Advances in Importance Sampling

TL;DR

This paper reviews recent advances in importance sampling, a Monte Carlo method for approximating complex distributions, focusing on multiple and adaptive importance sampling techniques that enhance efficiency and flexibility.

Contribution

It provides a comprehensive overview of recent developments in multiple and adaptive importance sampling methods, highlighting their theoretical and practical improvements.

Findings

Enhanced efficiency of multiple IS methods

Improved adaptability in AIS algorithms

Broader applicability in complex Bayesian models

Abstract

Importance sampling (IS) is a Monte Carlo technique for the approximation of intractable distributions and integrals with respect to them. The origin of IS dates from the early 1950s. In the last decades, the rise of the Bayesian paradigm and the increase of the available computational resources have propelled the interest in this theoretically sound methodology. In this paper, we first describe the basic IS algorithm and then revisit the recent advances in this methodology. We pay particular attention to two sophisticated lines. First, we focus on multiple IS (MIS), the case where more than one proposal is available. Second, we describe adaptive IS (AIS), the generic methodology for adapting one or more proposals.