Spatial Prediction for Multivariate Non-Gaussian Data

Abstract

With the ever increasing volume of geo-referenced datasets, there is a real need for better statistical estimation and prediction techniques for spatial analysis. Most existing approaches focus on predicting multivariate Gaussian spatial processes, but as the data may consist of non-Gaussian (or mixed type) variables, this creates two challenges: (1) how to accurately capture the dependencies among different data types, both Gaussian and non-Gaussian; and (2) how to efficiently predict multivariate non-Gaussian spatial processes. In this article, we propose a generic approach for predicting multiple response variables of mixed types. The proposed approach accurately captures cross-spatial dependencies among response variables and reduces the computational burden by projecting the spatial process to a lower dimensional space with knot-based techniques. Efficient approximations are provided to estimate posterior marginals of latent variables for the predictive process, and extensive experimental evaluations based on both simulation and real-life datasets are provided to demonstrate the effectiveness and efficiency of this new approach.