Bayesian Spatial Nonparametric Models for Confounding Manifest Variables with an Application to China Earthquake Data

Abstract

We consider a Bayesian nonparametric models for spatial data of mixed category. Moreover, we adopt joint modeling strategy by assuming that responses and confounding variables are corresponding to continuous latent variables with multivariate Gaussian distribution. The model is built on a class of Gaussian Conditional Autoregressive (CAR) models, in combination with dependent sampling models (SSM) as well as probit stick-breaking process prior for accounting for complex interactions and high correlations of data. The key idea is to introducing spatial dependence by modeling the weights via probit transformation of Gaussian Markov random fields or discrete random probability measures of SSM. We illustrate the usefulness and effectiveness of the methodology through a real example from a China earthquake data set.