Hierarchical Bayesian analysis of a discrete time series of Poisson counts

A problem involving non-stationary, discrete-time series of counts from a Poisson process with a varying but smooth intensity function is studied. A smoothness prior for the underlying intensity process is modelled using the hierarchical Bayesian approach, which is shown to provide an AR(1) representation for the intensity process. Since conjugate priors are not assumed, analytic derivation of estimates and predictions of the Poisson series are not available. Some reasonably good approximations are given and illustrated using data on British road casualties before and after the introduction of the seatbelt law.