The essential equivalence of pairwise and mutual conditional independence

• 成果类型: Article
• 署名作者: Hammond, PJ; Sun, YN
• 署名单位: Stanford University; National University of Singapore; National University of Singapore
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-005-0468-x
• 发表日期: 2006
• 页码: 415-427
• 关键词: measure-spaces; exchangeability; nonstandard

摘要

For a large collection of random variables, pairwise conditional independence and mutual conditional independence are shown to be essentially equivalent - i.e., equivalent to up to null sets. Unlike in the finite setting, a large collection of random variables remains essentially conditionally independent under further conditioning. The essential equivalence of pairwise and multiple versions of exchangeability also follows as a corollary. Our result relies on an iterated extension of Bledsoe and Morse's completion of the product of two measure spaces.