Improving MCMC Using E cient Importance Sampling

This paper develops a systematic Markov Chain Monte Carlo (MCMC) framework based upon E cient Importance Sampling (EIS) which can be used for the analysis of a wide range of econometric models involving integrals without an analytical solution. EIS is a simple, generic and yet accurate Monte-Carlo integration procedure based on sampling densities which are chosen to be global approximations to the integrand. By embedding EIS within MCMC procedures based on Metropolis-Hastings (MH) one can signi cantly improve their numerical properties, essentially by providing a fully automated selection of critical MCMC components such as auxiliary sampling densities, normalizing constants and starting values. The potential of this integrated MCMCEIS approach is illustrated with simple univariate integration problems and with the Bayesian posterior analysis of stochastic volatility models and stationary autoregressive processes.