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An adaptive importance sampling for locally stable point processes

Author

Listed:
  • Hee-Geon Kang

    (University of Seoul)

  • Sunggon Kim

    (University of Seoul)

Abstract

The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance point process to the family of homogeneous Poisson point processes, which enables us to generate quickly independent samples of the importance point process. The optimal intensity of the importance point process is found by applying the cross-entropy minimization method. In the proposed scheme, the expected value of the statistic and the optimal intensity are iteratively estimated in an adaptive manner. We show that the proposed estimator converges to the target value almost surely, and prove the asymptotic normality of it. We explain how to apply the proposed scheme to the estimation of the intensity of a stationary pairwise interaction point process. The performance of the proposed scheme is compared numerically with Markov chain Monte Carlo simulation and perfect sampling.

Suggested Citation

  • Hee-Geon Kang & Sunggon Kim, 2025. "An adaptive importance sampling for locally stable point processes," Computational Statistics, Springer, vol. 40(7), pages 3745-3779, September.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:7:d:10.1007_s00180-025-01609-2
    DOI: 10.1007/s00180-025-01609-2
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    1. Peter W. Glynn & Ward Whitt, 1992. "The Asymptotic Efficiency of Simulation Estimators," Operations Research, INFORMS, vol. 40(3), pages 505-520, June.
    2. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
    3. Halis Sak & Wolfgang Hörmann, 2012. "Fast simulations in credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 12(10), pages 1557-1569, October.
    4. Baddeley, Adrian & Turner, Rolf, 2005. "spatstat: An R Package for Analyzing Spatial Point Patterns," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i06).
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