Models and Inference for Multivariate Spatial Extremes

Handle URI:
http://hdl.handle.net/10754/626361
Title:
Models and Inference for Multivariate Spatial Extremes
Authors:
Vettori, Sabrina ( 0000-0003-3442-5405 )
Abstract:
The development of flexible and interpretable statistical methods is necessary in order to provide appropriate risk assessment measures for extreme events and natural disasters. In this thesis, we address this challenge by contributing to the developing research field of Extreme-Value Theory. We initially study the performance of existing parametric and non-parametric estimators of extremal dependence for multivariate maxima. As the dimensionality increases, non-parametric estimators are more flexible than parametric methods but present some loss in efficiency that we quantify under various scenarios. We introduce a statistical tool which imposes the required shape constraints on non-parametric estimators in high dimensions, significantly improving their performance. Furthermore, by embedding the tree-based max-stable nested logistic distribution in the Bayesian framework, we develop a statistical algorithm that identifies the most likely tree structures representing the data's extremal dependence using the reversible jump Monte Carlo Markov Chain method. A mixture of these trees is then used for uncertainty assessment in prediction through Bayesian model averaging. The computational complexity of full likelihood inference is significantly decreased by deriving a recursive formula for the nested logistic model likelihood. The algorithm performance is verified through simulation experiments which also compare different likelihood procedures. Finally, we extend the nested logistic representation to the spatial framework in order to jointly model multivariate variables collected across a spatial region. This situation emerges often in environmental applications but is not often considered in the current literature. Simulation experiments show that the new class of multivariate max-stable processes is able to detect both the cross and inner spatial dependence of a number of extreme variables at a relatively low computational cost, thanks to its Bayesian hierarchical representation. These innovative methods and models are implemented to study the concentration maxima of various air pollutants and how these are related to extreme weather conditions for a number of sites in California, one of the most populated and polluted states of the US. As a result, we provide comprehensive measures of air quality that can be used by communities and policymakers worldwide to better assess and manage the health, environmental and financial impacts of air pollution extremes.
Advisors:
Genton, Marc G. ( 0000-0001-6467-2998 ) ; Huser, Raphaël ( 0000-0002-1228-2071 )
Committee Member:
Sun, Ying ( 0000-0001-6703-4270 ) ; Davison, Anthony C.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Statistics
Issue Date:
7-Dec-2017
Type:
Dissertation
Appears in Collections:
Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.advisorGenton, Marc G.en
dc.contributor.advisorHuser, Raphaëlen
dc.contributor.authorVettori, Sabrinaen
dc.date.accessioned2017-12-13T12:00:46Z-
dc.date.available2017-12-13T12:00:46Z-
dc.date.issued2017-12-07-
dc.identifier.urihttp://hdl.handle.net/10754/626361-
dc.description.abstractThe development of flexible and interpretable statistical methods is necessary in order to provide appropriate risk assessment measures for extreme events and natural disasters. In this thesis, we address this challenge by contributing to the developing research field of Extreme-Value Theory. We initially study the performance of existing parametric and non-parametric estimators of extremal dependence for multivariate maxima. As the dimensionality increases, non-parametric estimators are more flexible than parametric methods but present some loss in efficiency that we quantify under various scenarios. We introduce a statistical tool which imposes the required shape constraints on non-parametric estimators in high dimensions, significantly improving their performance. Furthermore, by embedding the tree-based max-stable nested logistic distribution in the Bayesian framework, we develop a statistical algorithm that identifies the most likely tree structures representing the data's extremal dependence using the reversible jump Monte Carlo Markov Chain method. A mixture of these trees is then used for uncertainty assessment in prediction through Bayesian model averaging. The computational complexity of full likelihood inference is significantly decreased by deriving a recursive formula for the nested logistic model likelihood. The algorithm performance is verified through simulation experiments which also compare different likelihood procedures. Finally, we extend the nested logistic representation to the spatial framework in order to jointly model multivariate variables collected across a spatial region. This situation emerges often in environmental applications but is not often considered in the current literature. Simulation experiments show that the new class of multivariate max-stable processes is able to detect both the cross and inner spatial dependence of a number of extreme variables at a relatively low computational cost, thanks to its Bayesian hierarchical representation. These innovative methods and models are implemented to study the concentration maxima of various air pollutants and how these are related to extreme weather conditions for a number of sites in California, one of the most populated and polluted states of the US. As a result, we provide comprehensive measures of air quality that can be used by communities and policymakers worldwide to better assess and manage the health, environmental and financial impacts of air pollution extremes.en
dc.language.isoenen
dc.subjectair pollutionen
dc.subjectBayesian modellingen
dc.subjectExtreme eventen
dc.subjectMax-stable processesen
dc.subjectneste logistic modelen
dc.titleModels and Inference for Multivariate Spatial Extremesen
dc.typeDissertationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen
dc.contributor.committeememberSun, Yingen
dc.contributor.committeememberDavison, Anthony C.en
thesis.degree.disciplineStatisticsen
thesis.degree.nameDoctor of Philosophyen
dc.person.id129146en
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