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Space‐time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds

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  • Anders Brix
  • Jesper Moller

Abstract

Log Gaussian Cox processes as introduced in Moller et al. (1998) are extended to space‐time models called log Gaussian Cox birth processes. These processes allow modelling of spatial and temporal heterogeneity in time series of increasing point processes consisting of different types of points. The models are shown to be easy to analyse yet flexible enough for a detailed statistical analysis of a particular agricultural experiment concerning the development of two weed species on an organic barley field. Particularly, the aspects of estimation, model validation and intensity surface prediction are discussed.

Suggested Citation

  • Anders Brix & Jesper Moller, 2001. "Space‐time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 471-488, September.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:3:p:471-488
    DOI: 10.1111/1467-9469.00249
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    Cited by:

    1. Michaela Prokešová & Jiří Dvořák, 2014. "Statistics for Inhomogeneous Space-Time Shot-Noise Cox Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 433-449, June.
    2. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Athanasios Kottas, 2018. "Discussion of paper “nonparametric Bayesian inference in applications” by Peter Müller, Fernando A. Quintana and Garritt L. Page," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 219-225, June.
    4. Kenneth A. Flagg & Andrew Hoegh & John J. Borkowski, 2020. "Modeling Partially Surveyed Point Process Data: Inferring Spatial Point Intensity of Geomagnetic Anomalies," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(2), pages 186-205, June.
    5. Renshaw, Eric & Mateu, Jorge & Saura, Fuensanta, 2007. "Disentangling mark/point interaction in marked-point processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3123-3144, March.
    6. Yurij Kozachenko & Oleksandr Pogoriliak, 2011. "Simulation of Cox Processes Driven by Random Gaussian Field," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 511-521, September.
    7. Jesper Møller & Carlos Díaz‐Avalos, 2010. "Structured Spatio‐Temporal Shot‐Noise Cox Point Process Models, with a View to Modelling Forest Fires," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 2-25, March.
    8. Reis, Edna A. & Gamerman, Dani & Paez, Marina S. & Martins, Thiago G., 2013. "Bayesian dynamic models for space–time point processes," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 146-156.
    9. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    10. Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2012. "Spatio-Temporal Model for a Random Set Given by a Union of Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 883-894, September.
    11. Sarkka, Aila & Renshaw, Eric, 2006. "The analysis of marked point patterns evolving through space and time," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1698-1718, December.
    12. Møller, Jesper & Torrisi, Giovanni Luca, 2007. "The pair correlation function of spatial Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 995-1003, June.
    13. Jiří Dvořák & Michaela Prokešová, 2016. "Parameter Estimation for Inhomogeneous Space-Time Shot-Noise Cox Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 939-961, December.
    14. 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.
    15. Yehua Li & Yongtao Guan, 2014. "Functional Principal Component Analysis of Spatiotemporal Point Processes With Applications in Disease Surveillance," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1205-1215, September.
    16. Bourgeois, A. & Gaba, S. & Munier-Jolain, N. & Borgy, B. & Monestiez, P. & Soubeyrand, S., 2012. "Inferring weed spatial distribution from multi-type data," Ecological Modelling, Elsevier, vol. 226(C), pages 92-98.
    17. Waagepetersen, Rasmus, 2004. "Convergence of posteriors for discretized log Gaussian Cox processes," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 229-235, February.
    18. 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.

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