Bayesian geostatistical modeling for discrete‐valued processes

We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on nearest-neighbor mixture processes (NNMP), referred to as NNMP. To define the joint probability mass function (pmf) over set spatial locations, we build from local mixtures conditional pmfs using directed graphical model, with acyclic graph that summarizes nearest neighbor structure. The approach supports direct, modeling multivariate dependence through specification general bivariate distributions pmfs. In particular, develop inferential framework copula-based NNMPs can attain structures, motivating use copula families processes. Moreover, allows construction given pre-specified family marginal vary in space, facilitating covariate inclusion. Compared traditional generalized linear mixed models, where is introduced transformation response means, our process-based provides both computational advantages. illustrate methodology synthetic data examples an analysis North American Breeding Bird Survey data.