Introduction to Rare Event Simulation
This is a very interesting monograph that attempts to present a unified theory of rare events simulation. Two basic tools used are importance sampling and the theory of large deviations. This framework allows an assortment of simulation problems to be viewed from a single unified perspective and gives a great deal of insight into the fundamental nature of rare events simulation. After a short summary of random number generation and simulation of selected stochastic models (such as Markov chains, processes and fields) the author presents basic results of large deviation theory and importance sampling methodology. A key part of the book is chapter 5, which deals with the large deviation theory of importance sampling. It shows the way to cover efficiently rare events simulations and includes, in the form of examples, many important models from different fields of statistics. The rest of the book is devoted to special applications of the methodology, including conditional importance sampling, Chernoff's bound for rare events simulation, level crossing and queuing models. One small point I would like to make is that, unlike the author, I am a bit skeptical about the blind simulation as described in chapter 12. I recommend the book to everybody who is interested in rare events and/or Monte Carlo simulation.