A Comparison of Bayesian Approximation Methods for Analyzing Large Spatial Skewed Data

Commonly, environmental processes are observed across different locations, and observations present skewed distributions. Recent proposals for analyzing data in their original scale, accommodating spatial structure and skewness, involve two independent Gaussian processes (GP). We focus on a skewed spatial process defined through a convolution of Gaussian and log Gaussian (GLGC) processes. Because of the inclusion of two GPs, the inference procedure quickly becomes challenging as the sample size increases. We aim to investigate how recently developed approximate GPs perform in modeling high-dimensional GLGC processes. Three methods are formulated based on the nearest neighbor (NN) and Hilbert space (HS) methods, and their performances are investigated in comparison with the exact inference using simulation studies. All the approximate methods yield results comparable to exact inference, but the HS-based method provides the fastest inference of moderate to very smooth processes. A hybrid approach incorporating NN and HS methods is preferred for faster inference with improved MCMC efficiency for a wiggly process.Supplementary materials accompanying this paper appear online.