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Reversible jump, birth‐and‐death and more general continuous time Markov chain Monte Carlo samplers
Author(s) -
Cappé Olivier,
Robert Christian P.,
Rydén Tobias
Publication year - 2003
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00409
Subject(s) - reversible jump markov chain monte carlo , birth–death process , markov chain monte carlo , statistical physics , jump , markov chain , monte carlo method , mathematics , dimension (graph theory) , similarity (geometry) , computer science , statistics , physics , artificial intelligence , combinatorics , medicine , population , environmental health , quantum mechanics , image (mathematics)
Summary. 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.