Importance Sampling

Abstract

Roughly speaking, a particle filter is an algorithm that iterates importance sampling and resampling steps, in order to approximate a sequence of filtering (or related) distributions. This chapter covers the basics of importance sampling; resampling will be treated in the following chapter. We describe in particular the two versions of importance sampling (normalised and auto-normalised), we make a connection with the probabilistic notion of change of measure, we derive the variance of importance sampling estimators, we describe different empirical measures of efficiency such as effective sample size, we discuss the inherent curse of dimensionality of importance sampling, and we extend importance sampling to situations where importance weights are randomised.