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    Multivariate Max-Stable Spatial Processes

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    Type
    Presentation
    Authors
    Genton, Marc G. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2014-01-06
    Permanent link to this record
    http://hdl.handle.net/10754/624023
    
    Metadata
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    Abstract
    Analysis of spatial extremes is currently based on univariate processes. Max-stable processes allow the spatial dependence of extremes to be modelled and explicitly quantified, they are therefore widely adopted in applications. For a better understanding of extreme events of real processes, such as environmental phenomena, it may be useful to study several spatial variables simultaneously. To this end, we extend some theoretical results and applications of max-stable processes to the multivariate setting to analyze extreme events of several variables observed across space. In particular, we study the maxima of independent replicates of multivariate processes, both in the Gaussian and Student-t cases. Then, we define a Poisson process construction in the multivariate setting and introduce multivariate versions of the Smith Gaussian extremevalue, the Schlather extremal-Gaussian and extremal-t, and the BrownResnick models. Inferential aspects of those models based on composite likelihoods are developed. We present results of various Monte Carlo simulations and of an application to a dataset of summer daily temperature maxima and minima in Oklahoma, U.S.A., highlighting the utility of working with multivariate models in contrast to the univariate case. Based on joint work with Simone Padoan and Huiyan Sang.
    Conference/Event name
    Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)
    Collections
    Applied Mathematics and Computational Science Program; Presentations; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)

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