Closed form expressions for Bayesian sample size

• 成果类型: Article
• 署名作者: Clarke, B.; Yuan, Ao
• 署名单位: University of British Columbia; Howard University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000308
• 发表日期: 2006
• 页码: 1293-1330
• 关键词: posterior; CHOICE

摘要

Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the data. Thus, when a sample size criterion is formalized in terms of a functional of the posterior, its value is a random variable. Generally, such functionals have means under the true distribution. We give asymptotic expressions for the expected value, under a fixed parameter, for certain types of functionals of the posterior density in a Bayesian analysis. The generality of our treatment permits us to choose functionals that encapsulate a variety of inference criteria and large ranges of error bounds. Consequently, we get simple inequalities which can be solved to give minimal sample sizes needed for various estimation goals. In several parametric examples, we verify that our asymptotic bounds give good approximations to the expected values of the functionals they approximate. Also, our numerical computations suggest our treatment gives reasonable results.