Asymptotic Normality of Poly-T Densities with Bayesian Applications.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1987
- Accession Number
- ADA185718
Entities
People
- George Y. Wong