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Title: Spatial modeling of georeferenced count data Authors:  Diego Morales Navarrete - Pontificia Universidad Catolica de Chile (Chile) [presenting]
Moreno Bevilacqua - Universidad de Valparaiso (Chile)
Luis Mauricio Castro Cepero - Pontificia Universidad Catolica de Chile (Chile)
Christian Caamano Carrillo - Universidad del Bío-Bío (Chile)
Abstract: Modeling spatial data is a challenging task in statistics. In many applications, the observed data can be modeled using Gaussian, skew-Gaussian, or even restricted random field models. However, in several fields, such as population genetics, epidemiology, and aquaculture, the data of interest are counts, and therefore the mentioned models are not suitable for their analysis. Consequently, there is a need for spatial models that can adequately describe data coming from counting processes. Three approaches are used to model this type of data: GLMMs with Gaussian random field (GRF) effects, hierarchical models, and copula models. Unfortunately, these approaches do not explicitly characterize the random field like their q-dimensional distribution or correlation function. It is important to stress that GLMMs and hierarchical models induce a discontinuity in the path. Hence, we propose a novel approach to efficiently and accurately model spatial count data to deal with this. Briefly, starting from independent copies of a parent GRF, a set of transformations can be applied, and the result is a non-Gaussian random field. This approach is based on a random field characterization for count data that inherit some well-known geometric properties from GFRs.