A BAYESIAN METHOD FOR WEIGHTED SAMPLING

• 成果类型: Article
• 署名作者: LO, AY
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349414
• 发表日期: 1993
• 页码: 2138-2148
• 关键词: empirical distributions; STOCHASTIC-PROCESSES; bootstrap; models

摘要

Bayesian statistical inference for sampling from weighted distribution models is studied. Small-sample Bayesian bootstrap clone (BBC) approximations to the posterior distribution are discussed. A second-order ProPertY for the BBC in unweighted i.i.d. sampling is given. A consequence is that BBC approximations to a posterior distribution of the mean and to the sampling distribution of the sample average, can be made asymptotically accurate by a proper choice of the random variables that generate the clones. It also follows from this result that in weighted sampling models, BBC approximations to a posterior distribution of the reciprocal of the weighted mean are asymptotically accurate; BBC approximations to a sampling distribution of the reciprocal of the empirical weighted mean are also asymptotically accurate.