Abstract

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