Improper regular conditional distributions

• 成果类型: Article
• 署名作者: Seidenfeld, T; Schervish, MJ; Kadane, JB
• 署名单位: Carnegie Mellon University; Carnegie Mellon University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2001
• 页码: 1612-1624
• 关键词: conglomerability; probabilities

摘要

Improper regular conditional distributions (red's) given a sigma-field A have the following anomalous property. For sets A is an element of A, Pr(A \ A) is not always equal to the indicator of A. Such a property makes the conditional probability puzzling as a representation of uncertainty. When red's exist and the sigma-field,A is countably generated, then almost surely the red is proper. We give sufficient conditions for an red to be improper in a maximal sense, and show that these conditions apply to the tail afield and the sigma-field of symmetric events.