Department of Mathematics

Title: Bayesian modelling of nonlinear dynamical systems

Abstract: I will in this talk introduce the idea underlying the Sequential Monte Carlo (SMC) method and show how it can be used for Bayesian inference in nonlinear dynamical systems by coupling it with standard Markov chain Monte Carlo methods. SMC provide approximate solutions to integration problems where there is a sequential structure present, akin to what we have in dynamical systems. The particle filter is arguably the most popular SMC method and it is used to compute an approximation of the filtering distribution. We will then sketch how SMC can be used to construct the high-dimensional proposal density for a Markov chain Monte Carlo sampler. The first results along these lines emerged in 2010 and since then we have
witnessed a steadily increasing activity within this area. The resulting family of algorithms is referred to as Particle Markov Chain Monte Carlo (PMCMC). Towards the end of the talk I will show some experimental results where we use these tools for inference in a non-trivial Gaussian process nonlinear state space model.