Reversible jump, birth-and-death and more general continuous time Markov chain Monte Carlo samplers
Cappé, Olivier; Robert, Christian P.; Ryden, Tobias (2003), Reversible jump, birth-and-death and more general continuous time Markov chain Monte Carlo samplers, Journal of the Royal Statistical Society. Series B, Statistical Methodology, 65, 3, p. 679-700. http://dx.doi.org/10.1111/1467-9868.00409
TypeArticle accepté pour publication ou publié
Journal nameJournal of the Royal Statistical Society. Series B, Statistical Methodology
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Abstract (EN)Reversible jump methods are the most commonly used Markov chain Monte Carlo tool for exploring variable dimension statistical models. Recently, however, an alternative approach based on birth-and-death processes has been proposed by Stephens for mixtures of distributions. We show that the birth-and-death setting can be generalized to include other types of continuous time jumps like split-and-combine moves in the spirit of Richardson and Green. We illustrate these extensions both for mixtures of distributions and for hidden Markov models. We demonstrate the strong similarity of reversible jump and continuous time methodologies by showing that, on appropriate rescaling of time, the reversible jump chain converges to a limiting continuous time birth-and-death process. A numerical comparison in the setting of mixtures of distributions highlights this similarity.
Subjects / KeywordsBirth-and-death process; Hidden Markov model; Markov chain Monte Carlo algorithms; Mixture distribution; Rao–Blackwellization; Rescaling
Showing items related by title and author.
Jacob, Pierre E.; Chopin, Nicolas; Robert, Christian P.; Rue, Havard (2009) Document de travail / Working paper
Kilbinger, Martin; Wraith, Darren; Robert, Christian P.; Benabed, Karim; Cappé, Olivier; Cardoso, Jean-François; Fort, Gersende; Prunet, Simon; Bouchet, François R. (2010) Article accepté pour publication ou publié