Modelling zero-inflated spatio-temporal processes

摘要

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 firstcase, 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 zero-inflated models, by assuming that the value observed at location s and time t, 1'1(0, is a realization ofa mixture between a Bernoulli distribution with a probability of success θ_t (s) and a probability densityfunction or probability function p (yr (s) | .).For both cases, we include spatio-temporal latent processesin the model to account for the possible extra variation present in the mean structure of θ_t(s) and/orP (yt (s) |. ).In the context of point-referenced data, we model the amount of rainfall over city Riode Janeiro during 75 weeks; whereas in the areal data level case, we consider weekly cases of denguefever in the city of Rio de Janeiro during the years of 2001-02.