ABSTRACT
The extension of Bayesian small area health models to space-time (ST) varies in complexity depending on the nature of the observational process and the type of model envisaged. This chapter focuses on the simplest observational situation: where a map of small areas is repeatedly observed over discrete time periods. This is known as map evolutions. It examines a small selection of the classic space-time models that have been proposed so far. These include the temporal trend model of Bernardinelli, the interaction models of Knorr-Held and a variant Kalman filtering approach. Many of the ST models fitted using nimble or BUGS can be fitted using CARBayesST. It is common in engineering to model the dynamic systems via two level models describing the system and observation mechanism. Kalman filtering time series is based on this idea. Latent structure is a common feature of Bayesian models for in fact any random effect model includes a latent effect: a random effect.
