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Second‐order semi‐parametric inference for multivariate log Gaussian Cox processes

Author

Listed:
  • Kristian Bjørn Hessellund
  • Ganggang Xu
  • Yongtao Guan
  • Rasmus Waagepetersen

Abstract

This paper introduces a new approach to inferring the second‐order properties of a multivariate log Gaussian Cox process (LGCP) with a complex intensity function. We assume a semi‐parametric model for the multivariate intensity function containing an unspecified complex factor common to all types of points. Given this model, we construct a second‐order conditional composite likelihood to infer the pair correlation and cross pair correlation functions of the LGCP. Crucially this likelihood does not depend on the unspecified part of the intensity function. We also introduce a cross‐validation method for model selection and an algorithm for regularized inference that can be used to obtain sparse models for cross pair correlation functions. The methodology is applied to simulated data as well as data examples from microscopy and criminology. This shows how the new approach outperforms existing alternatives where the intensity functions are estimated non‐parametrically.

Suggested Citation

  • Kristian Bjørn Hessellund & Ganggang Xu & Yongtao Guan & Rasmus Waagepetersen, 2022. "Second‐order semi‐parametric inference for multivariate log Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 244-268, January.
    • Handle: RePEc:bla:jorssc:v:71:y:2022:i:1:p:244-268
    DOI: 10.1111/rssc.12530
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    References listed on IDEAS

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    1. Adrian Baddeley & Aruna Jammalamadaka & Gopalan Nair, 2014. "Multitype point process analysis of spines on the dendrite network of a neuron," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(5), pages 673-694, November.
    2. Yiyi Yan & Alexey A Leontovich & Michael J Gerdes & Keyur Desai & Jinhong Dong & Anup Sood & Alberto Santamaria-Pang & Aaron S Mansfield & Chrystal Chadwick & Rong Zhang & Wendy K Nevala & Thomas J Fl, 2019. "Understanding heterogeneous tumor microenvironment in metastatic melanoma," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-23, June.
    3. Abdollah Jalilian & Yongtao Guan & Jorge Mateu & Rasmus Waagepetersen, 2015. "Multivariate product-shot-noise Cox point process models," Biometrics, The International Biometric Society, vol. 71(4), pages 1022-1033, December.
    4. Guan, Yongtao & Waagepetersen, Rasmus & Beale, Colin M., 2008. "Second-Order Analysis of Inhomogeneous Spatial Point Processes With Proportional Intensity Functions," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 769-777, June.
    5. T. Rajala & D. J. Murrell & S. C. Olhede, 2018. "Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1237-1273, November.
    6. O Cronie & M N M Van Lieshout, 2018. "A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions," Biometrika, Biometrika Trust, vol. 105(2), pages 455-462.
    7. P. J. Diggle & V. Gómez-Rubio & P. E. Brown & A. G. Chetwynd & S. Gooding, 2007. "Second-Order Analysis of Inhomogeneous Spatial Point Processes Using Case–Control Data," Biometrics, The International Biometric Society, vol. 63(2), pages 550-557, June.
    8. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    9. Rasmus Waagepetersen & Yongtao Guan & Abdollah Jalilian & Jorge Mateu, 2016. "Analysis of multispecies point patterns by using multivariate log-Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(1), pages 77-96, January.
    10. Roy S. Herbst & Jean-Charles Soria & Marcin Kowanetz & Gregg D. Fine & Omid Hamid & Michael S. Gordon & Jeffery A. Sosman & David F. McDermott & John D. Powderly & Scott N. Gettinger & Holbrook E. K. , 2014. "Predictive correlates of response to the anti-PD-L1 antibody MPDL3280A in cancer patients," Nature, Nature, vol. 515(7528), pages 563-567, November.
    11. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    12. P. A. Henrys & P. E. Brown, 2009. "Inference for Clustered Inhomogeneous Spatial Point Processes," Biometrics, The International Biometric Society, vol. 65(2), pages 423-430, June.
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