Predictive and sensitive analysis of a bivariate skewed spatial process based on the Bayesian framework

Abstract

Bivariate spatial process is a natural tool for the assessments of environmental justice. Integrating the skewness arising in spatial data sets remains a challenge. While in terms of which, classical bivariate spatial skewness analysis receives relative little attention. As an attempt, this article provides a fully hierarchical bivariate approach for spatial modelling, using a Bayesian framework implemented via Markov chain Monte Carlo (MCMC) methods, called the bivariate double zero expectile normal with measurement error (BDZEXPNM). The BDZEXPNM modelling is derived by considering two variables simultaneously, where the covariance parameters representing the marginal and cross‐spatial dependence structure are measured. The posterior performance of BDZEXPNM is probed by leveraging multivariate spatial analysis. In addition, MCMC methods allows a straightforward interpretation of parameters. Simulation studies validate our method as well as a real data example.