Conditioning as disintegration
Conditioning as disintegration
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DOI：
10.1111/1467-9574.00056
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发表时间：
1997-11-01
影响因子：
1.5
通讯作者：
Pollard, D
中科院分区：
文献类型：
--
作者：
Chang, JT;Pollard, D
当谈到严格的条件处理时，条件概率分布似乎名声不佳。尽管我们都使用条件概率的基本定义秘密地进行启发式计算，但技术论据是作为 Radon-Nikodym 导数的操纵而发表的。在印刷品中，可测量性和平均属性取代了关于随机变量在给定特定条件信息的情况下表现得像常数的直观想法。对条件分布进行严格的罪恶树操作的一种方法是将它们视为分解测度 - 专注于条件统计水平集的概率测度系列。在本文中，我们提出了一些理论和一系列示例——从 EM 算法和内曼分解，到贝叶斯理论和边缘化悖论——表明分解既具有直观的吸引力，又具有数理统计中许多问题所需的严谨性。
Conditional probability distributions seem to have a bad reputation when it comes to rigorous treatment of conditioning. Technical arguments are published as manipulations of Radon-Nikodym derivatives, although we all secretly perform heuristic calculations using elementary definitions of conditional probabilities. In print, measurability and averaging properties substitute for intuitive ideas about random variables behaving like constants given particular conditioning information.One way to engage In rigorous, guilt-tree manipulation of conditional distributions is to treat them as disintegrating measures-families of probability measures concentrating on the level sets of a conditioning statistic. In this paper we present a little theory and a range of examples-from EM algorithms and the Neyman factorization, through Bayes theory and marginalization paradoxes-to suggest that disintegrations have both intuitive appeal and the rigor needed for many problems in mathematical statistics.