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The Multiset Sampler
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DOI：10.1198/jasa.2009.tm08047.png)
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We introduce the multiset sampler (MSS), a new Metropolis-Hastings algorithm for drawing samples from a posterior distribution. The MSS is designed to be effective when the posterior has the feature that the parameters can be divided into two. sets, X, the parameters of interest and Y, the nuisance parameters. We contemplate a sampler that iterates between X move,; and Y moves. We consider the case where either (a) Y is discrete and lives on a finite set or (b) Y is continuous and lives on a bounded set. After presenting some background, we define a multiset and show how to construct a distribution on one. The construction may seem artificial and pointless at first, but several small examples illustrate its value. Finally, we demonstrate the MSS in several realistic examples and compare it with alternatives.
Keyword:
Data augmentation
Gibbs sampler
Markov chain Monte Carlo
Metropolis-Hastings algorithm
Multimodal
Proposal distribution
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