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.