Journal Article

Adaptive sampling for Bayesian variable selection

David J. Nott and Robert Kohn

in Biometrika

Published on behalf of Biometrika Trust

Volume 92, issue 4, pages 747-763
Published in print December 2005 | ISSN: 0006-3444
Published online December 2005 | e-ISSN: 1464-3510 | DOI: http://dx.doi.org/10.1093/biomet/92.4.747
Adaptive sampling for Bayesian variable selection

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Our paper proposes adaptive Monte Carlo sampling schemes for Bayesian variable selection in linear regression that improve on standard Markov chain methods. We do so by considering Metropolis–Hastings proposals that make use of accumulated information about the posterior distribution obtained during sampling. Adaptation needs to be done carefully to ensure that sampling is from the correct ergodic distribution. We give conditions for the validity of an adaptive sampling scheme in this problem, and for simulating from a distribution on a finite state space in general, and suggest a class of adaptive proposal densities which uses best linear prediction to approximate the Gibbs sampler. Our sampling scheme is computationally much faster per iteration than the Gibbs sampler, and when this is taken into account the efficiency gains when using our sampling scheme compared to alternative approaches are substantial in terms of precision of estimation of posterior quantities of interest for a given amount of computation time. We compare our method with other sampling schemes for examples involving both real and simulated data. The methodology developed in the paper can be extended to variable selection in more general problems.

Keywords: Adaptive sampling; Bayesian model averaging; Markov chain Monte Carlo

Journal Article.  0 words. 

Subjects: Probability and Statistics

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