Description

Abstract: We consider the problem of modeling point-level (‘geostatistical’) spatial count

data with a large number of zeros. We develop a model that is compatible with the scientific assumptions about the data generating process. We use a two-stage spatial Generalized linear mixed model framework for the counts, modeling incidence, resulting in 0-1 outcomes, and abundance, resulting in positive counts, as separate but dependent processes, and utilize a bivariate Gaussian process model for characterizing the underlying spatial dependence. We describe a Bayesian approach and study several variants of our two-stage model, consisting of varying covariance and cross-covariance structures for the underlying bivariate Gaussian random process. We fit the models via Markov chain Monte Carlo (MCMC) methods We study several MCMC algorithms, including a version of the Langevin-Hastings algorithm, for exploring the complicated posterior distribution efficiently, and recommend an algorithm that is fairly automated. Finally, we demonstrate the application of our modeling and computational approach on both simulated data and a real data set from an ecological study and compare the performance of the various two-stage models based on inference and prediction.