Modelling zero-inflated spatio-temporal processes

Abstract

We consider models for spatio-temporal processes which assume either non-negative values, and often are observed as zero, or discrete values and are also inflated by zeros. Typically, in the first case, the spatial observations are obtained at fixed locations (point-referenced data) over a region D; whereas in the second, the region D is divided into a finite number of regular or irregular subregions (areal level), resulting in observations for each subregion. Our main idea is based on those of zeroinflated models, by assuming that the value observed at location s and time t, Y_t (s), is a realization of a mixture between a Bernoulli distribution with a probability of success θ_t (s) and a probability density function or probability function p(y_t (s) | .) For both cases, we include spatio-temporal latent processes in the model to account for the possible extra variation present in the mean structure of θ_t (s) and/or p(y_t(s) | .). In the context of point-referenced data, we model the amount of rainfall over the city of Rio de Janeiro during 75 weeks; whereas in the areal data level case, we consider weekly cases of dengue fever in the city of Rio de Janeiro during the years of 2001–02.