Trees of Polya urns are used to generate sequences of exchangeable random variables. By a theorem of de Finetti each such sequence is a mixture of independent, identically distributed variables and the mixing measure can be viewed as a prior on distribution functions. The collection of these Polya tree priors forms a convenient conjugate family which was mentioned by Ferguson and includes the Dirichlet processes of Ferguson. Unlike Dirichlet processes, Polya tree priors can assign probability 1 to the class of continuous distributions. This property and a few others are investigated.
Publié le : 1992-09-14
Classification:
Prior distributions,
random measures,
Polya urns,
Derechlet distributions,
62A15,
62G99,
60G09,
60G57
@article{1176348766,
author = {Mauldin, R. Daniel and Sudderth, William D. and Williams, S. C.},
title = {Polya Trees and Random Distributions},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1203-1221},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348766}
}
Mauldin, R. Daniel; Sudderth, William D.; Williams, S. C. Polya Trees and Random Distributions. Ann. Statist., Tome 20 (1992) no. 1, pp. 1203-1221. http://gdmltest.u-ga.fr/item/1176348766/