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Studies in the history of probability and statistics XLIX On the Matern correlation family

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  • Peter Guttorp
  • Tilmann Gneiting

Abstract

Handcock & Stein (1993) introduced the Matern family of spatial correlations into statistics as a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field. We document the varied history of this family, which includes contributions by eminent physical scientists and statisticians. Copyright 2006, Oxford University Press.

Suggested Citation

  • Peter Guttorp & Tilmann Gneiting, 2006. "Studies in the history of probability and statistics XLIX On the Matern correlation family," Biometrika, Biometrika Trust, vol. 93(4), pages 989-995, December.
    • Handle: RePEc:oup:biomet:v:93:y:2006:i:4:p:989-995
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    File URL: http://hdl.handle.net/10.1093/biomet/93.4.989
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    1. Girard, Didier A., 2016. "Asymptotic near-efficiency of the “Gibbs-energy and empirical-variance” estimating functions for fitting Matérn models — I: Densely sampled processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 191-197.
    2. Kristjana Ýr Jónsdóttir & Anders Rønn-Nielsen & Kim Mouridsen & Eva B. Vedel Jensen, 2013. "Lévy-based Modelling in Brain Imaging," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 511-529, September.
    3. Kleiber, William & Nychka, Douglas, 2012. "Nonstationary modeling for multivariate spatial processes," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 76-91.
    4. Akim Adekpedjou & Sophie Dabo‐Niang, 2021. "Semiparametric estimation with spatially correlated recurrent events," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1097-1126, December.
    5. Ghada Atteia & Nagwan Abdel Samee & El-Sayed M. El-Kenawy & Abdelhameed Ibrahim, 2022. "CNN-Hyperparameter Optimization for Diabetic Maculopathy Diagnosis in Optical Coherence Tomography and Fundus Retinography," Mathematics, MDPI, vol. 10(18), pages 1-30, September.
    6. Cheng, Dan, 2024. "Smooth Matérn Gaussian random fields: Euler characteristic, expected number and height distribution of critical points," Statistics & Probability Letters, Elsevier, vol. 210(C).
    7. Litvinenko, Alexander & Sun, Ying & Genton, Marc G. & Keyes, David E., 2019. "Likelihood approximation with hierarchical matrices for large spatial datasets," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 115-132.
    8. Ghulam A. Qadir & Ying Sun, 2021. "Semiparametric estimation of cross‐covariance functions for multivariate random fields," Biometrics, The International Biometric Society, vol. 77(2), pages 547-560, June.
    9. Hansen, Linda V. & Thorarinsdottir, Thordis L., 2013. "A note on moving average models for Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 850-855.
    10. Heinrich, Claudio & Pakkanen, Mikko S. & Veraart, Almut E.D., 2019. "Hybrid simulation scheme for volatility modulated moving average fields," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 224-244.
    11. Nesbitt, Peter & Blake, Lewis R. & Lamas, Patricio & Goycoolea, Marcos & Pagnoncelli, Bernardo K. & Newman, Alexandra & Brickey, Andrea, 2021. "Underground mine scheduling under uncertainty," European Journal of Operational Research, Elsevier, vol. 294(1), pages 340-352.
    12. Unn Dahlén & Johan Lindström & Marko Scholze, 2020. "Spatiotemporal reconstructions of global CO2‐fluxes using Gaussian Markov random fields," Environmetrics, John Wiley & Sons, Ltd., vol. 31(4), June.
    13. Zifeng Zhao & Peng Shi & Xiaoping Feng, 2021. "Knowledge Learning of Insurance Risks Using Dependence Models," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1177-1196, July.
    14. Petrus Strydom, 2017. "Macro economic cycle effect on mortgage and personal loan default rates," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 7(6), pages 1-1.
    15. Thea Roksvåg & Ingelin Steinsland & Kolbjørn Engeland, 2021. "A two‐field geostatistical model combining point and areal observations—A case study of annual runoff predictions in the Voss area," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(4), pages 934-960, August.
    16. Ip, Ryan H.L. & Li, W.K., 2017. "A class of valid Matérn cross-covariance functions for multivariate spatio-temporal random fields," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 115-119.
    17. Guinness, Joseph & Fuentes, Montserrat, 2016. "Isotropic covariance functions on spheres: Some properties and modeling considerations," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 143-152.
    18. Joseph Guinness, 2022. "Inverses of Matérn covariances on grids [Spatial modeling with R-INLA: A review]," Biometrika, Biometrika Trust, vol. 109(2), pages 535-541.
    19. Silius M. Vandeskog & Sara Martino & Daniela Castro-Camilo & Håvard Rue, 2022. "Modelling Sub-daily Precipitation Extremes with the Blended Generalised Extreme Value Distribution," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 598-621, December.
    20. Bevilacqua, Moreno & Caamaño-Carrillo, Christian & Porcu, Emilio, 2022. "Unifying compactly supported and Matérn covariance functions in spatial statistics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    21. Victor De Oliveira & Zifei Han, 2022. "On Information About Covariance Parameters in Gaussian Matérn Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 690-712, December.
    22. Sandra De Iaco & Donato Posa & Claudia Cappello & Sabrina Maggio, 2021. "On Some Characteristics of Gaussian Covariance Functions," International Statistical Review, International Statistical Institute, vol. 89(1), pages 36-53, April.

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