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 (21)

• Pareto Smoothed Importance Sampling
• Adaptive Importance Sampling in General Mixture Classes
• Effective Sample Size for Importance Sampling based on discrepancy measures
• Generalized Multiple Importance Sampling
• Layered Adaptive Importance Sampling
• Improving Population Monte Carlo: Alternative Weighting and Resampling Schemes
• Efficient Multiple Importance Sampling Estimators
• Adapting the Number of Particles in Sequential Monte Carlo Methods through an Online Scheme for Convergence Assessment
• Rethinking the Effective Sample Size
• Group Importance Sampling for Particle Filtering and MCMC
• Importance Gaussian Quadrature
• A population Monte Carlo scheme with transformed weights and its application to stochastic kinetic models
• Heretical Multiple Importance Sampling
• Robust Covariance Adaptation in Adaptive Importance Sampling
• Adaptive Importance Sampling via Stochastic Convex Programming
• Multiple Importance Sampling for Efficient Symbol Error Rate Estimation
• Sequential Monte Carlo as Approximate Sampling: bounds, adaptive resampling via $\infty$-ESS, and an application to Particle Gibbs
• Gradient Importance Sampling
• Optimal mixture weights in multiple importance sampling
• On Exploration, Exploitation and Learning in Adaptive Importance Sampling
• Revisiting the balance heuristic for estimating normalising constants

Cited by in corpus (1)

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