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Bayesian modeling and analysis for gradients in spatiotemporal processes


  • Harrison Quick
  • Sudipto Banerjee
  • Bradley P. Carlin


Stochastic process models are widely employed for analyzing spatiotemporal datasets in various scientific disciplines including, but not limited to, environmental monitoring, ecological systems, forestry, hydrology, meteorology, and public health. After inferring on a spatiotemporal process for a given dataset, inferential interest may turn to estimating rates of change, or gradients, over space and time. This manuscript develops fully model‐based inference on spatiotemporal gradients under continuous space, continuous time settings. Our contribution is to offer, within a flexible spatiotemporal process model setting, a framework to estimate arbitrary directional gradients over space at any given timepoint, temporal derivatives at any given spatial location and, finally, mixed spatiotemporal gradients that reflect rapid change in spatial gradients over time and vice‐versa. We achieve such inference without compromising on rich and flexible spatiotemporal process models and use nonseparable covariance structures. We illustrate our methodology using a simulated data example and subsequently apply it to a dataset of daily PM2.5 concentrations in California, where the spatiotemporal gradient process reveals the effects of California's unique topography on pollution and detects the aftermath of a devastating series of wildfires.

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  • Harrison Quick & Sudipto Banerjee & Bradley P. Carlin, 2015. "Bayesian modeling and analysis for gradients in spatiotemporal processes," Biometrics, The International Biometric Society, vol. 71(3), pages 575-584, September.
  • Handle: RePEc:bla:biomet:v:71:y:2015:i:3:p:575-584

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    References listed on IDEAS

    1. Patrick E. Brown & Gareth O. Roberts & Kjetil F. Kåresen & Stefano Tonellato, 2000. "Blur‐generated non‐separable space–time models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 847-860.
    2. Michael L. Stein, 2005. "Space-Time Covariance Functions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 310-321, March.
    3. Shengde Liang & Sudipto Banerjee & Bradley P. Carlin, 2009. "Bayesian Wombling for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 65(4), pages 1243-1253, December.
    4. Huiyan Sang & Jianhua Z. Huang, 2012. "A full scale approximation of covariance functions for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 111-132, January.
    5. Majumdar, Anandamayee & Munneke, Henry J. & Gelfand, Alan E. & Banerjee, Sudipto & Sirmans, C.F., 2006. "Gradients in Spatial Response Surfaces With Application to Urban Land Values," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 77-90, January.
    6. De Iaco, S. & Myers, D. E. & Posa, D., 2002. "Space-time variograms and a functional form for total air pollution measurements," Computational Statistics & Data Analysis, Elsevier, vol. 41(2), pages 311-328, December.
    7. Banerjee, Sudipto & Gelfand, Alan E., 2006. "Bayesian Wombling: Curvilinear Gradient Assessment Under Spatial Process Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1487-1501, December.
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    1. repec:spr:testjl:v:27:y:2018:i:4:d:10.1007_s11749-018-0619-x is not listed on IDEAS
    2. repec:spr:testjl:v:27:y:2018:i:4:d:10.1007_s11749-018-0623-1 is not listed on IDEAS
    3. repec:spr:testjl:v:27:y:2018:i:4:d:10.1007_s11749-018-0621-3 is not listed on IDEAS

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