Bayesian Inference in Econometric Models Using Monte Carlo Integration
Jun 30 1986
Methods for the systematic application of the Monte Carlo integration with importance sampling to Bayesian inference in econometric models are developed. Conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of Monte Carlo replications increases, and the numerical accuracy of this approximation may be assessed reliably, are set forth. Methods for the analytical verification of these conditions are discussed. Importance sampling densities are delivered from the asymptotic density modified by possible substitution of the multivariout normal by a multivariate to whose degrees of freedom are determined analytically, and by automatic rescaling of the density along each axis. the concept of relative numerical efficiency is introduced to evaluate the adequacy of a chosen importance sampling density. The practical procedures based on these innovations are illustrated in two different models.