Overview
Handbook of Statistics of Extremes
Contents
Each chapter opens with a short, informal blurb offering a high-level overview of what follows—what we call an Outline. To give a flavour of the Handbook, these Outlines are reproduced below.
Outlines
Chapter 1M. de Carvalho, R. Huser, P. Naveau & B. J. Reich
Outline: This opening chapter sets the stage for the Handbook. It explains why statistical models for extremes are essential, introduces the structure of the volume, and provides a concise historical perspective on the field, together with guidance to further resources.
Chapter 2A. C. Davison & O. Miralles
Outline: This chapter provides a brief overview of extreme value theory, previewing key concepts from later chapters, introduces fundamental models for analyzing extremes, and discusses their application in risk assessment.
Chapter 3M. de Carvalho & V. Carcaiso
Outline: This chapter continues the discussion from the previous chapter and provides an introductory treatment of how to learn about extreme value distributions from data. It also sets the stage for the next chapter on Bayesian inference for extremes.
Chapter 4R. Majumder, B. A. Shaby & B. J. Reich
Outline: This chapter continues the discussion on learning extreme value distributions from data, building on the previous chapter by introducing the Bayesian approach to statistical inference. It highlights how Bayesian methods incorporate prior knowledge, improve inference through hierarchical modeling, and apply to extreme value analysis.
Chapter 5P. Naveau
Outline: This chapter explores statistical methods for modeling both extreme values and the entire distribution of a variable. By integrating extreme value theory with broader distributional modeling, it highlights how these approaches can bypass threshold selection and clarify the role of explanatory variables in shaping both high and low extremes.
Chapter 6M. de Carvalho, V. Palacios, L. Henriques-Rodrigues & M. W. Lee
Outline: This chapter introduces regression models for extreme events, which track how the risk of extremes shifts with covariates like time or temperature. The core idea is to link covariates to the parameters of extreme value distributions and learn those links directly from data.
Chapter 7P. Naveau & J. Segers
Outline: Extreme events, whether in geosciences, finance, or other fields, are inherently multivariate as they arise from the interplay of multiple factors. This chapter introduces the foundational models for multivariate extremes, including multivariate generalized Pareto distributions and multivariate extreme value distributions.
Chapter 8David L. Carl, S. A. Padoan & S. Rizzelli
Outline: This chapter explores how to quantify the interplay between extreme events across multiple variables, such as simultaneous extreme financial losses. While the previous chapter focused on introducing key models for multivariate extremes, here the focus will be placed on evaluating extremal dependence.
Chapter 9M. de Carvalho & D. Castro-Camilo
Outline: This chapter introduces regression models for extreme events occurring in pairs, such as financial crashes affecting multiple stock markets. It explores how the strength of dependence between extreme values changes over time or along with another covariate.
Chapter 10E. S. Simpson & J. L. Wadsworth
Outline: A key advantage of the methods covered below is their ability to capture both asymptotic dependence and asymptotic independence, offering greater flexibility than many traditional approaches. A dataset comprising two compo- nents of air pollution in the UK is used to illustrate the bivariate conditional extremes model, while the spatial conditional extremes model is applied to gridded temperature data across the Netherlands.
Chapter 11D. Cooley, A. Sabourin & T. Wixson
Outline: While previous chapters focused on modeling multivariate extremes, we now turn to dimension reduction methods. This chapter explores ways to reduce the dimensionality of the data while preserving key information relevant to the analysis of multivariate extreme values.
Chapter 12Phyllis Wan & Anja Janßen
Outline: We now move from the task of dimension reduction to the task of clustering. As with dimension reduction, clustering for multivariate extremes is a relatively recent addition to the statistical toolbox, and this chapter introduces three available approaches.
Chapter 13S. Engelke, M. Hentschel, M. Lalancette & Frank Röttger
Outline: Graphical models for extremes reveal relationships between extreme events in complex, interconnected systems. This chapter introduces key concepts, recent advances, and demonstrates their application to analyzing flight delays at US airports.
Chapter 14G. Auld, L. De Monte & I. Papastathopoulos
Outline: This chapter introduces statistical methods for modeling extreme events in time series data. It covers both classical results and modern approaches that capture the tendency of extremes to cluster over short time scales, and discusses recent developments based on the conditional extremes framework detailed in Chapter 10; a case study on persistent high temperatures in Talavera la Real, Spain, illustrates the methods.
Chapter 15K. Strokorb & M. Oesting
Outline: Extreme events often unfold across space, not just time. This chapter introduces max-stable processes, which extend the generalized extreme value distribution to describe spatial extremes, capturing both how extreme events vary across different locations and how they are related.
