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Determinantal point process models and statistical inference

Author

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  • Frédéric Lavancier
  • Jesper Møller
  • Ege Rubak

Abstract

type="main" xml:id="rssb12096-abs-0001"> Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern data sets where nearby points repel each other. Such data are usually modelled by Gibbs point processes, where the likelihood and moment expressions are intractable and simulations are time consuming. We exploit the appealing probabilistic properties of DPPs to develop parametric models, where the likelihood and moment expressions can be easily evaluated and realizations can be quickly simulated. We discuss how statistical inference is conducted by using the likelihood or moment properties of DPP models, and we provide freely available software for simulation and statistical inference.

Suggested Citation

  • Frédéric Lavancier & Jesper Møller & Ege Rubak, 2015. "Determinantal point process models and statistical inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 853-877, September.
    • Handle: RePEc:bla:jorssb:v:77:y:2015:i:4:p:853-877
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    File URL: http://hdl.handle.net/10.1111/rssb.2015.77.issue-4
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    Citations

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    Cited by:

    1. Frédéric Lavancier & Arnaud Poinas & Rasmus Waagepetersen, 2021. "Adaptive estimating function inference for nonstationary determinantal point processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 87-107, March.
    2. Chong Deng & Yongtao Guan & Rasmus P. Waagepetersen & Jingfei Zhang, 2017. "Second‐order quasi‐likelihood for spatial point processes," Biometrics, The International Biometric Society, vol. 73(4), pages 1311-1320, December.
    3. José J. Quinlan & Fernando A. Quintana & Garritt L. Page, 2021. "On a class of repulsive mixture models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 445-461, June.
    4. Ian Flint & Nicolas Privault, 2021. "Computation of Coverage Probabilities in a Spherical Germ-Grain Model," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 491-502, June.
    5. Jesper Møller & Heidi S. Christensen & Francisco Cuevas-Pacheco & Andreas D. Christoffersen, 2021. "Structured Space-Sphere Point Processes and K-Functions," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 569-591, June.
    6. Jean-François Coeurjolly & Jesper Møller & Rasmus Waagepetersen, 2017. "A Tutorial on Palm Distributions for Spatial Point Processes," International Statistical Review, International Statistical Institute, vol. 85(3), pages 404-420, December.
    7. Christophe Ange Napoléon Biscio & Frédéric Lavancier, 2017. "Contrast Estimation for Parametric Stationary Determinantal Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 204-229, March.
    8. Poinas, Arnaud, 2019. "A bound of the β-mixing coefficient for point processes in terms of their intensity functions," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 88-93.
    9. Subhroshekhar Ghosh & Soumendu Sundar Mukherjee, 2022. "Learning with latent group sparsity via heat flow dynamics on networks," Papers 2201.08326, arXiv.org.
    10. Frédéric Lavancier & Jesper Møller, 2016. "Modelling Aggregation on the Large Scale and Regularity on the Small Scale in Spatial Point Pattern Datasets," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 587-609, June.
    11. Jesper Møller & Ninna Vihrs, 2022. "Should We Condition on the Number of Points When Modelling Spatial Point Patterns?," International Statistical Review, International Statistical Institute, vol. 90(3), pages 551-562, December.
    12. Zhenchong Mo & Lin Gong & Mingren Zhu & Junde Lan, 2024. "The Generative Generic-Field Design Method Based on Design Cognition and Knowledge Reasoning," Sustainability, MDPI, vol. 16(22), pages 1-34, November.

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