A Spatial Mean‐Mixture Gaussian Model for Skewed Geostatistical Data

Abstract

Gaussian random fields (GRFs) are often used to model spatial dependence in many geostatistical applications. However, environmental data, such as water quality measurements, often exhibit substantial skewness which violates the Gaussian assumption. Ignoring this skewness can result in biased parameter estimates and unreliable spatial predictions. To address this limitation, we propose a spatial extension of the multivariate mean‐mixture Gaussian (MMG) distribution that accommodates unbounded skewness while preserving a coherent spatial dependence structure. Our approach incorporates a global latent mixing variable to induce marginal skewness and utilizes a Gaussian process to capture spatial correlation. Identifiability is ensured by a centering transformation and replicated spatial observations, which separate mixture variance from spatial covariance. Model estimation is performed using a generalized expectation‐maximization (GEM) and quasi‐Newton algorithm, providing stable, closed‐form updates for both regression and skewness parameters. We evaluate the model through simulation studies and apply it to highly skewed geo‐referenced electrical conductivity (EC) data from groundwater monitoring stations in Golestan Province, Iran, with the primary aim of predicting values at unknown spatial locations. The results demonstrate substantial improvements over standard Gaussian and transformed Gaussian models in both estimation and prediction accuracy.