Improving MCMC Using Efficient Importance Sampling - Roman Liesenfeld; Jean-François Richard (Kiel University, Department of Economics, 2006)
This paper develops a systematic Markov Chain Monte Carlo (MCMC) framework based upon Efficient 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 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.
Keywords: 330; Autoregressive models; Bayesian posterior analysis; Dynamic latent variables; Gibbs sampling; Metropolis Hastings; Stochastic volatility; Monte-Carlo-Methode; Stochastischer Prozess; Stichprobenverfahren; Theorie