Objective Bayesian model selection in Gaussian graphical models

• 成果类型: Article
• 署名作者: Carvalho, C. M.; Scott, J. G.
• 署名单位: University of Chicago; Duke University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asp017
• 发表日期: 2009
• 页码: 497512
• 关键词: wishart distributions

摘要

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.