Christian Caamaño-Carrillo

Summary: Positive spatial data in remote sensing and infrastructure monitoring are often strictly positive, skewed and spatially dependent. Motivated by LiDAR intensity returns from mining haul roads, we propose a geostatistical framework based on Weibull random fields for modelling spatial degradation patterns within a condition‐monitoring setting. Three constructions are studied: a Weibull field obtained from a transformation of Gaussian random fields, a Gaussian‐copula Weibull field and a new Clayton‐copula Weibull field with a parameter controlling departures from reflection symmetry. For the Clayton–Weibull construction, we establish stationarity, mean‐square continuity and mean‐square differentiability under conditions inherited from the latent Gaussian correlation model. For all three models, closed‐form bivariate densities enable scalable inference through nearest‐neighbour weighted pairwise composite likelihood. An expanded simulation study evaluates parameter recovery, model discrimination and standard‐error calibration across sample sizes, spatial dependence levels, marginal skewness and Clayton asymmetry. The method is applied to LiDAR intensity data from an open‐pit copper mine in Chile (), where information criteria favour a Clayton‐based specification with moderate asymmetry and improved agreement with empirical spatial dependence. The methods are implemented in the GeoModels R package.

The Pareto–Feller distribution has been widely used across various disciplines to model “heavy-tailed” phenomena, where extreme events such as high incomes or large losses are of interest. In this paper, we present a new bivariate distribution based on the Appell hypergeometric function with marginal Pareto–Feller distributions obtained from two independent gamma random variables. The proposed distribution has the beta prime marginal distributions as special case, which were obtained using a Kibble-type bivariate gamma distribution, and the stochastic representation was obtained by the quotient of a scale mixture of two gamma random variables. This result can be viewed as a generalization of the standard bivariate beta I (or inverted bivariate beta distribution). Moreover, the obtained bivariate density is based on two confluent hypergeometric functions. Then, we derive the probability distribution function, the cumulative distribution function, the moment-generating function, the characteristic function, the approximated differential entropy, and the approximated mutual information index. Based on numerical examples, the exact and approximated expressions are shown.

In this work, we use a cointegration state space approach to estimate the quarterly series of the Chilean Gross Domestic Product (GDP) in the period 1965–2009. First, the equation of Engle–Granger is estimated using the data of the yearly GPD and some related variables, such as the price of copper, the exports of goods and services, and the mining production index. The estimated coefficients of this regression are then used to obtain a first estimation of the quarterly GDP series with measurement errors. A state space model is then applied to improve the preliminary estimation of the GDP with the main purpose of eliminating the maximum error of measurement such that the sum of the three-month values coincide swith the yearly GDP. The results are then compared with the traditional disaggregation methods. The resulting quarterly GDP series reflects the major events of the historical Chilean economy.

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.

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. Supplementary materials for this article, including technical proofs and R code for reproducing the work, are available as an online supplement.

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 by 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 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. Supplementary materials for this article, include technical proofs and R code for reproducing the work, are available as an online supplement.

In this paper we propose a highly scalable method for (non-)Gaussian random fields estimation.In particular, we propose a novel (a)symmetric weight function based on nearest neighboursfor the method of maximum weighted composite likelihood based on pairs (WCLP). The proposed weight function allows estimating massive (up to millions) spatial datasetsand improves the statistical efficiency of the WCLP method using symmetric weights based on distances, as shown in the numerical examples. As an application of the proposed method we consider the estimation of a novel non-Gaussian random field named Tukey-hh random field that has flexible marginal distributions, possibly skewed and/or heavy-tailed. In an extensive simulation study we explore the statistical efficiency of the proposed nearest neighbours WCLP method with respect to the WCLP method using weights based on distances when estimating the parameters of the Tukey-hh random field. In the Gaussian case we also compare the proposed method with the Vecchia approximation from computational and statistical viewpoints.Finally, the effectiveness of the proposed methodology is illustrated by estimating a large dataset of mean temperatures in South-America.Our developments have been implemented in an open-source package for the R statistical environment.