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Stochastic Reconstruction for Inhomogeneous Point Patterns

Author

Listed:
  • Kateřina Koňasová

    (Charles University)

  • Jiří Dvořák

    (Charles University)

Abstract

The stochastic reconstruction approach for point processes aims at producing independent patterns with the same properties as the observed pattern, without specifying any particular model. Instead a so-called energy functional is defined, based on a set of point process summary characteristics. It measures the dissimilarity between the observed pattern (input) and another pattern. The reconstructed pattern (output) is sought iteratively by minimising the energy functional. Hence, the output has approximately the same values of the prescribed summary characteristics as the input pattern. In this paper, we focus on inhomogeneous point patterns and apply formal hypotheses tests to check the quality of reconstructions in terms of the intensity function and morphological properties of the underlying point patterns. We argue that the current version of the algorithm available in the literature for inhomogeneous point processes does not produce outputs with appropriate intensity function. We propose modifications to the algorithm which can remedy this issue.

Suggested Citation

  • Kateřina Koňasová & Jiří Dvořák, 2021. "Stochastic Reconstruction for Inhomogeneous Point Patterns," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 527-547, June.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:2:d:10.1007_s11009-019-09738-0
    DOI: 10.1007/s11009-019-09738-0
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    References listed on IDEAS

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    4. Tscheschel, A. & Stoyan, D., 2006. "Statistical reconstruction of random point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 859-871, November.
    5. Naveen N. Narisetty & Vijayan N. Nair, 2016. "Extremal Depth for Functional Data and Applications," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1705-1714, October.
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