MORE ASPECTS OF POLYA TREE DISTRIBUTIONS FOR STATISTICAL MODELING
MORE ASPECTS OF POLYA TREE DISTRIBUTIONS FOR STATISTICAL MODELING
复制标题
DOI：
10.1214/aos/1176325623
复制
发表时间：
1994-09-01
影响因子：
4.5
通讯作者：
LAVINE, M
中科院分区：
文献类型：
--
作者：
LAVINE, M
综述了Polya树分布的定义和基本性质。给出了两个定理，证明了Polya树可以构造成任意紧密地集中在任意期望的pdf上，并且Polya树先验可以将正质量放在具有有限熵的每一个正密度的每一个相对熵邻域中，从而满足一致性条件。这样的定理对于狄利克雷过程是假的。模型是将部分指定的Polya树与其他信息（如单调性或单模性）结合在一起构建的。它展示了如何在给定规范的所有先验类上计算后验期望的界限。给出了一个数值算例。将Dirichlet过程的Diaconis和Freedman定理推广到Polya树，使得Polya树可以作为回归问题误差的模型。最后将Dirichlet过程的经验贝叶斯模型推广到Polya树。Berry和Christensen用Polya树模型重新分析了一个例子。
The definition and elementary properties of Polya tree distributions are reviewed. Two theorems are presented showing that Polya trees can be constructed to concentrate arbitrarily closely about any desired pdf, and that Polya tree priors can put positive mass in every relative entropy neighborhood of every positive density with finite entropy, thereby satisfying a consistency condition. Such theorems are false for Dirichlet processes. Models are constructed combining partially specified Polya trees with other information such as monotonicity or unimodality. It is shown how to compute bounds on posterior expectations over the class of all priors with the given specifications. A numerical example is given. A theorem of Diaconis and Freedman about Dirichlet processes is generalized to Polya trees, allowing Polya trees to be the models for errors in regression problems. Finally empirical Bayes models using Dirichlet processes are generalized to Polya trees. An example from Berry and Christensen is reanalyzed with a Polya tree model.