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.