Statistica Sinica 34 (2024), 1067-1070

ON SEQUENTIAL MONTE CARLO: AN OVERVIEW

Jun S. Liu^{*}

Harvard University

The sequential Monte Carlo (SMC) methodology is a family of powerful Monte Carlo methods for high dimensional static or dynamic problems. It is built upon sequential importance sampling and incorporates various other Monte Carlo techniques such as resampling, rejection sampling, auxiliary variable method, Markov chain Monte Carlo (MCMC), etc. As an alternative to Markov Chain Monte Carlo (MCMC) method, SMC can be very useful in cases where MCMC methods are ine?cient or are inappropriate (such as on-line updating). One of the earliest forms of SMC can be dated to Hammersley and Morton (1954) and Rosenbluth and Rosenbluth (1955), who noticed that sequentially simulating a self-avoiding random walk (SAW) with one-step look-ahead is a good strategy but is biased. They demonstrated that this bias can be corrected by sample reweighting. Since the SAW model serves as a prototype for biopolymer modeling, this idea opens up new frontiers for cross-fertilization between computational science and many application areas......