Bayesian Sequential Inference for Dynamic Regression Models

Many processes evolve over time and statistical models need to be adaptive to change. This thesis proposes flexible models and statistical methods for inference about a data generating process that varies over time. The models considered are quite general dynamic predictive models with parameters linked to a set of covariates via link functions. The dynamics can arise from time-varying regression coefficients and from changes in the link function over time. The covariates can be time-varying and may also have incomplete information. An efficient Bayesian inference methodology is developed for analyzing the posterior of dynamic regression models sequentially, with a particular focus on online learning and real-time prediction. The core inferential algorithm belongs to a family of sequential Monte Carlo methods commonly known as particle filters, and a key contribution is the development of a tailored proposal distribution. The algorithm is shown to outperform a state-of-the-art Markov Chain Monte Carlo method and is also extended to mixture-of-experts models. The performance of the inference methodology is assessed through various simulation experiments and real data from clinical and social-demographic studies, as well as from an industrial software development project