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Analysis, Simulation and Prediction of Multivariate Random Fields with Package RandomFields

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  • Schlather, Martin
  • Malinowski, Alexander
  • Menck, Peter J.
  • Oesting, Marco
  • Strokorb, Kirstin

Abstract

Modeling of and inference on multivariate data that have been measured in space, such as temperature and pressure, are challenging tasks in environmental sciences, physics and materials science. We give an overview over and some background on modeling with crosscovariance models. The R package RandomFields supports the simulation, the parameter estimation and the prediction in particular for the linear model of coregionalization, the multivariate Matérn models, the delay model, and a spectrum of physically motivated vector valued models. An example on weather data is considered, illustrating the use of RandomFields for parameter estimation and prediction.

Suggested Citation

  • Schlather, Martin & Malinowski, Alexander & Menck, Peter J. & Oesting, Marco & Strokorb, Kirstin, 2015. "Analysis, Simulation and Prediction of Multivariate Random Fields with Package RandomFields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i08).
    • Handle: RePEc:jss:jstsof:v:063:i08
    DOI: http://hdl.handle.net/10.18637/jss.v063.i08
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    8. Padoan, Simone A. & Bevilacqua, Moreno, 2015. "Analysis of Random Fields Using CompRandFld," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i09).
    9. Sigrist, Fabio & Künsch, Hans R. & Stahel, Werner A., 2015. "spate: An R Package for Spatio-Temporal Modeling with a Stochastic Advection-Diffusion Process," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i14).
    10. 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).
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    12. Cécile Hardouin & Noel Cressie, 2018. "Two-scale spatial models for binary data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 1-24, March.
    13. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    14. de Iaco, Sandra, 2017. "The cgeostat Software for Analyzing Complex-Valued Random Fields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i05).
    15. Xavier Barber & David Conesa & Antonio López-Quílez & Joaquín Martínez-Minaya & Iosu Paradinas & Maria Grazia Pennino, 2021. "Incorporating Biotic Information in Species Distribution Models: A Coregionalized Approach," Mathematics, MDPI, vol. 9(4), pages 1-12, February.
    16. Aaron Osgood‐Zimmerman & Jon Wakefield, 2023. "A Statistical Review of Template Model Builder: A Flexible Tool for Spatial Modelling," International Statistical Review, International Statistical Institute, vol. 91(2), pages 318-342, August.
    17. Isabelle Grenier & Bruno Sansó & Jessica L. Matthews, 2024. "Multivariate nearest‐neighbors Gaussian processes with random covariance matrices," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.
    18. Matthias Katzfuss, 2017. "A Multi-Resolution Approximation for Massive Spatial Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 201-214, January.
    19. Ghorbani, Mohammad & Vafaei, Nafiseh & Dvořák, Jiří & Myllymäki, Mari, 2021. "Testing the first-order separability hypothesis for spatio-temporal point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    20. Dolder, Paul J. & Minto, Cóilín & Guarini, Jean-Marc & Poos, Jan Jaap, 2020. "Highly resolved spatiotemporal simulations for exploring mixed fishery dynamics," Ecological Modelling, Elsevier, vol. 424(C).
    21. Ninna Vihrs & Jesper Møller & Alan E. Gelfand, 2022. "Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 185-210, March.
    22. Sameh Abdulah & Yuxiao Li & Jian Cao & Hatem Ltaief & David E. Keyes & Marc G. Genton & Ying Sun, 2023. "Large‐scale environmental data science with ExaGeoStatR," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    23. Thurner, Stephanie D & Converse, Sarah J & Branch, Trevor A, 2021. "Modeling opportunistic exploitation: increased extinction risk when targeting more than one species," Ecological Modelling, Elsevier, vol. 454(C).
    24. Pebesma, Edzer & Bivand, Roger & Ribeiro, Paulo Justiniano, 2015. "Software for Spatial Statistics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i01).

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