Non-Gaussian Geostatistical Modeling using (skew) t Processes

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 Australi

MULTI CRITERION PRIORITY ON KRIGING OF GOLD RESOURCES PREDICTION

This paper describes of three things. First, the Kriging estimation on gold grade which is distributed in the vein. The empirical variogram method based on Matheron classical and robust of Cressie-Hawkins. The two empirical fitting on variogram theory of spherical and exponential equations of weighted least squares and ordinary least squares used. The predictions of six sizes block-Kriging respectively, 15×15, 25×25, 35×35, 50×50, 75×75 and 100×100 based on four variographic models. Second, determine the priority of 24 prediction combinations based on TOPSIS method. Finally, the multiple criterion decision making method namely, 15×15 block Kriging based on a robust empirical variogram of exponential weighted least squares model represents as the best result

Statistical models for animal movement and landscape connectivity

2013 Summer.Includes bibliographical references.This dissertation considers statistical approaches to the study of animal movement behavior and landscape connectivity, with particular attention paid to modeling how movement and connectivity are influenced by landscape characteristics. For animal movement data, a novel continuous-time, discrete-space model of animal movement is proposed. This model yields increased computational efficiency relative to existing discrete-space models for animal movement, and a more flexible modeling framework than existing continuous-space models. In landscape genetic approaches to landscape connectivity, spatially-referenced genetic allele data are used to study landscape effects on gene flow. An explicit link is described between a common circuit-theoretic approach to landscape genetics and variogram fitting for Gaussian Markov random fields. A hierarchical model for landscape genetic data is also proposed, with a multinomial data model and latent spatial random effects to model spatial correlation

Positive definite nonparametric regression using an evolutionary algorithm with application to covariance function estimation

We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive definiteness, as well as isotropy and monotonicity, on the estimators, and its hyperparameters can be decided using cross validation. We define our estimators by taking integral transforms of kernel-based distribution surrogates. We then use the iterated density estimation evolutionary algorithm, a variant of estimation of distribution algorithms, to fit the estimators. We also extend our method to estimate covariance functions for point-referenced data. Compared to alternative approaches, our method provides more reliable estimates for long-range dependence. Several numerical studies are performed to demonstrate the efficacy and performance of our method. Also, we illustrate our method using precipitation data from the Spatial Interpolation Comparison 97 project.Comment: Accepted at the 2023 Genetic and Evolutionary Computation Conference (GECCO) as a full paper. 14 pages with references and appendices, 11 figure