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Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes

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  • Tilman M. Davies
  • Martin L. Hazelton

Abstract

The univariate log‐Gaussian Cox process (LGCP) has shown considerable potential for the flexible modelling of the spatial, and more recently, spatiotemporal, intensity functions of planar point patterns within a restricted region in space. Its flexibility and mathematical tractability are partly offset by the need to acquire sensible estimates of the parameters controlling the dependence structure of the Gaussian field given the observed data. The method of minimum contrast, which compares theoretical descriptors of the process with their non‐parametric counterparts in order to obtain the required estimates, is arguably the most popular in practice to date. This article provides a comprehensive set of simulation studies focused on gauging the performance and impact of minimum contrast methods for parameter estimation of these processes. Results indicate that concerns over arbitrariness of implementation of minimum contrast give way to satisfactory practical performance.

Suggested Citation

  • Tilman M. Davies & Martin L. Hazelton, 2013. "Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 355-389, November.
    • Handle: RePEc:bla:stanee:v:67:y:2013:i:4:p:355-389
    DOI: 10.1111/stan.12011
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    References listed on IDEAS

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    1. Anders Brix & Peter J. Diggle, 2003. "Corrigendum: Spatiotemporal prediction for log‐Gaussian Cox processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 946-946, November.
    2. I. S. Weir & A. N. Pettitt, 2000. "Binary probability maps using a hidden conditional autoregressive Gaussian process with an application to Finnish common toad data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(4), pages 473-484.
    3. Anders Brix & Peter J. Diggle, 2001. "Spatiotemporal prediction for log‐Gaussian Cox processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 823-841.
    4. Guan, Yongtao, 2007. "A least-squares cross-validation bandwidth selection approach in pair correlation function estimations," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1722-1729, December.
    5. Benjamin M. Taylor & Peter J. Diggle, 2013. "Corrigendum: Spatiotemporal prediction for log-Gaussian Cox processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 601-602, June.
    6. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    7. Yongtao Guan & Michael Sherman, 2007. "On least squares fitting for stationary spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 31-49, February.
    8. Ole F. Christensen & Rasmus Waagepetersen, 2002. "Bayesian Prediction of Spatial Count Data Using Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 58(2), pages 280-286, June.
    9. Rasmus Waagepetersen & Yongtao Guan, 2009. "Two‐step estimation for inhomogeneous spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 685-702, June.
    10. Davies, Tilman M. & Bryant, David, 2013. "On Circulant Embedding for Gaussian Random Fields in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i09).
    11. 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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    1. Taylor, Benjamin M. & Davies, Tilman M. & Rowlingson, Barry S. & Diggle, Peter J., 2015. "Bayesian Inference and Data Augmentation Schemes for Spatial, Spatiotemporal and Multivariate Log-Gaussian Cox Processes in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i07).
    2. 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).
    3. 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.
    4. Tang, Jinjun & Zhao, Chuyun & Liu, Fang & Hao, Wei & Gao, Fan, 2022. "Analyzing travel destinations distribution using large-scaled GPS trajectories: A spatio-temporal Log-Gaussian Cox process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    5. Taylor, Benjamin M. & Davies, Tilman M. & Rowlingson, Barry S. & Diggle, Peter J., 2013. "lgcp: An R Package for Inference with Spatial and Spatio-Temporal Log-Gaussian Cox Processes," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 52(i04).

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