Efficient High-Dimensional Importance Sampling

• Activity Number: 405
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Jean Francois Richard*+
• Companies: Pittsburgh University
• Keywords: Monte Carlo ; simulation ; importance sampling ; efficient sampler ; latent variables ; likelihood evaluation

Abstract

In 1998 Richard and Zhang proposed a generic efficient importance sampling (EIS) technique which relies upon a simple sequence of auxiliary least squares regressions to construct accurate GLOBAL approximations to high-dimensional integrands. We applied their technique to a wide range of stochastic volatility models (bivariate, two-components, semiparametric) to compute exact likelihood functions with unparalleled numerical accuracy for large sample sizes (up to 8,000+) using very small numbers of draws (from 50 to 100). In a recent paper we compare posterior means obtained by Watanabe using a multimove Markov Chain Monte Carlo (MCMC) sampler based upon an algorithm initially proposed by Jacquier, Polson, and Rossi. The reconciliation of results led to a correction of the algorithm used by Watanabe. We argue that EIS and MCMC are complements rather than substitutes. We are currently exploring the possibility of constructing mixed EIS/MCMC algorithms, combining EIS for large dimensional vectors of latent variables with MCMC for posterior densities of the parameters of interest. We expect such a combination to be exceptionally performant for a very wide range of latent variable models.