Non-Gaussian Covariate-Dependent Spatial Measurement Error Model for Analyzing Big Spatial Data

Spatial models based on the Gaussian distribution have been widely used in environmental sciences. However, real data could be highly non-Gaussian and may show heavy tails features. Moreover, as in any type of statistical models, in spatial statistical models, it is commonly assumed that the covariates are observed without errors. Nonetheless, for various reasons such as measurement techniques or instruments used, measurement error (ME) can be present in the covariates of interest. This article concentrates on modeling heavy-tailed geostatistical data using a more flexible class of ME models. One novelty of this article is to allow the spatial covariance structure to depend on ME. For this purpose, we adopt a Bayesian modeling approach and utilize Markov chain Monte Carlo techniques and data augmentations to carry out the inference. However, when the number of observations is large, statistical inference is computationally burdensome, since the covariance matrix needs to be inverted at each iteration. As another novelty, we use a prediction-oriented Bayesian site selection scheme to tackle this difficulty. The proposed approach is illustrated with a simulation study and an application to nitrate concentration data. Supplementary materials accompanying this paper appear online.