Bayesian residual analysis for spatially correlated data. (April 2020)

• Record Type: Journal Article
• Authors: Lobo, Viviana GR; Fonseca, Thaís CO
• Is Part Of: Statistical modelling. Volume 20:Number 2(2020)
• Page Start: 171
• Page End: 194
• Publication Date: 2020-04
• Subjects: Residual analysis -- spatial statistics -- outlier detection -- predictive performance -- Bayesian inference -- non-Gaussian process; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X18811529
• Languages: English
• ISSNs: 1471-082X

Abstract

This work considers residual analysis and predictive techniques for the identification of individual and multiple outliers in geostatistical data. The standardized Bayesian spatial residual is proposed and computed for three competing models: the Gaussian, Student-t and Gaussian-log-Gaussian spatial processes. In this context, the spatial models are investigated regarding their plausibility for datasets contaminated with outliers. The posterior probability of an outlying observation is computed based on the standardized residuals and different thresholds for outlier discrimination are tested. From a predictive point of view, methods such as the conditional predictive ordinate, the predictive concordance and the Savage–Dickey density ratio for hypothesis testing are investigated for identification of outliers in the spatial setting. For illustration, contaminated datasets are considered to assess the performance of the three spatial models for identification of outliers in spatial data. Furthermore, an application to wind speed modelling is presented to illustrate the usefulness of the proposed tools to detect regions with large wind speeds.