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Approximating Point Process Likelihoods with Glim

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  • Mark Berman
  • T. Rolf Turner

Abstract

This paper shows how approximate maximum likelihood estimation for fairly general point processes on the line can be performed with GLIM. The approximation is based on a weighted sum approximation to an integral in the likelihood. Various weighting schemes are briefly examined. The methodology is illustrated with an example, and its extension to Poisson processes in higher dimensions is briefly described.

Suggested Citation

  • Mark Berman & T. Rolf Turner, 1992. "Approximating Point Process Likelihoods with Glim," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 31-38, March.
    • Handle: RePEc:bla:jorssc:v:41:y:1992:i:1:p:31-38
    DOI: 10.2307/2347614
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    1. Giuseppe Espa & Giuseppe Arbia & Diego Giuliani, 2013. "Conditional versus unconditional industrial agglomeration: disentangling spatial dependence and spatial heterogeneity in the analysis of ICT firms’ distribution in Milan," Journal of Geographical Systems, Springer, vol. 15(1), pages 31-50, January.
    2. Florian Ploeckl, 2012. "Space, settlements, towns: the influence of geography and market access on settlement distribution and urbanization," Working Papers 2012/23, Institut d'Economia de Barcelona (IEB).
    3. Christophe Botella & Alexis Joly & Pascal Monestiez & Pierre Bonnet & François Munoz, 2020. "Bias in presence-only niche models related to sampling effort and species niches: Lessons for background point selection," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-18, May.
    4. Giuseppe Arbia & Patrizia Cella & Giuseppe Espa & Diego Giuliani, 2015. "A micro spatial analysis of firm demography: the case of food stores in the area of Trento (Italy)," Empirical Economics, Springer, vol. 48(3), pages 923-937, May.
    5. Edith Gabriel, 2014. "Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 411-431, June.
    6. Ploeckl, Florian, 2021. "The next town over: On the clustering of towns and settlements before modern economic growth," Regional Science and Urban Economics, Elsevier, vol. 89(C).
    7. Leandro, Camila & Jay-Robert, Pierre & Mériguet, Bruno & Houard, Xavier & Renner, Ian W., 2020. "Is my sdm good enough? insights from a citizen science dataset in a point process modeling framework," Ecological Modelling, Elsevier, vol. 438(C).
    8. repec:jss:jstsof:08:i16 is not listed on IDEAS
    9. Amanda M E D’Andrea & Vera L D Tomazella & Hassan M Aljohani & Pedro L Ramos & Marco P Almeida & Francisco Louzada & Bruna A W Verssani & Amanda B Gazon & Ahmed Z Afify, 2021. "Objective bayesian analysis for multiple repairable systems," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-19, November.
    10. Hossain, Md. Monir & Lawson, Andrew B., 2009. "Approximate methods in Bayesian point process spatial models," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2831-2842, June.
    11. D'Angelo, Nicoletta & Adelfio, Giada & Mateu, Jorge, 2023. "Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    12. repec:jss:jstsof:12:i06 is not listed on IDEAS
    13. Florian Ploeckl, 2012. "Space, settlements, towns: the influence of geography and market access on settlement distribution and urbanization," Working Papers 2012/23, Institut d'Economia de Barcelona (IEB).
    14. Nicoletta D’Angelo & Giada Adelfio, 2024. "Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes," Statistical Papers, Springer, vol. 65(6), pages 3651-3679, August.
    15. Jeffrey Daniel & Julie Horrocks & Gary J. Umphrey, 2020. "Efficient Modelling of Presence-Only Species Data via Local Background Sampling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 90-111, March.
    16. Matthew Bognar, 2008. "Bayesian modeling of continuously marked spatial point patterns," Computational Statistics, Springer, vol. 23(3), pages 361-379, July.
    17. Gao, Lisa & Shi, Peng, 2022. "Leveraging high-resolution weather information to predict hail damage claims: A spatial point process for replicated point patterns," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 161-179.
    18. Ottmar Cronie & Mehdi Moradi & Christophe A N Biscio, 2024. "A cross-validation-based statistical theory for point processes," Biometrika, Biometrika Trust, vol. 111(2), pages 625-641.

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