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Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference are developed. Conditions under which the numerical approximation converges almost surely to the true value with the number of Monte Carlo replications, and its numerical accuracy may be assessed reliably, are given. Importance sampling densities are derived from multivariate normal or student approximations to the posterior density. These densities are modified by automatic rescaling along each axis. The concept of relative numerical efficiency is introduced to evaluate the adequacy of a chosen importance sampling density. Applications in two illustrative models are presented. Copyright 1989 by The Econometric Society.