Sequential Monte Carlo methods for conjugate state-space models

Sammanfattning: Bayesian inference in state-space models requires the solution of high-dimensional integrals, which is intractable in general. A viable alternative is to use sample-based methods, like sequential Monte Carlo, but this introduces variance into the inferred quantities that can sometimes render the estimates useless. This thesis explores how conjugacy relations that allow for replacing numerical integration with analytic updates can be used to reduce the variance in sequential Monte Carlo based methods for both state and parameter inference.In the context of state inference, a new type of proposal distribution for sequential Monte Carlo tailored for moderately high-dimensional systems with intractable transition densities is suggested. It combines the standard and the locally optimal proposal by adding conjugate artificial process noise to the model. The resulting bias-variance trade-off allows for a reduced Monte Carlo variance in exchange for model bias.In Bayesian inference using particle Gibbs samplers, conjugacy relations between parameter and state updates can be exploited to reduce the inherent correlation between consecutive samples by eliminating parameters from the state update. Despite the resulting non-Markovian model dependencies that arise from the marginalization, the computational complexity of the marginalized particle Gibbs samplers is shown to scale linearly with the number of observations.Furthermore, the marginalized framework is extended to the case of multiple state-space models with shared parameters to reduce Monte Carlo variance while simultaneously aggregating information from all datasets. For these models, multiple update structures are possible for the marginalized particle Gibbs sampler. Two distinct structures with complementary attributes are described and strategies for combining them to form more efficient samplers are discussed. The improved performance is illustrated for a compartmental model describing multiple outbreaks of mosquito-borne diseases that share either disease- or location-dependent parameters.                           The thesis also contributes to making sequential Monte Carlo methods available to a wider range of users through a tutorial-style paper aimed for the control community and an implementation of marginalized particle Gibbs samplers in a probabilistic programming language that automatically exploits conjugacy relations in the models.