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Bayesian Adaptive Sampling for Variable Selection and Model Averaging
Journal article   Peer reviewed

Bayesian Adaptive Sampling for Variable Selection and Model Averaging

Merlise A Clyde, Joyee Ghosh and Michael L Littman
Journal of Computational and Graphical Statistics, Vol.20(1), pp.80-101
01/01/2011
DOI: 10.1198/jcgs.2010.09049

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Abstract

For the problem of model choice in linear regression, we introduce a Bayesian adaptive sampling algorithm (BAS), that samples models without replacement from the space of models. For problems that permit enumeration of all models, BAS is guaranteed to enumerate the model space in 2 p iterations where p is the number of potential variables under consideration. For larger problems where sampling is required, we provide conditions under which BAS provides perfect samples without replacement. When the sampling probabilities in the algorithm are the marginal variable inclusion probabilities, BAS may be viewed as sampling models "near" the median probability model of Barbieri and Berger. As marginal inclusion probabilities are not known in advance, we discuss several strategies to estimate adaptively the marginal inclusion probabilities within BAS. We illustrate the performance of the algorithm using simulated and real data and show that BAS can outperform Markov chain Monte Carlo methods. The algorithm is implemented in the R package BAS available at CRAN. This article has supplementary material online.
 Sampling without replacement Bayesian model averaging Median probability model Model uncertainty Markov chain Monte Carlo Inclusion probability

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