Browsing by Author "Bevilacqua, Moreno"

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    A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers
    (2022) Bevilacqua, Moreno; Caamano-Carrillo, Christian; Arellano-Valle, Reinaldo B.; Gomez, Camilo
    In this paper, we propose a new class of non-Gaussian random fields named two-piece random fields. The proposed class allows to generate random fields that have flexible marginal distributions, possibly skewed and/or heavy-tailed and, as a consequence, has a wide range of applications. We study the second-order properties of this class and provide analytical expressions for the bivariate distribution and the associated correlation functions. We exemplify our general construction by studying two examples: two-piece Gaussian and two-piece Tukey-h random fields. An interesting feature of the proposed class is that it offers a specific type of dependence that can be useful when modeling data displaying spatial outliers, a property that has been somewhat ignored from modeling viewpoint in the literature for spatial point referenced data. Since the likelihood function involves analytically intractable integrals, we adopt the weighted pairwise likelihood as a method of estimation. The effectiveness of our methodology is illustrated with simulation experiments as well as with the analysis of a georeferenced dataset of mean temperatures in Middle East.
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    Modeling Point Referenced Spatial Count Data: A Poisson Process Approach
    (2024) Morales-Navarrete, Diego; Bevilacqua, Moreno; Caamano-Carrillo, Christian; Castro, Luis M.
    Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and mathematical tractability. However, this assumption seems to be restrictive when dealing with counting data. To deal with this situation, we propose a random field with a Poisson marginal distribution considering a sequence of independent copies of a random field with an exponential marginal distribution as "inter-arrival times " in the counting renewal processes framework. Our proposal can be viewed as a spatial generalization of the Poisson counting process. Unlike the classical hierarchical Poisson Log-Gaussian model, our proposal generates a (non)-stationary random field that is mean square continuous and with Poisson marginal distributions. For the proposed Poisson spatial random field, analytic expressions for the covariance function and the bivariate distribution are provided. In an extensive simulation study, we investigate the weighted pairwise likelihood as a method for estimating the Poisson random field parameters. Finally, the effectiveness of our methodology is illustrated by an analysis of reindeer pellet-group survey data, where a zero-inflated version of the proposed model is compared with zero-inflated Poisson Log-Gaussian and Poisson Gaussian copula models. for this article, including technical proofs and R code for reproducing the work, are available as an online supplement.