# Accession Number:

## ADA185718

# Title:

## Asymptotic Normality of Poly-T Densities with Bayesian Applications.

# Descriptive Note:

## Technical rept. 1 Sep 85-1 Aug 87,

# Corporate Author:

## DEWITT WALLACE RESEARCH LAB NEW YORK

# Personal Author(s):

# Report Date:

## 1987-10-01

# Pagination or Media Count:

## 23.0

# Abstract:

A poly-t density is a density which is proportional to a product of at least two t-like factors, each of which is of a certain form where d is a positive number, micron underlined is an arbitrary location vector and M underlines is a symmetric semi-positive definite scale matrix. In general, M underlines is a function of d. Such a density arises, for example, in the Bayesian analysis of a linear model with a normal error term, independent normal priors on the linear parameters and inverted-gamma priors on the variance components. A theorem about the asymptotic normality of the density as a subset of the individual ds tend to infinity is proved under very general conditions. A corollary specifically related to the Bayesian linear regression model with two variance components. The Tiao-Zellner expansion for approximating the particular poly-t form involving two proper multivariate t factors is extended to the case of two arbitrary t-like factors.

# Descriptors:

# Subject Categories:

- Statistics and Probability