Estimating Marginal Posterior Densities in Generalized Linear Models using Quantile Integration

Valen E. Johnson
Duke University

Nov 30 1990

Generalized linear models (GLMs) represent an important extension of standard linear models to applications in which disturbance terms are non -Gaussian. Well known numerical techniques have been developed to obtain maximum likelihood estimates in these models, but Bayesian analyses have been hindered due to the intractability of the joint posterior distributions. In this paper, we describe a method for estimating the marginal posterior densities of regression parameters arising in GLMs using quantile integration and results from number theory.
Applications to log-linear and logistic regression models are presented.


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