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An Analysis of an Incomplete Marked Point Pattern of Heat-Related 911 Calls

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  • Matthew J. Heaton
  • Stephan R. Sain
  • Andrew J. Monaghan
  • Olga V. Wilhelmi
  • Mary H. Hayden

Abstract

We analyze an incomplete marked point pattern of heat-related 911 calls between the years 2006-2010 in Houston, TX, to primarily investigate conditions that are associated with increased vulnerability to heat-related morbidity and, secondarily, build a statistical model that can be used as a public health tool to predict the volume of 911 calls given a time frame and heat exposure. We model the calls as arising from a nonhomogenous Cox process with unknown intensity measure. By using the kernel convolution construction of a Gaussian process, the intensity surface is modeled using a low-dimensional representation and properly adheres to circular domain constraints. We account for the incomplete observations by marginalizing the joint intensity measure over the domain of the missing marks and also demonstrate model based imputation. We find that spatial regions of high risk for heat-related 911 calls are temporally dynamic with the highest risk occurring in urban areas during the day. We also find that elderly populations have an increased probability of calling 911 with heat-related issues than younger populations. Finally, the age of individuals and hour of the day with the highest intensity of heat-related 911 calls varies by race/ethnicity. Supplementary materials are included with this article.

Suggested Citation

  • Matthew J. Heaton & Stephan R. Sain & Andrew J. Monaghan & Olga V. Wilhelmi & Mary H. Hayden, 2015. "An Analysis of an Incomplete Marked Point Pattern of Heat-Related 911 Calls," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 123-135, March.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:509:p:123-135
    DOI: 10.1080/01621459.2014.983229
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    References listed on IDEAS

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    1. Anders Brix & Peter J. Diggle, 2001. "Spatiotemporal prediction for log‐Gaussian Cox processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 823-841.
    2. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
    3. Michael J. Daniels & Robert E. Kass, 2001. "Shrinkage Estimators for Covariance Matrices," Biometrics, The International Biometric Society, vol. 57(4), pages 1173-1184, December.
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    1. David Payares-Garcia & Javier Platero & Jorge Mateu, 2023. "A Dynamic Spatio-Temporal Stochastic Modeling Approach of Emergency Calls in an Urban Context," Mathematics, MDPI, vol. 11(4), pages 1-28, February.

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