Multivariate Spatial Modeling of Conditional Dependence to Study Arsenic Contamination in Drinking Water

• Activity Number: 50
• Type: Invited
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: The International Environmetrics Society
• Author(s): Montserrat Fuentes*+ and Joe Guinness
• Companies: North Carolina State University and North Carolina State University
• Keywords: spatial analysis ; big data ; spectral analysis ; cross-dependence ; environmental sciences

Abstract

Elevated concentrations of toxic trace elements, such as arsenic, pose threats to human health through contamination of drinking water. Toxic trace elements are regulated in part by soils. We describe an experiment to study the reactivity of arsenic in soils, by mapping the composition of elements on a sand grain using X-ray fluorescence analyses, before and after the grain is treated with arsenic, resulting in multivariate spatial maps of elemental abundance. To understand the behavior of arsenic in soils, it is important to disentangle the multivariate relationships among the elements in the sample. The abundance of most elements, including arsenic, correlates strongly with that of iron, but conditional on the amount of iron, some elements may mitigate or potentiate the accumulation of arsenic. This problem motivates our work to define conditional correlation in spatial lattice models and give general conditions under which two components are conditionally uncorrelated given the rest. We describe how to enforce that two components are conditionally uncorrelated given a third in parametric models and we apply our results to big datasets using the Whittle likelihood.