Non-linear state-space methods for Bayesian time series modelling

Abstract

State-space methods are used in many fields of science to solve so called filtering, smoothing, prediction and parameter inference problems using multivariate time series data. Analytical solutions to these inference problems exist mainly for linear Gaussian state-space models and discrete state-space models. Outside these special cases, the inference is typically based on approximate methods, or simulation-based methods such as particle filters. This thesis develops new methods for Bayesian inference of general state- space models and applies existing methods in challenging non-linear problems involving multivariate time series data. The new methods presented in this thesis are conditional particle filters that are relevant for the inference of models that involve uninformative initial state distributions and models that have slowly-mixing state dynamics and/or weakly informative observation processes. The applied problems develop new non-linear state-space models in order to solve a prediction problem related to childhood acute lymphoblastic leukaemia and a filtering problem related to the identification of wolf territories based on presence-only citizen science data.