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Accounting for roughness of circular processes: Using Gaussian random processes to model the anisotropic spread of airborne plant disease

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  • Soubeyrand, Samuel
  • Enjalbert, Jérôme
  • Sache, Ivan

Abstract

Variables with values in the circle or indexed by the circle have been studied in order to investigate questions in ecology, epidemiology, climatology and oceanography for example. To model circular variables with rough behaviors, the use of Gaussian random processes (GRPs) can be particularly convenient as will be seen in this paper. The roughness of a GRP being mainly determined by its correlation function, a circular correlation function convenient for rough processes is proposed. These mathematical tools are applied to describe the anisotropic spread of an airborne plant disease from a point source: a hierarchical model including two circular GRPs is built and used to analyze data coming from a field experiment. This random-effect model is fitted to data using a Monte-Carlo expectation–maximization (MCEM) algorithm.

Suggested Citation

  • Soubeyrand, Samuel & Enjalbert, Jérôme & Sache, Ivan, 2008. "Accounting for roughness of circular processes: Using Gaussian random processes to model the anisotropic spread of airborne plant disease," Theoretical Population Biology, Elsevier, vol. 73(1), pages 92-103.
    • Handle: RePEc:eee:thpobi:v:73:y:2008:i:1:p:92-103
    DOI: 10.1016/j.tpb.2007.09.005
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    References listed on IDEAS

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    1. Michael L. Stein, 2005. "Statistical methods for regular monitoring data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 667-687, November.
    2. Hao Zhang, 2002. "On Estimation and Prediction for Spatial Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 58(1), pages 129-136, March.
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    1. Arafat, Ahmed & Porcu, Emilio & Bevilacqua, Moreno & Mateu, Jorge, 2018. "Equivalence and orthogonality of Gaussian measures on spheres," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 306-318.
    2. Emilio Porcu & Moreno Bevilacqua & Marc G. Genton, 2016. "Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 888-898, April.
    3. Wälder, Konrad & Näther, Wolfgang & Wagner, Sven, 2009. "Improving inverse model fitting in trees—Anisotropy, multiplicative effects, and Bayes estimation," Ecological Modelling, Elsevier, vol. 220(8), pages 1044-1053.
    4. Garnett P. McMillan & Timothy E. Hanson & Gabrielle Saunders & Frederick J. Gallun, 2013. "A two-component circular regression model for repeated measures auditory localization data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 515-534, August.

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