Accession Number:

ADA238689

Title:

A Constructive Definition of Dirichlet Priors

Descriptive Note:

Technical rept.

Corporate Author:

FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

Personal Author(s):

Report Date:

1991-05-01

Pagination or Media Count:

15.0

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.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE