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    Constructing Priors that Penalize the Complexity of Gaussian Random Fields

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    Type
    Dataset
    Authors
    Fuglstad, Geir-Arne
    Simpson, Daniel
    Lindgren, Finn
    Rue, Haavard cc
    KAUST Department
    Statistics Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019
    Permanent link to this record
    http://hdl.handle.net/10754/664473
    
    Metadata
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    Abstract
    Priors are important for achieving proper posteriors with physically meaningful covariance structures for Gaussian random fields (GRFs) since the likelihood typically only provides limited information about the covariance structure under in-fill asymptotics. We extend the recent penalized complexity prior framework and develop a principled joint prior for the range and the marginal variance of one-dimensional, two-dimensional, and three-dimensional Matérn GRFs with fixed smoothness. The prior is weakly informative and penalizes complexity by shrinking the range toward infinity and the marginal variance toward zero. We propose guidelines for selecting the hyperparameters, and a simulation study shows that the new prior provides a principled alternative to reference priors that can leverage prior knowledge to achieve shorter credible intervals while maintaining good coverage. We extend the prior to a nonstationary GRF parameterized through local ranges and marginal standard deviations, and introduce a scheme for selecting the hyperparameters based on the coverage of the parameters when fitting simulated stationary data. The approach is applied to a dataset of annual precipitation in southern Norway and the scheme for selecting the hyperparameters leads to conservative estimates of nonstationarity and improved predictive performance over the stationary model. Supplementary materials for this article are available online.
    Citation
    Geir-Arne Fuglstad, Simpson, D., Lindgren, F., & Rue, H. (2019). Constructing Priors that Penalize the Complexity of Gaussian Random Fields [Data set]. Taylor & Francis. https://doi.org/10.6084/M9.FIGSHARE.5807358.V2
    Publisher
    figshare
    DOI
    10.6084/m9.figshare.5807358.v2
    Relations
    Is Supplement To:
    • [Article]
      Fuglstad G-A, Simpson D, Lindgren F, Rue H (2018) Constructing Priors that Penalize the Complexity of Gaussian Random Fields. Journal of the American Statistical Association: 1–8. Available: http://dx.doi.org/10.1080/01621459.2017.1415907.. DOI: 10.1080/01621459.2017.1415907 HANDLE: 10754/631279
    ae974a485f413a2113503eed53cd6c53
    10.6084/m9.figshare.5807358.v2
    Scopus Count
    Collections
    Datasets; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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