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Comparative evaluation of point process forecasts

Author

Listed:
  • Jonas R. Brehmer

    (Heidelberg Institute for Theoretical Studies)

  • Tilmann Gneiting

    (Heidelberg Institute for Theoretical Studies
    Karlsruhe Institute of Technology (KIT))

  • Marcus Herrmann

    (University of Naples Federico II, Complesso di Monte Sant’Angelo)

  • Warner Marzocchi

    (University of Naples Federico II, Complesso di Monte Sant’Angelo)

  • Martin Schlather

    (University of Mannheim)

  • Kirstin Strokorb

    (Cardiff University)

Abstract

Stochastic models of point patterns in space and time are widely used to issue forecasts or assess risk, and often they affect societally relevant decisions. We adapt the concept of consistent scoring functions and proper scoring rules, which are statistically principled tools for the comparative evaluation of predictive performance, to the point process setting, and place both new and existing methodology in this framework. With reference to earthquake likelihood model testing, we demonstrate that extant techniques apply in much broader contexts than previously thought. In particular, the Poisson log-likelihood can be used for theoretically principled comparative forecast evaluation in terms of cell expectations. We illustrate the approach in a simulation study and in a comparative evaluation of operational earthquake forecasts for Italy.

Suggested Citation

  • Jonas R. Brehmer & Tilmann Gneiting & Marcus Herrmann & Warner Marzocchi & Martin Schlather & Kirstin Strokorb, 2024. "Comparative evaluation of point process forecasts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(1), pages 47-71, February.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:1:d:10.1007_s10463-023-00875-5
    DOI: 10.1007/s10463-023-00875-5
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