Over the last fifteen years, sequential Monte Carlo (SMC) methods gained popularity as powerful tools for solving intractable inference problems arising in the modelling of sequential data. Much effort was devoted to the development of SMC methods, known as particle filters (PFs), for estimating the filtering distribution of the latent variables in dynamic models. This line of research produced many algorithms, including auxiliary-variable PFs, marginal PFs, the resample-move algorithm and Rao-Blackwellised PFs. It also led to many applications in tracking, computer vision, robotics and econometrics. The theoretical properties of these methods were also studied extensively in this period.

Although PFs occupied the center-stage, significant progress was also attained in the development of SMC methods for parameter estimation, online EM, particle smoothing and SMC techniques for control and planning. Various SMC algorithms were also designed to approximate sequences of unnormalized functions, thus allowing for the computation of eigen-pairs of large matrices and kernel operators.

Recently, frameworks for building efficient high-dimensional proposal distributions for MCMC using SMC methods were proposed. These allow us to design effective MCMC algorithms in complex scenarios where standard strategies failed. Such methods have been demonstrated on a number of domains, including simulated tempering, Dirichlet process mixtures, nonlinear non-Gaussian state-space models, protein folding and stochastic differential equations.

Finally, SMC methods were also generalized to carry out approximate inference in static models. This is typically done by constructing a sequence of probability distributions, which starts with an easy-to-sample-from distribution and which converges to the desired target distribution. These SMC methods have been successfully applied to notoriously hard problems, such as inference in Boltzmann machines, marginal parameter estimation and nonlinear Bayesian experimental design.

In this tutorial, we will introduce the classical SMC methods and expose the audience to the new developments in the field.