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    Spherical Process Models for Global Spatial Statistics

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    euclid.ss.1511838025.pdf
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    Type
    Article
    Authors
    Jeong, Jaehong
    Jun, Mikyoung
    Genton, Marc G. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    KAUST Grant Number
    OSR-2015-CRG4-2640
    Date
    2017-11-28
    Online Publication Date
    2017-11-28
    Print Publication Date
    2017-11
    Permanent link to this record
    http://hdl.handle.net/10754/626285
    
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    Abstract
    Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.
    Citation
    Jeong J, Jun M, Genton MG (2017) Spherical Process Models for Global Spatial Statistics. Statistical Science 32: 501–513. Available: http://dx.doi.org/10.1214/17-sts620.
    Sponsors
    This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No: OSR-2015-CRG4-2640.
    Publisher
    Institute of Mathematical Statistics
    Journal
    Statistical Science
    DOI
    10.1214/17-sts620
    Additional Links
    https://projecteuclid.org/euclid.ss/1511838025
    ae974a485f413a2113503eed53cd6c53
    10.1214/17-sts620
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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