More Aspects of Polya Tree Distributions for Statistical Modelling

More Aspects of Polya Tree Distributions for Statistical Modelling (1994)

by Michael Lavine

Venue:	Ann. Statist
Citations:	44 - 1 self

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Datum	Value	Source
TITLE	More Aspects of Polya Tree Distributions for Statistical Modelling	user correction - Legacy Corrections
AUTHOR NAME	Michael Lavine	SVM HeaderParse 0.1
AUTHOR AFFIL	Duke University	SVM HeaderParse 0.2
ABSTRACT	: 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 like 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 Chris...	user correction - Legacy Corrections
YEAR	1994	user correction - Legacy Corrections
VENUE	Ann. Statist	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	1222--1235	INFERENCE
VOLUME	20	INFERENCE
CITATIONS	22 found	ParsCit 1.0