Comparative Study and Sensitivity Analysis of Skewed Spatial Processes

• Activity Number: 685
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jiangyan Wang* and Miao Yang and Anandamayee Majumdar
• Companies: Soochow University and Soochow University and Soochow University
• Keywords: Bayesian Modeling ; Double Normal Process ; Double Zero Expectile Normal Process ; Posterior Inference ; Skewed Normal Process ; Spatial Process

Abstract

In this paper, we compare two difference classes of models. One of them, proposed by Majumdar and Paul (2014), is the Double Zero Expectile (DZEXP) normal process and the other is a version of the "skewed normal process", proposed by Minozzo and Ferracuti (2012), with closed skew normal multivariate marginal distributions. Both spatial models have useful properties in the sense that they are ergodic and strongly stationary. We also compare these two models with a variant of the DZEXP Normal process that includes an additional measurement error. All three models have the desired property of being parsimonious and computationally tractable. We use a hierarchical model for describing the aforementioned skew normal process, and employ a computationally efficient MCMC scheme for obtaining samples from the posterior distributions. Under a Bayesian paradigm, we compare performance of the aforementioned three different spatial processes and study their performance, 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.