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Dynamic models for spatiotemporal data

Author

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  • Jonathan R. Stroud
  • Peter Müller
  • Bruno Sansó

Abstract

We propose a model for non‐stationary spatiotemporal data. To account for spatial variability, we model the mean function at each time period as a locally weighted mixture of linear regressions. To incorporate temporal variation, we allow the regression coefficients to change through time. The model is cast in a Gaussian state space framework, which allows us to include temporal components such as trends, seasonal effects and autoregressions, and permits a fast implementation and full probabilistic inference for the parameters, interpolations and forecasts. To illustrate the model, we apply it to two large environmental data sets: tropical rainfall levels and Atlantic Ocean temperatures.

Suggested Citation

  • Jonathan R. Stroud & Peter Müller & Bruno Sansó, 2001. "Dynamic models for spatiotemporal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 673-689.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:4:p:673-689
    DOI: 10.1111/1467-9868.00305
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    Cited by:

    1. Kai Yang & Peihua Qiu, 2022. "A three-step local smoothing approach for estimating the mean and covariance functions of spatio-temporal Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 49-68, February.
    2. Christopher K. Wikle, 2003. "Hierarchical Models in Environmental Science," International Statistical Review, International Statistical Institute, vol. 71(2), pages 181-199, August.
    3. Andrew Hoegh & Scotland Leman, 2015. "A spatio-temporal model for assessing winter damage risk to east coast vineyards," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(4), pages 834-845, April.
    4. Philipp Otto & Wolfgang Schmid & Robert Garthoff, 2021. "Stochastic properties of spatial and spatiotemporal ARCH models," Statistical Papers, Springer, vol. 62(2), pages 623-638, April.
    5. Andrew Finley & Sudipto Banerjee & Alan Gelfand, 2012. "Bayesian dynamic modeling for large space-time datasets using Gaussian predictive processes," Journal of Geographical Systems, Springer, vol. 14(1), pages 29-47, January.
    6. J. Zhu & J. C. Eickhoff & P. Yan, 2005. "Generalized Linear Latent Variable Models for Repeated Measures of Spatially Correlated Multivariate Data," Biometrics, The International Biometric Society, vol. 61(3), pages 674-683, September.
    7. Noel Cressie & Gardar Johannesson, 2008. "Fixed rank kriging for very large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 209-226, February.
    8. Margaret C Johnson & Brian J Reich & Josh M Gray, 2021. "Multisensor fusion of remotely sensed vegetation indices using space‐time dynamic linear models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 793-812, June.
    9. Christopher J. Geoga & Mihai Anitescu & Michael L. Stein, 2021. "Flexible nonstationary spatiotemporal modeling of high‐frequency monitoring data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(5), August.
    10. Xiaofeng Cao & Ostap Okhrin & Martin Odening & Matthias Ritter, 2015. "Modelling spatio-temporal variability of temperature," Computational Statistics, Springer, vol. 30(3), pages 745-766, September.
    11. Tilman M. Davies & Sudipto Banerjee & Adam P. Martin & Rose E. Turnbull, 2022. "A nearest‐neighbour Gaussian process spatial factor model for censored, multi‐depth geochemical data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 1014-1043, August.
    12. K. Shuvo Bakar, 2020. "Interpolation of daily rainfall data using censored Bayesian spatially varying model," Computational Statistics, Springer, vol. 35(1), pages 135-152, March.
    13. F. S. Nathoo, 2010. "Joint Spatial Modeling of Recurrent Infection and Growth with Processes under Intermittent Observation," Biometrics, The International Biometric Society, vol. 66(2), pages 336-346, June.
    14. Santos-Fernandez, Edgar & Ver Hoef, Jay M. & Peterson, Erin E. & McGree, James & Isaak, Daniel J. & Mengersen, Kerrie, 2022. "Bayesian spatio-temporal models for stream networks," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    15. Lyndsay Shand & Bo Li, 2017. "Modeling nonstationarity in space and time," Biometrics, The International Biometric Society, vol. 73(3), pages 759-768, September.
    16. Huang, H.-C. & Martinez, F. & Mateu, J. & Montes, F., 2007. "Model comparison and selection for stationary space-time models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4577-4596, May.
    17. Liu, Jialuo & Chu, Tingjin & Zhu, Jun & Wang, Haonan, 2021. "Semiparametric method and theory for continuously indexed spatio-temporal processes," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    18. 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.

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