COMPUTATIONAL APPROACHES FOR EMPIRICAL BAYES METHODS AND BAYESIAN SENSITIVITY ANALYSIS

• 成果类型: Article
• 署名作者: Buta, Eugenia; Doss, Hani
• 署名单位: Yale University; State University System of Florida; University of Florida
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS913
• 发表日期: 2011
• 页码: 2658-2685
• 关键词: exploring posterior distributions; monte-carlo integration; variable selection; markov-chains; models; mixtures; priors

摘要

We consider situations in Bayesian analysis where we have a family of priors v(h) on the parameter theta, where h varies continuously over a space H, and we deal with two related problems. The first involves sensitivity analysis and is stated as follows. Suppose we fix a function f of theta. How do we efficiently estimate the posterior expectation of f(theta) simultaneously for all h in H? The second problem is how do we identify subsets of H which give rise to reasonable choices of v(h)? We assume that we are able to generate Markov chain samples from the posterior for a finite number of the priors, and we develop a methodology, based on a combination of importance sampling and the use of control variates, for dealing with these two problems. The methodology applies very generally, and we show how it applies in particular to a commonly used model for variable selection in Bayesian linear regression, and give an illustration on the US crime data of Vandaele.