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Dynamic models for spatiotemporal data

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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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    File URL: https://doi.org/10.1111/1467-9868.00305
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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. Lyndsay Shand & Bo Li, 2017. "Modeling nonstationarity in space and time," Biometrics, The International Biometric Society, vol. 73(3), pages 759-768, September.
    8. 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.
    9. 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.
    10. 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.
    11. Christopher K. Wikle, 2003. "Hierarchical Models in Environmental Science," International Statistical Review, International Statistical Institute, vol. 71(2), pages 181-199, August.

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