WHEN IS CONFLICT NORMAL

• 成果类型: Article
• 署名作者: LUCAS, TW
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2291288
• 发表日期: 1993
• 页码: 1433-1437
• 关键词: DISTRIBUTIONS; inference

摘要

When data conflicts with quantified prior beliefs, seemingly small changes in the functional form of the prior and/or likelihood can have a profound effect on posterior inferences. This article provides results on asymptotic forms of the posterior when two information sources conflict. In particular, let x be from the likelihood p2(x - theta) with an unknown location parameter 0, with p1 (theta) the prior on 0. Sufficient conditions on p1 and p2 are provided to ensure that as x --> infinity the posterior is asymptotically normal. The conditions cover all combinations in which p1 and P2 are proportional to exp {- \theta - x(i)\tau(i), With tau(i) > 1. Conditions are also provided that ensure that as some of the data become extreme, the posterior variance goes to 0, converges to a constant, or diverges to infinity. Other asymptotic behavior involving conflicting information sources is also discussed.