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Title: Multivariate Poisson processes with random effects to model spatial dependence Authors:  Ana C Cebrian - University of Zaragoza (Spain) [presenting]
Jesus Asin - University of Zaragoza (Spain)
Abstract: Modeling the occurrence of events in many real problems related involves several Poisson processes. Frequently, these processes are dependent, and this feature should be considered when modeling. A common example of this situation is the spatial dependence appearing between the occurrence of events in different locations. Dependence between Poisson processes can be captured by allowing the intensities of the marginal models to be a function of common covariates. However, in many cases, adequate variables are not available, or the existing dependence is not totally captured by them. In those cases, we propose a multivariate vector of Poisson processes with random effects, where the intensities of the marginal processes are modeled as a function of covariates plus a common random effect. Under quite mild conditions, an integrated nested Laplace approximation can be used to estimate this model. This approach is used to model the dependence between the occurrence of extreme heat events (EHEs) in several locations in the North-East of Spain (Aragon). The pairwise dependence is analyzed and a multivariate Poisson process with random effects is used to obtain a joint model for the occurrence of EHEs.