Sequential Monte Carlo : particle filtering and beyond

Sequential Monte Carlo methods are a family of computational algorithms which use an ensemble of weighted samples to approximate, in turn, each of a sequence of distributions and their associated normalizing constants. These algorithms first came to prominence as efficient methods for approximating the optimal filter in the context of hidden Markov models on general state spaces, online as observations become available, but are very much more widely applicable. This article seeks to provide a high‐level overview of these methods, introducing the methods themselves and some of their key theoretical properties before discussing their application in a range of settings which include inference for hidden Markov models; Bayesian inference more generally; maximum‐likelihood estimation and rare event estimation