DILATION FOR SETS OF PROBABILITIES

• 成果类型: Article
• 署名作者: SEIDENFELD, T; WASSERMAN, L
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349254
• 发表日期: 1993
• 页码: 1139-1154
• 关键词: sensitivity; Capacities; inference; BAYES

摘要

Suppose that a probability measure P is known to lie in a set of probability measures M. Upper and lower bounds on the probability of any event may then be computed. Sometimes, the bounds on the probability of an event A conditional on an event B may strictly contain the bounds on the unconditional probability of A. Surprisingly, this might happen for every B in a partition B. If so, we say that dilation has occurred. In addition to being an interesting statistical curiosity, this counterintuitive phenomenon has important implications in robust Bayesian inference and in the theory of upper and lower probabilities. We investigate conditions under which dilation occurs and we study some of its implications. We characterize dilation immune neighborhoods of the uniform measure.