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Dependence Modelling for Complex Extreme Events

English title Dependence Modelling for Complex Extreme Events
Applicant Davison Anthony
Number 140686
Funding scheme Project funding (Div. I-III)
Research institution EPFL - SB - MATHAA
Institution of higher education EPF Lausanne - EPFL
Main discipline Mathematics
Start/End 01.08.2012 - 31.10.2014
Approved amount 185'150.00
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Keywords (5)

Extreme value theory; Max-stability; Clustering; Asymptotic independence; Threshold model

Lay Summary (English)

Lead
Lay summary

Catastrophic events due to complex chains of circumstances typically depend not on a single rare event, but on a group of them.  Extremely heavy rainfall or a major heatwave have extent in space and time, and financial crises arise involve concatenations of events and decisions as different players in markets interact.  Thus the modelling of rare events almost invariably involves consideration of multivariate extremes and of the dependencies among them.  Existing models for such dependencies are, however, limited in various ways.  Classical statistics of extremes comprises a well-developed and rather successful theory, but in some circumstances it can be of doubtful practical value, because it involves extrapolation of dependence structures that may be known or suspected to be inappropriate for very rare events. Over the last decade or so a new theory has emerged that addresses this difficulty, but it remains fragmentary and unsatisfactory, not least because of a sharp distinction between the classical and more novel approaches, whereas an approach that merges them would be more appealing for applications.  

The purpose of this proposal is to tackle this problem, constructing new classes of models and methods for use in applications.  The project will address general ways to build models that bridge classical dependence and asymptotic independence in multivariate extremes, with potential for broad use in a range of applications.  It will involve theoretical and methodological development culminating in illustrative application to real data.

Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants

Employees

Publications

Publication
A Lévy-derived process on the real line seen from its supremum and max-stable processes
Engelke S., Ivanovs J. (2016), A Lévy-derived process on the real line seen from its supremum and max-stable processes, in Electronic Journal of Probability, 21, 14.
Extremes on river networks
Asadi P., Davison A. C., Engelke S. (2015), Extremes on river networks, in Annals of Applied Statistics, 9, 2023-2050.
Max-stable processes and stationary systems of Lévy particles
Engelke S., Kabluchko Z. (2015), Max-stable processes and stationary systems of Lévy particles, in Stochastic Processes and their Applications, 125, 4272-4299.
Efficient inference for spatial extreme value processes associated to log-Gaussian random functions
Wadsworth J. L., Tawn J. A. (2014), Efficient inference for spatial extreme value processes associated to log-Gaussian random functions, in Biometrika, 101, 1-15.
Geostatistics of dependent and asymptotically independent extremes
Davison A. C., Huser R., Thibaud E. (2013), Geostatistics of dependent and asymptotically independent extremes, in Mathematical Geosciences, 45, 511-529.
Modelling across extremal dependence classes
Wadsworth J. L., Tawn J. A., Davison A. C., Elton D. M. (2013), Modelling across extremal dependence classes, in Journal of the Royal Statistical Society, series B, 79(1), 149-175.
Threshold modeling of extreme spatial rainfall
Thibaud E., Mutzner R., Davison A. C. (2013), Threshold modeling of extreme spatial rainfall, in Water Resources Research, 49, 4633-4644.

Collaboration

Group / person Country
Types of collaboration
Statistics/Münster Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Statistics/Lancaster University Great Britain and Northern Ireland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
HEC/Lausanne Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Statistics/Mannheim Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
ERCIM, 2014 Talk given at a conference Max-stable processes on river networks 06.12.2014 Pisa, Italy Davison Anthony;
ERCIM 2014 Talk given at a conference Modelling across extremal dependence classes 06.12.2014 Pisa, Italy Wadsworth Jennifer;
ERCIM 2014 Talk given at a conference Markov particle systems and Lévy-driven Brown-Resnick processes 06.12.2014 Pisa, Italy Engelke Sebastian;
High-dimensional and Multivariate Extremes: Sustain Workshop Talk given at a conference Modelling across extremal dependence classes 02.07.2014 Bristol, Great Britain and Northern Ireland Wadsworth Jennifer;
Second Conference of the International Society for Nonparametric Statistics Talk given at a conference Max-stable processes on river networks 12.06.2014 Cadiz, Spain Engelke Sebastian;
Joint Statistical Meetings Talk given at a conference Extremal modelling for complex data 03.08.2013 Montreal, Canada Wadsworth Jennifer;
8th Conference on Extreme Values and Applications Talk given at a conference Extremal modelling for complex data 08.07.2013 Shangai, China Wadsworth Jennifer; Davison Anthony;
45ème journée de Statistique Talk given at a conference Spatial modelling of extreme rainfall 03.05.2013 Toulouse, France Davison Anthony;
ERCIM 2012 Talk given at a conference Efficient inference for spatial extreme value processes 01.12.2012 Oviedo, Spain Wadsworth Jennifer;
RSS 2012 International Conference Talk given at a conference Extremal models and environmental risk 03.09.2012 Telford, Great Britain and Northern Ireland Davison Anthony;
GeoEnv2012 Talk given at a conference Geostatistics of extremes 03.09.2012 Valencia, Spain Davison Anthony;


Awards

Title Year
Royal Statistical Society Guy Medal in Silver 2015
Royal Statistical Society Research Prize 2015

Associated projects

Number Title Start Funding scheme
132307 Statistics for Complex Processes: Extremes and Applications 01.10.2010 Project funding (Div. I-III)
156069 Complex Extremes: Inference and Applications 01.11.2014 Project funding (Div. I-III)

Abstract

Catastrophic events due to complex chains of circumstances typically depend not on a single rare event, but on a group of them. Extremely heavy rainfall or a major heatwave have extent in space and time, and financial crises arise involve concatenations of events and decisions as different players in markets interact. Thus the modelling of rare events almost invariably involves consideration of multivariate extremes and of the dependencies among them. Existing models for such dependencies are, however, limited in various ways. Classical statistics of extremes comprises a well-developed theory that is often of doubtful practical value, because it involves extrapolation of dependence structures that may be known or suspected to be inappropriate for very rare events. Over the last decade or so a new theory has emerged that addresses this difficulty, but it remains fragmentary and unsatisfactory, not least because of a sharp distinction between the classical and more novel approaches, whereas an approach that merges them would be more appealing for applications. A further lacuna in the literature is the lack of a broadly flexible class of models for time series extremes. The purpose of this proposal is to tackle these problems, in each case constructing new classes of models and methods for use in applications. The first sub-project will address general ways to build models that bridge classical dependence and asymptotic independence in multivariate extremes, with potential for broad use in a range of applications. The second sub-project will tackle the special case of clusters of extremes in time series, which arise very commonly in applications, but for which no general classes of models have yet been formulated. Both sub-projects will involve theoretical and methodological development culminating in illustrative application to real data. The resource requested is support for two post-doctoral researchers for two years.
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