paper a day : importance sampling in rare-event simulations

Introduction to importance sampling in rare-event simulations
Mark Denny
European Journal of Physics, 22 (2001) : 403–411

This paper is about importance sampling (IS), which a method to improve the error behavior of Monte Carlo (MC) methods. In engineering systems, getting good simulation results for rare events (such as decoding error) on the order of 10-10 would require an obscene amount of computation if you just did things the naive way. For example, the quality of a numerical bound on the tail probability of a random variable gets worse and worse as you look farther and farther out. Importance sampling is a method of reweighting the distribution to either get a smaller error in the regime of interest and/or uniformize the estimation error. This paper gives some motivation, a simple IS algorithm, analysis, and some simulations. It’s pretty readable, and I went from knowing nothing about importance sampling to getting a decent idea of how to use it in practice, along with its potential problems and benefits.

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0 thoughts on “paper a day : importance sampling in rare-event simulations

  1. Other methods / names you might want to look into: Chandler/Bennett method, transition path sampling (Geissler, Dellago, Bolhuis), finite temperature string (Eric Vanden-Eijnden).

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