title: Exploration of the use of Bayesian modeling of gradients for censored spatiotemporal data from theDeepwater Horizonoil spill.
abstract: This paper develops a hierarchical framework for identifying spatiotemporal patterns in data with a high degree of censoring using the gradient process. To do this, we impute censored values using a sampling-based inverse CDF method within our Markov chain Monte Carlo algorithm, thereby avoiding burdensome integration and facilitating efficient estimation of other model parameters. We illustrate use of our methodology using a simulated data example, and uncover the danger of simply substituting a space- and time-constant function of the level of detection for all missing values. We then fit our model to area measurement data of volatile organic compounds (VOC) air concentrations collected on vessels supporting the response and clean-up efforts of theDeepwater Horizonoil release that occurred starting April 20, 2010. These data contained a high percentage of observations below the detectable limits of the measuring instrument. Despite this, we were still able to make some interesting discoveries, including elevated levels of VOC near the site of the oil well on June 26th. Using the results from this preliminary analysis, we hope to inform future research on theDeepwater Horizonstudy, including the use of gradient methods for assigning workers to exposure categories.
authors.affiliation: Department of Statistics, University of Missouri, Columbia, Missouri 65211.
authors.forename: Harrison
authors.initials: H
authors.lastname: Quick
authors.affiliation: Division of Biostatistics, University of Minnesota, Minneapolis, Minnesota 55455.
authors.forename: Caroline
authors.initials: C
authors.lastname: Groth
authors.affiliation: Division of Biostatistics, University of Minnesota, Minneapolis, Minnesota 55455.
authors.forename: Sudipto
authors.initials: S
authors.lastname: Banerjee
authors.affiliation: Division of Biostatistics, University of Minnesota, Minneapolis, Minnesota 55455.
authors.forename: Bradley P
authors.initials: BP
authors.lastname: Carlin
authors.affiliation: Exposure Assessments Applications, LLC, Arlington, Virginia 22207.
authors.forename: Mark R
authors.initials: MR
authors.lastname: Stenzel
authors.affiliation: Stewart Exposure Assessments, LLC, Arlington, Virginia 22207.
authors.forename: Patricia A
authors.initials: PA
authors.lastname: Stewart
authors.affiliation: National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina 27709.
authors.forename: Dale P
authors.initials: DP
authors.lastname: Sandler
authors.affiliation: Department of Epidemiology, University of North Carolina, Chapel Hill, North Carolina 27599.
authors.forename: Lawrence S
authors.initials: LS
authors.lastname: Engel
authors.affiliation: National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina 27709.
authors.forename: Richard K
authors.initials: RK
authors.lastname: Kwok
keywords: Censored data; Gaussian process; Gradients; Hierarchical modeling; Markov chain Monte Carlo; Spatiotemporal data