关于广义测度与泛函空间积分下随机变量Bayes公式的拓广  

Popularizion to Random Variable Bares Formula Under the Generalized Measure and Functional Space Integration

作　　者：萧筱南[1] 

机构地区：[1]西安石油学院数理研究所

出　　处：《工程数学学报》1996年第1期101-105,共5页Chinese Journal of Engineering Mathematics

摘　　要：在讨论了可测空间（，），（Ｘ，）中条件数学期望Ｅ［ｇ（θ）ξ］的Ｂａｙｅｓ公式的基础上，进一步研究了广义测度Ｇ＝Ｇ（Ａ），Ａ∈下Ｅ［ｇ（θ）｜ξ］的Ｂａｙｅｓ公式的拓广以及将泛函空间积分代替按基本结局空间积分的Ｅ［ｇ（ξ，θ）｜］（ω）的Ｂａｙｅｓ公式的拓广，为进一步扩大Ｂａｙｅｓ估计的应用范围提供了可靠的理论依据与一种新的有价值的方法。On the basis of discussing Bayes formula of conditional mathematical expectations E[g(θ)|ξ]in measurable space(),(X, x),this article further reviews the popularizion to Bayes formula of E[g(θ)|ξ] under generalized measure G=G(A),A∈and it also revieus the popularizion to Bayes formula of E[g(ξ,θ)|] (ω) using functional spacial integration to replace basin resultant spacial integration.It provides reliable theoretical basis and a valuable new method to amplity the applicable range of Bayes estimator.

关 键 词：广义测度 泛函空间积分 随机变量 贝叶斯估计 

分 类 号：O211.67[理学—概率论与数理统计]