Dynamic Models

Abstract

This chapter presents an overview of dynamic Bayesian models. Dynamic Bayesian modelling and forecasting of time series is one of the most important areas emerged in Statistics at the end of the last century. The chapter describes the class of DLM both to set the notation and to introduce important arguments of Bayesian dynamic models, such as model superposition. Inference and practical aspects of Bayesian forecasting are also addresses in the chapter. It also discusses nonlinear and nonnormal models, giving particular attention to the class of dynamic generalized linear models, an extension of dynamic normal linear models to the exponential family. Dynamic linear models are a broad class of models with time varying parameters, useful to modeling time series data and regression. Moreover, the chapter discusses a sequential Bayesian decision monitor for application in quality control, allowing monitoring the natural parameters of many exponential family models with conjugate prior. This proposal is able to discern whether the deterioration is due to the change in level, slope, regression coefficient, or seasonal pattern, individually. Finally, this chapter briefly summarizes the class of dynamic hierarchical models.