Locally uniform prior distributions

• 成果类型: Article
• 署名作者: Hartigan, JA
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 160-173
• 关键词: Complexity

摘要

Suppose that X(sigma)\theta similar to N(theta, sigma(2)) and that sigma --> 0. For which prior distributions on theta is the posterior distribution of theta given X(sigma) asymptotically N(X(sigma), sigma(2)) when in fact X(sigma) similar to N(theta(0), sigma(2))? It is well known that the stated convergence occurs when theta has a prior density that is positive and continuous at theta(0). It turns out that the necessary and sufficient conditions for convergence allow a wider class of prior distributions-the locally uniform and tail-bounded prior distributions. This class includes certain discrete prior distributions that may be used to reproduce minimum description length approaches to estimation and model selection.