ABSTRACT
Tools for posterior inference and forecasting in dynamic linear models (DLMs) and conditionally Gaussian dynamic linear models (CDLMs) were presented in Chapter 4. Filtering within the class of Normal DLMs (NDLMs) is available in closed form via the Kalman filtering recursions. Markov chain Monte Carlo (MCMC) algorithms can be used for filtering and prediction in conditionally Gaussian DLMs, as was also illustrated in Chapter 4. These classes of models are broad and flexible; however, more general state-space models that deal with nonlinear and often non-Gaussian structures at the state level and/or at the observational level are often needed in practice. MCMC algorithms can be customized to achieve posterior inference and prediction in general state-space models (e.g., Carlin, Polson, and Stoffer 1992). However, designing efficient algorithms when the models have strong nonlinearities can be very challenging.
