# 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.

# Descriptors:

# Subject Categories:

- Statistics and Probability