A CONSTRUCTIVE DEFINITION OF DIRICHLET PRIORS
A CONSTRUCTIVE DEFINITION OF DIRICHLET PRIORS
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DOI：
10.21236/ada238689
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发表时间：
1991-05
期刊：
影响因子：
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通讯作者：
J. Sethuraman
中科院分区：
文献类型：
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作者：
J. Sethuraman
摘要：贝叶斯非参数问题中的参数是观测值\(X\)的未知分布\(P\)。贝叶斯学者会为\(P\)设定一个先验分布，在观测到\(X\)之后，通过使用\(P\)的后验分布来解决统计推断问题，后验分布是给定\(X\)时\(P\)的条件分布。要使贝叶斯非参数方法取得成功，需要有一大类先验分布，其能够容易地计算后验分布。除非\(X\)在有限空间中取值，否则未知分布\(P\)在一个无穷维空间中变化。因此，人们必须讨论像在一个大空间上的所有概率测度空间这样复杂空间中的测度。这总是需要更加仔细地关注相关的测度理论问题。当随机变量\(X\)在\(R_{K}\)中取值时，一类被称为狄利克雷测度的先验分布已被用于\(X\)的分布。
Abstract : The parameter in a Bayesian nonparametric problem is the unknown distribution P of the observation X. A Bayesian uses a prior distribution for P, and after observing X, solves the statistical inference problem by using the posterior distribution of P, which is the conditional distribution of P given X. For Bayesian nonparametrics to be successful one needs a large class of priors for which posterior distributions can be easily calculated. Unless X takes values in a finite space, the unknown distribution P varies in an infinite dimensional space. Thus one has to talk about measures in a complicated space like the space of all probability measures on a large space. This has always required a more careful attention to the attendant measure theoretic problems. A class of priors known as Dirichlet measures have been used for the distribution of a random variable X when it takes values in R sub K.