Modeling left-censored skewed spatial processes: The case of arsenic drinking water contamination

Abstract

Commonly, observations from environmental processes are spatially structured and present skewed distributions. Recently, different models have been proposed to model spatial processes in their original scale. This work was motivated by modeling the levels of arsenic groundwater concentration in Comilla, a district of Bangladesh. Some of the observations are left censored. We propose spatial gamma models and explore different parametrizations of the gamma distribution. The gamma model naturally accounts for the skewness present in the data and the fact that arsenic levels are positive. We compare our proposed approaches with two skewed models proposed in the literature. Inference is performed under the Bayesian paradigm and interpolation to unobserved locations of interest naturally accounts for the estimation of the parameters in the proposed model. For the arsenic dataset, one of our proposed gamma models performs best in comparison to previous spatial models for skewed data, in terms of scoring rules criteria. Moreover, under the skewed models, some of the lower limits of the 95% posterior predictive distributions provide negative values violating the assumption that observations are strictly positive. The gamma distribution provides a reasonable, and simpler, alternative to account for the skewness present in the data and provide forecasts that are within the valid values of the observations.