| 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 the form {1 + (x-μ)' M (x-μ)-d/2whered is a positive number, μis an arbitrary location vector and M is a symmetric semi-positive definite scale matrix. In general, M 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 model is also given. Detailed results are illustrated in the familiar Bayesian multiple linear regression model with two variance components. The Tiao-Zellner expansion for approximating the particular po1y-t form involving two proper multivariate t factors is extended to the case of two arbitrary t-like factors. © 1988, Taylor & Francis Group, LLC. All rights reserved. |
