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) : Wong, George Y

PDF Url : ADA185718

Report Date : 01 Oct 1987

Pagination or Media Count : 23

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 d's 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 :   *ASYMPTOTIC NORMALITY, *NORMAL DENSITY FUNCTIONS, BAYES THEOREM, ERRORS, LINEAR REGRESSION ANALYSIS, LINEAR SYSTEMS, MATHEMATICAL MODELS, MULTIVARIATE ANALYSIS, PARAMETERS, VARIATIONS, VECTOR ANALYSIS, NUMERICAL INTEGRATION

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE