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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. [ABSTRACT FROM AUTHOR]

With the aim of mitigating the damage caused by the coronavirus disease 2019 (COVID-19) pandemic, it is important to use models that allow forecasting possible new infections accurately in order to face the pandemic in specific sociocultural contexts in the best possible way. Our first contribution is empirical. We use an extensive COVID-19 dataset from nine Latin American countries for the period of 1 April 2020 to 31 December 2021. Our second and third contributions are methodological. We extend relevant (i) state-space models with score-driven dynamics and (ii) nonlinear state-space models with unobserved components, respectively. We use weekly seasonal effects, in addition to the local-level and trend filters of the literature, for (i) and (ii), and the negative binomial distribution for (ii). We find that the statistical and forecasting performances of the novel score-driven specifications are superior to those of the nonlinear state-space models with unobserved components model, providing a potential valid alternative to forecasting the number of possible new COVID-19 infections. [ABSTRACT FROM AUTHOR]

We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with t marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew‐Gaussian process, thus obtaining a process with skew‐t marginal distributions. For the proposed (skew) t process, we study the second‐order and geometrical properties and in the t case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the t process. Moreover we compare the performance of the optimal linear predictor of the t process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australia. [ABSTRACT FROM AUTHOR]

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