A zero-inflated Bayesian spatial model with near-locating measurements

Zero-inflated data arise in many contexts. In this paper, we develop a zero-inflated Bayesian hierarchical model which deals with spatial effects, correlation among near-locating measurements as well as excess zeros simultaneously. Inference, including the sampling from the posterior distributions, predictions at new locations, and model selection, is carried out by using computationally efficient Markov chain Monte Carlo techniques. The posterior distributions are simulated using a Gibbs sampler with the embedded ratio-of-uniform method and the slice sampling algorithm. The approach is illustrated via an application to herbaceous data collected in the Missouri Ozark Forest Ecosystem Project. The results from the proposed model are compared with those generated from a non-zero inflated model. The proposed model fully incorporates the information from data collection and provides more reliable inference. A predictive $p$ value is computed for model checking and it indicates that the proposed model fits the data well.