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 compound (VOC) air concentrations collected on vessels supporting the response and clean-up efforts of the Deepwater Horizon oil 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 the Deepwater Horizon study, including the use of gradient methods for assigning workers to exposure categories.
Bibliographical noteFunding Information:
We would like to thank Wendy McDowell and other members of the GuLF STUDY for their continued efforts. This research was supported in part by the Intramural Research Program of the National Institutes of Health, National Institute of Environmental Health Sciences , as well as a contract with Social & Scientific Systems, Inc. (contract #S939000025). The opinions of this paper are those of the author and not necessarily of any funding body.
- Censored data
- Gaussian process
- Hierarchical modeling
- Markov chain Monte Carlo
- Spatiotemporal data