
Accession Number : ADA185718
Title : Asymptotic Normality of PolyT Densities with Bayesian Applications.
Descriptive Note : Technical rept. 1 Sep 851 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 polyt density is a density which is proportional to a product of at least two tlike 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 semipositive 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 invertedgamma 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 TiaoZellner expansion for approximating the particular polyt form involving two proper multivariate t factors is extended to the case of two arbitrary tlike 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