On Sampling Strategies in Bayesian Variable Selection Problems With Large Model Spaces

One important aspect of Bayesian model selection is how to deal with huge model spaces, since the exhaustive enumeration of all the models entertained is not feasible and inferences have to be based on the very small proportion of models visited. This is the case for the variable selection problem w...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2013-03, Vol.108 (501), p.340-352
Main Authors: García-donato, G, Martínez-beneito, M. A
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian method
Bayesian model selection
Bayesian theory
data analysis
equations
Estimating techniques
Estimation
g-priors
Internet
Review Article
Sampling
Sampling techniques
Searching strategies
Statistical analysis
Statistics
Strategic planning
Variables
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Summary:One important aspect of Bayesian model selection is how to deal with huge model spaces, since the exhaustive enumeration of all the models entertained is not feasible and inferences have to be based on the very small proportion of models visited. This is the case for the variable selection problem with a moderately large number of possible explanatory variables considered in this article. We review some of the strategies proposed in the literature, from a theoretical point of view using arguments of sampling theory and in practical terms using several examples with a known answer. All our results seem to indicate that sampling methods with frequency-based estimators outperform searching methods with renormalized estimators. Supplementary materials for this article are available online.
ISSN:1537-274X
0162-1459
1537-274X
DOI:10.1080/01621459.2012.742443