 11.2 presents the general theory of reversible jump algorithms, which were tailored for these models. Section 11.3 examines further algorithms and methods related to this issue.
KeywordsPosterior Distribution Prior Distribution Acceptance Probability Markov Jump Process MCMC Algorithm
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