Comparative study and sensitivity analysis of skewed spatial processes

Asymmetric spatial processes arise naturally in finance, economics, hydrology and ecology. For such processes, two different classes of models are considered in this paper. One of them, proposed by Majumdar and Paul (J Comput Graph Stat 25(3):727–747, 2016), is the Double Zero Expectile Normal (DZEXPN) process and the other is a version of the “skewed normal process”, proposed by Minozzo and Ferracuti (Chil J Stat 3:157–170, 2012), with closed skew normal multivariate marginal distributions. Both spatial models have useful properties in the sense that they are ergodic and stationary. As a brief treatise to test the sensitivity and flexibility of the new proposed DZEXPN model (Majumdar and Paul in J Comput Graph Stat 25(3):727–747, 2016), in relation to other skewed spatial processes in the literature using a Bayesian methodology, our results show that by adding measurement error to the DZEXPN model, a reasonably flexible model is obtained, which is also computationally tractable than many others mentioned in the literature. Meanwhile, we develop a full-fledged Bayesian methodology for the estimation and prediction of the skew normal process proposed in Minozzo and Ferracuti (Chil J Stat 3:157–170, 2012). Specifically, a hierarchical model is used to describe the skew normal process and a computationally efficient MCMC scheme is employed to obtain samples from the posterior distributions. Under a Bayesian paradigm, we compare the performances of the aforementioned three different spatial processes and study their sensitivity and robustness based on simulated examples. We further apply them to a skewed data set on maximum annual temperature obtained from weather stations in Louisiana and Texas.