Bayesian Estimation in the Linear Model: The Care of Unknown Dispersion Parameters

Valen E. Johnson
Duke University

Nov 30 1989

A numerical integration technique called quantile integration is used to obtain closed form approximations to the marginal posterior densities and moments arising in hierarchical linear models. The approximations take the form of weighted mixtures of multivariate normal densities and are applicable in a wide rage of application in which first and second stage dispersion parameters are not known a priori.

Two examples are provided. One example deals with experimental design models, the other with a prior model for exchangeability of regression parameters between related data sets. In the latter, a g-prior structure is used to model the second stage convariance matrix, and a novel approach to specifying the prior density of the associated dispersion parameters is described.


Hierarchical linear models, quantile integration, exchangeability, random effects, monte carlo integration


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