期刊
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
卷 141, 期 11, 页码 3463-3474出版社
ELSEVIER
DOI: 10.1016/j.jspi.2011.05.002
关键词
Bayesiar model selection; Growing number of parameters; Posterior model consistency; Consistency of Bayes factor; Consistency of posterior odds ratio; g-priors; Gibbs sampling
Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochastic search of informative variables, have gained popularity. In this paper, we will study the asymptotic properties related to Bayesian model selection when the model dimension p is growing with the sample size n. We consider p <= n and provide sufficient conditions under which: (1) with large probability, the posterior probability of the true model (from which samples are drawn) uniformly dominates the posterior probability of any incorrect models: and (2) the posterior probability of the true model converges to one in probability. Both (1) and (2) guarantee that the true model will be selected under a Bayesian framework. We also demonstrate several situations when (1) holds but (2) fails, which illustrates the difference between these two properties. Finally, we generalize our results to include g-priors, and provide simulation examples to illustrate the main results. (C) 2011 Elsevier B.V. All rights reserved.
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