Importance sampling for parametric estimation

Abstract

We consider a class of parametric estimation problems where the goal is efficient estimation of a quantity of interest for many instances that differ in some model or decision parameters. We have proposed an approach, called DataBase Monte Carlo (DBMC), that uses variance reduction techniques in a "constructive" way in this setting: Information is gathered through sampling at a set of parameter values and is used to construct effective variance reducing algorithms when estimating at other parameters. We have used DBMC along with the variance reduction techniques of stratification and control variates. In this paper we present results for the application of DBMC in conjunction with importance sampling. We use the optimal sampling measure at a nominal parameter as a sampling measure at neighboring parameters and analyze the variance of the resulting importance sampling estimator. Experimental results for this implementation are provided.