The selection of prior distributions by formal rules

• 成果类型: Review
• 署名作者: Kass, RE; Wasserman, L
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2291752
• 发表日期: 1996
• 页码: 1343-1370
• 关键词: bayesian-analysis; linear-models; noninformative priors; posterior distributions; statistical-inference; expectation consistency; conditional properties; frequentist validity; nuisance parameters; coherent inference

摘要

Subjectivism has become the dominant philosophical foundation for Bayesian inference. Yet in practice, most Bayesian analyses are performed with so-called ''noninformative'' priors, that is, priors constructed by some formal rule. We review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used. We give special emphasis to Jeffreys's rules and discuss the evolution of his viewpoint about the interpretation of priors, away from unique representation of ignorance toward the notion that they should be chosen by convention. We conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly: When sample sizes are small (relative to the number of parameters being estimated), it is dangerous to put faith in any ''default'' solution; but when asymptotics take over, Jeffreys's rules and their variants remain reasonable choices. We also provide an annotated bibliography.