Dynamic and semiparametric models

This paper surveys dynamic or state space models and their relationship to non- and semiparametric models that are based on the roughness penalty approach. We focus on recent advances in dynamic modelling of non-Gaussian, in particular discrete-valued, time series and longitudinal data, make the close correspondence to semiparametric smoothing methods evident, and show how ideas from dynamic models can be adopted for Bayesian semiparametric inference in generalized additive and varying coefficient models. Basic tools for corresponding inference techniques are penalized likelihood estimation, Kalman filtering and smoothing and Markov chain Monte Carlo (MCMC) simulation. Similarities, relative merits, advantages and disadvantages of these methods are illustrated through several applications