Improving MCMC, using efficient importance sampling

A generic Markov Chain Monte Carlo (MCMC) framework, based upon Efficient Importance Sampling (EIS) is developed, which can be used for the analysis of a wide range of econometric models involving integrals without analytical solution. EIS is a simple, generic and yet accurate Monte-Carlo integration procedure based on sampling densities which are global approximations to the integrand. By embedding EIS within MCMC procedures based on Metropolis-Hastings (MH) one can significantly 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 MCMC-EIS approach is illustrated with simple univariate integration problems, and with the Bayesian posterior analysis of stochastic volatility models and stationary autoregressive processes.