Cox Processes Associated with Spatial Copula Observed through Stratified Sampling

Cox processes, also called doubly stochastic Poisson processes, are used for describing phenomena for which overdispersion exists, as well as Poisson properties conditional on environmental effects. In this paper, we consider situations where spatial count data are not available for the whole study area but only for sampling units within identified strata. Moreover, we introduce a model of spatial dependency for environmental effects based on a Gaussian copula and gamma-distributed margins. The strength of dependency between spatial effects is related with the distance between stratum centers. Sampling properties are presented taking into account the spatial random field of covariates. Likelihood and Bayesian inference approaches are proposed to estimate the effect parameters and the covariate link function parameters. These techniques are illustrated using Black Leaf Streak Disease (BLSD) data collected in Martinique island.