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Non-Gaussian spatiotemporal modelling through scale mixing

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  • Thaís C. O. Fonseca
  • Mark F. J. Steel

Abstract

We construct non-Gaussian processes that vary continuously in space and time with nonseparable covariance functions. Starting from a general and flexible way of constructing valid nonseparable covariance functions through mixing over separable covariance functions, the resulting models are generalized by allowing for outliers as well as regions with larger variances. We induce this through scale mixing with separate positive-valued processes. Smooth mixing processes are applied to the underlying correlated processes in space and in time, thus leading to regions in space and time of increased spread. An uncorrelated mixing process on the nugget effect accommodates outliers. Posterior and predictive Bayesian inference with these models is implemented through a Markov chain Monte Carlo sampler. An application to temperature data in the Basque country illustrates the potential of this model in the identification of outliers and regions with inflated variance, and shows that this improves the predictive performance. Copyright 2011, Oxford University Press.

Suggested Citation

  • Thaís C. O. Fonseca & Mark F. J. Steel, 2011. "Non-Gaussian spatiotemporal modelling through scale mixing," Biometrika, Biometrika Trust, vol. 98(4), pages 761-774.
  • Handle: RePEc:oup:biomet:v:98:y:2011:i:4:p:761-774
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    File URL: http://hdl.handle.net/10.1093/biomet/asr047
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    Cited by:

    1. Vahid Tadayon & Abdolrahman Rasekh, 2019. "Non-Gaussian Covariate-Dependent Spatial Measurement Error Model for Analyzing Big Spatial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(1), pages 49-72, March.
    2. Jafari Khaledi, Majid & Zareifard, Hamid & Boojari, Hossein, 2023. "A spatial skew-Gaussian process with a specified covariance function," Statistics & Probability Letters, Elsevier, vol. 192(C).
    3. 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.
    4. Zareifard, Hamid & Jafari Khaledi, Majid, 2013. "Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 16-28.

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