Generelized Skew- Normal/Independent Fields with Applications

The last decade has witnessed major developments in Geographical Information Systems (GIS) technology resulting in the need for Statisticians to develop models that account for spatial clustering and variation. Study of spatial patterns are very important in epidemiological and environmental problems. Due to spatial characteristics it is extremely important to correctly incorporate spatial dependence in modeling. This paper develops a novel spatial process using generalized skew-normal/independent distributions when the usual Gaussian process assumptions are invalid and transformation to a Gaussian random field is not appropriate. Our proposed method incorporates skewness as well as heavy tail behavior of the data while maintaining spatial dependence using a Conditional Auto Regressive (CAR)structure. We use Bayesian hierarchical methods to fit such models. Consequently we use a Bayesian model selection approach to choose appropriate models for a empirical data set.