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.

本文开发了一种层次结构的框架，用于使用梯度过程在高度审查的情况下识别数据中的时空模式。为此，我们在马尔可夫链蒙特卡洛算法中使用基于采样的逆CDF方法估算检查值，从而避免了繁重的集成并促进了其他模型参数的有效估计。我们通过一个模拟数据示例说明了我们的方法的使用，并揭示了简单地为所有缺失值替换检测级别的时空常数的危险。然后，我们将模型拟合为船舶上收集的挥发性有机化合物（VOC）空气浓度的面积测量数据，以支持Deepwater Horizo​​n的响应和清理工作从2010年4月20日开始发生石油释放。这些数据包含了很高的观测值百分比，低于测量仪器的可检测极限。尽管如此，我们仍然能够做出一些有趣的发现，包括6月26日油井现场附近的VOC升高。利用这一初步分析的结果，我们希望为“深水地平线”研究的未来研究提供参考，包括使用梯度法将工人分配给暴露类别。