Handbook of Statistics of Extremes

Editors
Contributors
Basic Symbols

Part I Opening Remarks 

1. Handbook Outline - Miguel de Carvalho, Raphael Huser, Philippe Naveau & Brian J. Reich

Part II Univariate Extremes

2. Modeling Univariate Extremes—Why and How - Anthony Davison & Ophelia Miralles

3. Learning About Extreme Value Distributions from Data - Miguel de Carvalho & Viviana Carcaiso

4. Bayesian Methods for Extreme Value Analysis - Reetam Majumder, Benjamin A. Shaby & Brian J. Reich

5. Jointly Modeling the Bulk and Tails - Philippe Naveau

6. Regression Models for Extreme Events - Miguel de Carvalho, Vianey Palacios, Ligia Henriques-Rodrigues & Myung Won Lee

Part III Multivariate Extremes

7. Multivariate Extreme Value Theory - Philippe Naveau & Johan Segers

8. Measures of Extremal Dependence - David L. Carl, Simone A. Padoan & Stefano Rizzelli

9. Regression Models for Multivariate Extremes - Miguel de Carvalho & Daniela Castro-Camilo

10. Conditional Extremes Modeling - Emma S. Simpson & Jennifer L. Wadsworth

11. Principal Component Analysis for Multivariate Extremes - Daniel Cooley, Anne Sabourin & Troy Wixson

12. Clustering Methods for Multivariate Extremes - Phyllis Wan & Anja Janßen

13. Graphical Models for Multivariate Extremes - Sebastian Engelke, Manuel Hentschel, Michael Lalancette & Frank Roettger

Part IV Spatial and Temporal Extremes

14. Time Series in Extremes - Graeme Auld, Lambert De Monte & Ioannis Papastathopoulos

15. Max-Stable Processes for Spatial Extremes - Kirstin Strokorb & Marco Oesting

16. Pareto Processes for Threshold Exceedances in Spatial Extremes - Clement Dombry, Juliette Legrand & Thomas Opitz

17. Subasymptotic Models for Spatial Extremes - Likun Zhang, Christian Rohrbeck & Thomas Opitz

18. Space-Time Modeling of Extremes - Marco Oesting & Kirstin Strokorb

Part V Emerging Topics

19. Causality and Extremes - Valerie Chavez–Demoulin & Linda Mhalla

20. On the Simulation of Extreme Events with Neural Networks - Michael Allouche, Stephane Girard & Emmanuel Gobet

21. Extreme Quantile Regression with Deep Learning - Jordan Richards & Raphael Huser

22. Risk Measures Beyond Quantiles - Abdelaati Daouia & Gilles Stupfler

Part VI Applications and Case Studies

23. Detection and Attribution of Extreme Weather Events: A Statistical Review - Richard L. Smith

24. Evaluation of Extreme Forecasts and Projections - Thordis L. Thorarinsdottir

25. Statistical Modeling of Extreme Precipitation - Carlo Gaetan, Thomas Opitz & Gwladys Toulemonde

26. Statistics of Extremes for Wildfires - Jonathan Koh 

27. Statistics of Extremes for Landslides and Earthquakes - Rishikesh Yadav, Luigi Lombardo & Raphael Huser

28. Tail Risk Analysis for Financial Time Series - Anna Kiriliouk & Chen Zhou

29. Statistics of Extremes for the Insurance Industry - Hansjoerg Albrecher & Jan Beirlant

30. Statistics of Extremes for Neuroscience - Paolo V. Redondo, Matheus B. Guerrero, Raphael Huser & Hernando Ombao

31. Statistics of Extremes for Incomplete Data, with Application to Lifetime and Liability Claim Modeling - Leo R. Belzile & Johanna G. Neslehov

Sources

Index

Biography

Miguel de Carvalho is Professor and Chair of Statistical Data Science at the University of Edinburgh (UoE) as well as Honorary Professor at Universidade de Aveiro. He is elected fellow of the Generative AI Lab (UoE), co-director of the Edinburgh Centre for Financial Innovations, member of the Council of the International Statistical Institute, and past member of the board of directors of the International Society for Bayesian Analysis. Miguel’s research interests include, inter alia, extreme value theory, Bayesian analysis, and the interfaces between statistics and AI. He has been an AE for a variety of top tier journals such as Bayesian Analysis, The American Statistician, The Annals of Applied Statistics, and the Journal of the American Statistical Association. Miguel co-chaired the international conference EVA 2021 in Edinburgh, co-edited the Extremes special issue Bridging Heavy Tails &
AI, and co-founded GLE2N (Glasgow–Edinburgh Extremes Network).

Raphaël Huser is an Associate Professor of Statistics at the King Abdullah University of Science and Technology (KAUST), Saudi Arabia, where he leads the Extreme Statistics (XSTAT) research group. His research interests focus on statistics of extremes, risk modeling, spatio-temporal statistics, simulation-based inference, and statistical deep learning, with main applications to climate and geo-environmental data science, finance, and neuroscience. Raphael got several awards for his research, including the 2019 Early Investigator Award from the Section on Statistics and the Environment (ENVR) of the American Statistical Association, and the 2022 Abdel El-Shaarawi Early Investigator Award from The International Environmetrics Society. He has also served as an Associate Editor for several journals, including Extremes, Environmetrics, Spatial Statistics and the Journal of the Royal Statistical Society: Series C.

Philippe Naveau is a CNRS senior researcher at the Laboratoire des Sciences du Climat et de l’Environnement in France. His research interests are extreme value theory, time series analysis, spatial statistics with main applications to statistical climatology and hydrology. He has been part of various national and international grants dealing with climate extremes analysis and statistical risk modeling. Currently, he is the Associate Editor of Annals of Applied Statistics, Extremes and Environmetrics. He has co-organized more than twenty workshops and summer schools on extreme events analysis and he has had the pleasure to
co-advise 20 PhD students.

Brian J. Reich is the Gertrude M. Cox Distinguished Professor of Statistics at North Carolina State University. He is a fellow of the American Statistical Association and member of the International Statistical Institute. He has served as Associate Editor for the Journal of the American Statistical Association, the Annals of Applied Statistics and Biostatistics and as Editor-In-Chief for the Journal of Agricultural, Biological, and Environmental Statistics. His research interests include Bayesian methods, spatial statistics, extreme value analysis and machine learning. A major focus of his research is to develop new models for spatial extreme value analysis and computational approaches to fit these models. In addition to these methodological interests, Brian applies these methods to areas such as meteorology, climate change, air pollution and health effects. He co-authored the textbook Bayesian
Statistical Methods (Chapman & Hall/CRC Press, 2019).