State Space Models and Particle Methods

PhD Course by O. Papaspiliopoulos and N. Chopin.

The course is about sequential algorithms for statistical inference. There will be particular emphasis on inference for state space models (e.g. hidden Markov models,change point models, and more general partially observed Markov processes).

In the course we will develop an accessible introduction to the Feynman-Kac formalization of such sequential algorithms, and we will demonstrate the strength of this approach in deriving filtering/smoothing/prediction recursions and simulation algorithms. This machinery will be used to provide numerical methods for the estimation of hidden Markov models and linear-Gaussian state space models. We will then provide a rigorous description of importance sampling as a tool for obtaining Monte Carlo estimates of inferential quantities of interest. This Monte Carlo technique will be combined with the Feynman-Kac formalisation to yield the family of particle filtering methods, and more generally the family of Sequential Monte Carlo (SMC) methods. We will demonstrate the potential and limitations of SMC for statistical inference in a wide range of models and applications. The course will also discuss latest research developments in this field, including particle MCMC and SMC^2 methods. The material is largely based on a forthcoming book by Chopin and Papaspiliopoulos.