Modeling Overdispersed Spatial Data by Using Mixture Random Fields

Abstract

Modeling and estimating overdispersed count data present significant challenges, particularly when data are continuously indexed in space. We introduce a spatial random field model with negative binomial marginal distributions, called the spatial Poisson–Erlang mixture random field. We first construct a Poisson random field via a renewal-process representation with exponential inter-arrival times. We then model its random mean using an Erlang random field. The resulting Poisson–Erlang mixture random field is overdispersed, has negative binomial marginals, and enjoys desirable second-order properties, including mean-square continuity. For the proposed Poisson-Erlang spatial random field, analytic expressions for the covariance function and bivariate distribution are provided. These features facilitate likelihood-based inferences using (potentially misspecified) weighted pairwise likelihood methods. An extensive simulation study was conducted to investigate the performance of the weighted pairwise likelihood approach for estimating the parameters of the Poisson-Erlang random field. The model was applied to analyze weed count data from the Bjertop Farm in southwest Sweden.
Joint work with D. Morales-Navarrete (Universidad San Francisco de Quito) and M. Bevilacqua (Universidad Adolfo Ibañez).

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