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Abstract:
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We consider the problem of modeling point-level ('geostatistical') spatial count data with a large number of zeros. We use a 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 to characterize the underlying spatial dependence. We describe a Bayesian approach and find that our joint model specification offers interpretability and flexibility. We fit the model via Markov chain Monte Carlo (MCMC) methods. We study several MCMC algorithms, including the Langevin-Hastings algorithm, for exploring the complicated posterior distribution efficiently, and recommend a version that is nearly automated. Finally, we demonstrate the application of our modeling and computational approach on simulated and real data.
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