Date: 2023-06-01

Time: 14:00-15:00 (UK time)

Bush House (SE) 1.01

Abstract

In this talk I will describe state-space models based on point process theory and Lévy processes, allowing very flexible modelling of continuous time non-Gaussian behaviours subject to irregular discrete time observations. In contrast with most of the classical models which use Brownian motion assumptions, our approach is based on pure jump-driven Lévy processes driving stochastic diferential equations, leading to powerful models based on, for example, $\alpha$-stable or Generalised hyperbolic processes (including Student-t, variance-gamma and normal-inverse Gaussian). We are able to construct a full state-space model (The 'Lévy state-space model') driven by such continuous time processes, observed at discrete time, as well as deriving central limit style theorems that prove Gaussianity of certain series residual terms, and inference for these models can be carried out using highly efficient Rao-Blackwellised versions of particle filters and sequential Markov chain Monte Carlo. The models can find application tracking of agile objects such as birds or drones, in financial prediction and in analysis of vibrational data under non-Gaussian perturbation.

Speaker

Simon Godsill is Professor of Statistical Signal Processing in the Engineering Department at Cambridge University. He is also a Professorial Fellow and tutor at Corpus Christi College Cambridge. He coordinates an active research group in Signal Inference and its Applications within the Signal Processing and Communications Laboratory at Cambridge, specializing in Bayesian computational methodology, multiple object tracking, audio and music processing, and financial time series modeling. A particular methodological theme over recent years has been the development of novel techniques for optimal Bayesian filtering and smoothing, using Sequential Monte Carlo or Particle Filtering methods.