Handbook of Statistics of Extremes

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 toco-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 BayesianStatistical Methods (Chapman & Hall/CRC Press, 2019).

• Editors Contributors Basic Symbols Part I Opening Remarks 1. Handbook Outline Part II Univariate Extremes 2. Modeling Univariate Extremes—Why and How 3. Learning About Extreme Value Distributions from Data 4. Bayesian Methods for Extreme Value Analysis 5. Jointly Modeling the Bulk and Tails 6. Regression Models for Extreme Events Part III Multivariate Extremes 7. Multivariate Extreme Value Theory 8. Measures of Extremal Dependence 9. Regression Models for Multivariate Extremes 10. Conditional Extremes Modeling 11. Principal Component Analysis for Multivariate Extremes 12. Clustering Methods for Multivariate Extremes 13. Graphical Models for Multivariate Extremes Part IV Spatial and Temporal Extremes 14. Time Series in Extremes 15. Max-Stable Processes for Spatial Extremes 16. Pareto Processes for Threshold Exceedances in Spatial Extremes 17. Subasymptotic Models for Spatial Extremes 18. Space-Time Modeling of Extremes Part V Emerging Topics 19. Causality and Extremes 20. On the Simulation of Extreme Events with Neural Networks 21. Extreme Quantile Regression with Deep Learning 22. Risk Measures Beyond Quantiles Part VI Applications and Case Studies 23. Detection and Attribution of Extreme Weather Events: A Statistical Review 24. Evaluation of Extreme Forecasts and Projections 25. Statistical Modeling of Extreme Precipitation 26. Statistics of Extremes for Wildfires 27. Statistics of Extremes for Landslides and Earthquakes 28. Tail Risk Analysis for Financial Time Series 29. Statistics of Extremes for the Insurance Industry 30. Statistics of Extremes for Neuroscience 31. Statistics of Extremes for Incomplete Data, with Application to Lifetime and Liability Claim Modeling Sources Index