The Annals of Applied Statistics

Static and roving sensor data fusion for spatio-temporal hazard mapping with application to occupational exposure assessment

Guilherme Ludwig, Tingjin Chu, Jun Zhu, Haonan Wang, and Kirsten Koehler

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Rapid technological advances have drastically improved the data collection capacity in occupational exposure assessment. However, advanced statistical methods for analyzing such data and drawing proper inference remain limited. The objectives of this paper are (1) to provide new spatio-temporal methodology that combines data from both roving and static sensors for data processing and hazard mapping across space and over time in an indoor environment, and (2) to compare the new method with the current industry practice, demonstrating the distinct advantages of the new method and the impact on occupational hazard assessment and future policy making in environmental health as well as occupational health. A novel spatio-temporal model with a continuous index in both space and time is proposed, and a profile likelihood-based model fitting procedure is developed that allows fusion of the two types of data. To account for potential differences between the static and roving sensors, we extend the model to have nonhomogenous measurement error variances. Our methodology is applied to a case study conducted in an engine test facility, and dynamic hazard maps are drawn to show features in the data that would have been missed by existing approaches, but are captured by the new method.

Article information

Ann. Appl. Stat., Volume 11, Number 1 (2017), 139-160.

Received: November 2015
Revised: October 2016
First available in Project Euclid: 8 April 2017

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Zentralblatt MATH identifier

Geostatistics kriging semiparametric methods spatial statistics spatio-temporal statistics


Ludwig, Guilherme; Chu, Tingjin; Zhu, Jun; Wang, Haonan; Koehler, Kirsten. Static and roving sensor data fusion for spatio-temporal hazard mapping with application to occupational exposure assessment. Ann. Appl. Stat. 11 (2017), no. 1, 139--160. doi:10.1214/16-AOAS995.

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Supplemental materials

  • Appendix: Tuning parameter selection and simulation study. The Appendix contains a description of the leave-one-sensor-out cross-validation procedure for MSPE evaluation and tuning parameter selection, a detailed approach for the choice of tuning parameters for the smoother terms and number of components for the data analysis in Section 5, and a simulation study comparing the static and roving sensor data fusion for the spatio-temporal mapping (STDF) method to fixed-time universal kriging, thin-plate spline smoothing and least squares regression.
  • Animation: Animated versions of Figures 1–2 and Figures 4–5. This supplemental material contains animated versions, dynamic in time, for the indicated figures.