Optimal decision rules for marked point process models

Marie-Colette van Lieshout*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

We study a Markov decision problem in which the state space is the set of finite marked point patterns in the plane, the actions represent thinnings, the reward is proportional to the mark sum which is discounted over time, and the transitions are governed by a birth-death-growth process. We show that thinning points with large marks maximises the discounted total expected reward when births follow a Poisson process and marks grow logistically. Explicit values for the thinning threshold and the discounted total expected reward over finite and infinite horizons are also provided. When the points are required to respect a hard core distance, upper and lower bounds on the discounted total expected reward are derived.
Original languageEnglish
Pages (from-to)3607-3617
Number of pages11
JournalStochastic environmental research and risk assessment
Volume38
Issue number9
Early online date1 Aug 2024
DOIs
Publication statusPublished - Sept 2024

Keywords

  • UT-Hybrid-D
  • Logistic growth
  • Marked point process
  • Markov decision process
  • French thinning

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