Applications of a Method for the Efficient Computation of Posterior Distributions

J. C. Naylor and A. F. M. Smith

Journal of the Royal Statistical Society Series C, 1982, vol. 31, issue 3, 214-225

Abstract: For routine implementation with complicated likelihood functions, statistical procedures based on posterior distributions, or integrated likelihoods, require an efficient approach to numerical integration. In this paper we shall outline a numerical integration method using Gaussian quadrature which leads to efficient calculation of posterior densities for a rather wide range of problems. Several illustrative examples are provided, including a re‐analysis of the Stanford heart transplant data. Among other things, these examples reveal that inferences based upon integrated likelihoods may differ substantially from those based on maximized likelihoods and the standard normal form of approximation.

Date: 1982
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