Exploiting conjugacy in state-space models with sequential Monte Carlo

Sammanfattning: Many processes we encounter in our daily lives are dynamical systems that can be described mathematically using state-space models. Exact inference of both states and parameters in these models is, in general, intractable. Instead, approximate methods, such as sequential Monte Carlo and Markov chain Monte Carlo, are used to infer quantities of interest. However, sample based inference inherently introduce variance in the estimates. In this thesis we explore different aspects of how conjugacy relations in a model can improve the performance of sequential Monte Carlo-based inference methods.A conjugacy relation between the prior distribution and the likelihood implies that the posterior distribution has the same distributional form as the prior, allowing for analytic updates in place of numerical integration. In Paper I we consider state inference in state-space models where the transition density is intractable. By adding artificial noise conjugate to the observation density we can design an efficient proposal for sequential Monte Carlo inference that can reduce the variance of the state estimates. Conjugacy can also be utilized in the setting of parameter inference. In Paper II we show that the performance of particle Gibbs-type samplers, in terms of the autocorrelation of the samples, can be improved when conjugacy relations allow for marginalizing out the dependence on parameters in the state update.Despite enabling analytical evaluation of integrals, the derivation and implementation of conjugacy updates is cumbersome in all but the simplest cases, which limits the usefulness in practice. Recently, the emerging  field of probabilistic programming has changed this, by providing a framework for automating inference in probabilistic models - including identifying and utilizing conjugacy relations. In Paper II we make use of probabilistic programming to automatically exploit conjugacy in an epidemiological state-space model describing the spread of dengue fever.