A generalized Markov sampler

Jonathan M. Keith, Dirk P. Kroese, Darryn Bryant

Research output: Contribution to journalReview ArticleResearchpeer-review

32 Citations (Scopus)

Abstract

A recent development of the Markov chain Monte Carlo (MCMC) technique is the emergence of MCMC samplers that allow transitions between different models. Such samplers make possible a range of computational tasks involving models, including model selection, model evaluation, model averaging and hypothesis testing. An example of this type of sampler is the reversible jump MCMC sampler, which is a generalization of the Metropolis-Hastings algorithm. Here, we present a new MCMC sampler of this type. The new sampler is a generalization of the Gibbs sampler, but somewhat surprisingly, it also turns out to encompass as particular cases all of the well-known MCMC samplers, including those of Metropolis, Barker, and Hastings. Moreover, the new sampler generalizes the reversible jump MCMC. It therefore appears to be a very general framework for MCMC sampling. This paper describes the new sampler and illustrates its use in three applications in Computational Biology, specifically determination of consensus sequences, phylogenetic inference and delineation of isochores via multiple change-point analysis.

Original languageEnglish
Pages (from-to)29-53
Number of pages25
JournalMethodology and Computing in Applied Probability
Volume6
Issue number1
DOIs
Publication statusPublished - 1 Dec 2004

Keywords

  • Consensus sequence
  • Gibbs sampler
  • Isochores
  • Markov chain Monte Carlo
  • Model determination
  • Multiple change-point analysis
  • Phylogenetic inference
  • Simulated annealing
  • String sampler

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