State-space prior distribution for parameter of nonhomogeneous Poisson spatiotemporal models

This article proposes a new class of nonhomogeneous Poisson spatiotemporal model. In this approach, we use a state-space model-based prior distribution to handle the scale and shape parameters of the Weibull intensity function. The proposed prior distribution enables the inclusion of changes in the behavior of the intensity function over time. In defining the spatial correlation function of the model, we include anisotropy via spatial deformation. We estimate the model parameters from a Bayesian perspective, employ the Markov chain Monte Carlo approach, and validate this estimation procedure through a simulation exercise. Finally, the extreme rainfall in the southern semiarid region in northeastern Brazil is analyzed using the R10mm index. The proposed model showed better fit and prediction ability than did other nonhomogeneous Poisson spatiotemporal models available in the literature. This improvement in performance is mainly due to the flexibility of the intensity function that is achieved by allowing the incorporation, in time, of the climatic characteristics of this region.