Importance sampling: a review

We provide a short overview of importance sampling-a popular sampling tool used for Monte Carlo computing. We discuss its mathematical foundation and properties that determine its accuracy in Monte Carlo approximations. We review the fundamental developments in designing efficient importance sampling (IS) for practical use. This includes parametric approximation with optimization-based adaptation, sequential sampling with dynamic adaptation through resampling and population-based approaches that make use of Markov chain sampling. (C) 2009 John Wiley & Sons, Inc.