An Introduction to Rare Event Simulation and Importance Sampling

This chapter provides a relatively low-level introduction to the problem of rare event simulation with Monte Carlo methods and to a class of methods known as variance reduction techniques that have been devised to deal with this problem. Special emphasis is given to importance sampling, but several other techniques are also presented, including the cross-entropy method, rejection sampling, and Markov chain Monte Carlo methods such as the Metropolis method and Gibbs sampling. A brief discussion is also given about asymptotic efficiency and the connections with large deviations theory.