Advances in Importance Sampling

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.

References in corpus (7)

• Adaptive Importance Sampling in General Mixture Classes
• Efficient Multiple Importance Sampling Estimators
• Importance Gaussian Quadrature
• Heretical Multiple Importance Sampling
• Adaptive Importance Sampling via Stochastic Convex Programming
• Multiple Importance Sampling for Efficient Symbol Error Rate Estimation
• Revisiting the balance heuristic for estimating normalising constants

Cited by in corpus (1)

• Adaptive Importance Sampling meets Mirror Descent: a Bias-variance tradeoff