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Point Pattern Analysis of Spatial Deformation and Blurring Effects on Exceedances

Author

Listed:
  • A. E. Madrid

    (University Centre of Defence at the Spanish Air Force Academy)

  • J. M. Angulo

    (University of Granada)

  • J. Mateu

    (Universitat Jaume I)

Abstract

Structural characteristics of random field threshold exceedance sets (e.g., size, connectivity, and boundary regularity) are used in practice for definition of different indicators in spatial and spatio-temporal risk analysis. In this work, point process techniques are applied to study the structural changes derived from random field deformations and blurring transformations, meaningful from both physical and methodological points of view in a variety of contexts. Specifically, based on simulations from a flexible random field model class, features such as aggregation/inhibition of patterns defined by centroids of connected components, as well as by boundary A-exit points, are investigated in relation to the local contraction/dilation effects of deformation and the smoothing properties of blurring. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • A. E. Madrid & J. M. Angulo & J. Mateu, 2016. "Point Pattern Analysis of Spatial Deformation and Blurring Effects on Exceedances," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 512-530, September.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:3:d:10.1007_s13253-016-0262-5
    DOI: 10.1007/s13253-016-0262-5
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    References listed on IDEAS

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    1. C. A. Glasbey & K. V. Mardia, 1998. "A review of image-warping methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(2), pages 155-171.
    2. 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.
    3. Perrin, Olivier & Senoussi, Rachid, 1999. "Reducing non-stationary stochastic processes to stationarity by a time deformation," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 393-397, July.
    4. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    5. Wenceslao González‐Manteiga & Rosa M. Crujeiras & A.E. Madrid & J.M. Angulo & J. Mateu, 2012. "Spatial threshold exceedance analysis through marked point processes," Environmetrics, John Wiley & Sons, Ltd., vol. 23(1), pages 108-118, February.
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    Cited by:

    1. J. Mateu & E. Porcu, 2016. "Guest Editors’ Introduction to the Special Issue on “Seismomatics: Space–Time Analysis of Natural or Anthropogenic Catastrophes”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 403-406, September.

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