文章基本信息

标题：The Performance of Covariance Selection Methods That Consider Decomposable Models Only
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作者：A. Marie Fitch ; M. Beatrix Jones ; Hélène Massam 等
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2014
卷号：9
期号：3
页码：659-684
DOI：10.1214/14-BA874
语种：English
出版社：International Society for Bayesian Analysis
摘要：We consider the behavior of Bayesian procedures that perform model selection for decomposable Gaussian graphical models when the true model is in fact non-decomposable. We examine the asymptotic behavior of the posterior when models are misspecified in this way, and find that the posterior will converge to graphical structures that are minimal triangulations of the true structure. The marginal log likelihood ratio comparing different minimal triangulations is stochastically bounded, and appears to remain data dependent regardless of the sample size. The covariance matrices corresponding to the different minimal triangulations are essentially equivalent, so model averaging is of minimal benefit. Using simulated data sets and a particular high performing Bayesian method for fitting decomposable models, feature inclusion stochastic search, we illustrate that these predictions are borne out in practice. Finally, a comparison is made to penalized likelihood methods for graphical models, which make no decomposability restriction. Despite its inability to fit the true model, feature inclusion stochastic search produces models that are competitive or superior to the penalized likelihood methods, especially at higher dimensions.