期刊
BIOMETRIKA
卷 96, 期 3, 页码 497-512出版社
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asp017
关键词
Bayesian model selection; Fractional Bayes factor; Gaussian graphical model; Hyper-inverse Wishart distribution; Multiple hypothesis testing
资金
- IBM Corporation Scholar Fund at the University of Chicago Booth School of Business
- U.S. National Science Foundation
This paper presents a default model-selection procedure for Gaussian graphical models that involves two new developments. First, we develop a default version of the hyper-inverse Wishart prior for restricted covariance matrices, called the hyper-inverse Wishart g-prior, and show how it corresponds to the implied fractional prior for selecting a graph using fractional Bayes factors. Second, we apply a class of priors that automatically handles the problem of multiple hypothesis testing. We demonstrate our methods on a variety of simulated examples, concluding with a real example analyzing covariation in mutual-fund returns. These studies reveal that the combined use of a multiplicity-correction prior on graphs and fractional Bayes factors for computing marginal likelihoods yields better performance than existing Bayesian methods.
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