The multiset sampler

Scotland C. Leman, Yuguo Chen, Michael Lavine

Research output: Contribution to journalArticlepeer-review

Abstract

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 moves 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.

Original languageEnglish (US)
Pages (from-to)1029-1041
Number of pages13
JournalJournal of the American Statistical Association
Volume104
Issue number487
DOIs
StatePublished - Oct 14 2009

Keywords

  • Data augmentation
  • Gibbs sampler
  • Markov chain Monte Carlo
  • Metropolis-hastings algorithm
  • Multimodal
  • Proposal distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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