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Adaptive Proposal Construction for Reversible Jump MCMC
Author(s) -
EHLERS RICARDO S.,
BROOKS STEPHEN P.
Publication year - 2008
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2008.00606.x
Subject(s) - markov chain monte carlo , gibbs sampling , scheme (mathematics) , autoregressive model , bayesian probability , mathematics , variety (cybernetics) , algorithm , suite , mathematical optimization , jump , series (stratigraphy) , class (philosophy) , sampling (signal processing) , computer science , artificial intelligence , statistics , mathematical analysis , paleontology , physics , archaeology , filter (signal processing) , quantum mechanics , biology , computer vision , history
. In this paper, we show how the construction of a trans‐dimensional equivalent of the Gibbs sampler can be used to obtain a powerful suite of adaptive algorithms suitable for trans‐dimensional MCMC samplers. These algorithms adapt at the local scale, optimizing performance at each iteration in contrast to the globally adaptive scheme proposed by others for the fixeddimensional problem. Our adaptive scheme ensures suitably high acceptance rates for MCMC and RJMCMC proposals without the need for (often prohibitively) time‐consuming pilot‐tuning exercises. We illustrate our methods using the problem of Bayesian model discrimination for the important class of autoregressive time series models and, through the use of a variety of prior and proposal structures, demonstrate their ability to provide powerful and effective adaptive sampling schemes.