Chapter 16C. Dombry, J. Legrand & T. Opitz
Outline: The previous chapter introduced the GEV model for spatial extremes; here, we turn to Pareto processes for modeling threshold exceedances. While exceedances are easy to define in a single location, the challenge now is figuring out what ‘exceeding a threshold’ means across space.
Chapter 17L. Zhang, C. Rohrbeck & T. Opitz
Outline: Whereas the previous two chapters focused on spatial extreme mod- els derived from asymptotic arguments, we now shift the paradigm by introducing subasymptotic models. These models aim to enhance inference by capturing dependence at intermediate to extreme quantiles, rather than relying solely on theoretical limits.
Chapter 18M. Oesting & K. Strokorb
Outline: While previous chapters focused on modeling extreme events in space, this chapter extends these ideas, concepts and methods to capture both spatial and temporal characteristics. As shown below, modeling space-time dynamics of extremes requires more than simply adding a time dimension to spatial models.
Chapter 19V. Chavez-Demoulin & L. Mhalla
Outline: Understanding cause-and-effect relationships in extreme events is cru- cial across many applied fields. This chapter introduces key causal models, explores methods for learning causal structures, and demonstrates their application using real data from the Seine River network.
Chapter 20M. Allouche, S. Girard & E. Gobet
Outline: This chapter explores AI in the context of extreme events, with a focus on generative models. It highlights the limitations of mainstream AI approaches in simulating heavy-tailed phenomena and presents fresh solutions.
Chapter 21J. Richards & R. Huser
Outline: A further exploration of AI and extremes. While Chapter 20 show-cased how recent neural approaches can be used as generative models for extreme events, this chapter focuses on novel neural methods for modeling extremes and extrapolating beyond observed data.
Chapter 22A. Daouia & G. Stupfler
Outline: Quantiles are the foundation of most risk management methods, but they only account for how often extreme events occur, not how severe they are. This chapter explores novel alternative risk measures that address this limitation, discussing their strengths, mathematical challenges, and real-world applications in finance and natural disasters.
Chapter 23R. L. Smith
Outline: Detection and attribution is about understanding how much of the ob- served changes in climate—such as rising temperatures or stronger storms—can be traced to human activities rather than natural variations. This chapter reviews the topic from a statistical perspective, with a particular focus on detection and attribution of extreme weather events.
Chapter 24T. L. Thorarinsdottir
Outline: This chapter provides an overview of evaluation methods for extreme forecasts and projections, where predictive models are compared to available data. The methods we discuss are based on decision-theoretic principles and the prin- ciple of maximizing the information value in the prediction subject to a calibrated risk assessment.
Chapter 25C. Gaetan, T. Opitz & G. Toulemonde
Outline: Rainfall is a highly variable and complex phenomenon, making its sta- tistical modeling challenging, especially when capturing both typical and extreme events across space and time. This chapter explores the difficulties of modeling rainfall extremes, the role of dependence structures, and how combining extreme value theory and physical hydrometeorological knowledge can improve predictions, particularly for flood risk assessment.
Chapter 26J. Koh
Outline: Statistics of extremes is beginning to play a key role in wildfire science by improving predictions of rare and severe wildfire events. This chapter explores how extreme value theory can be extended to study spatial and temporal wildfire dependence, integrate with physical fire spread models, and address emerging challenges in fire risk assessment under climate change.
Chapter 27R. Yadav, L. Lombardo & R. Huser
Outline: In this chapter, we illustrate the use of split bulk–tail models and subasymptotic models motivated by extreme value theory in the context of hazard assessment for earthquake-induced landslides. A spatial joint areal model is presented for modeling both landslides counts and landslide sizes, paying particular attention to extreme landslides, which are the most devastating ones.
Chapter 28A. Kiriliouk & C. Zhou
Outline: This chapter explores how extreme value statistics can improve finan- cial risk assessment by estimating extreme losses, with a focus on challenges posed by serial dependence in financial data. It compares two key approaches— unconditional and conditional quantile estimation—and examines their implica- tions for capital requirements, risk monitoring, and multivariate systemic risk analysis.
Chapter 29H. Albrecher & J. Beirlant
Outline: Insurance risk is driven by rare but extreme losses, making extreme value statistics a vital tool for modeling large claims. This chapter explores how these methods support risk management and pricing, especially in reinsurance.
Chapter 30P. V. Redondo, M. B. Guerrero, R. Huser & H. Ombao
Outline: Brain activity is often analyzed through averages and central trends, but extreme events—like sudden surges in electrical signals—may hold key insights into neurological conditions. This chapter explores how extreme value theory can be applied to brain signal data, particularly EEG, to better understand abnormalities such as epileptic seizures.
Chapter 31L. R. Belzile & J. G. Nešlehová
Outline: This chapter presents two examples of extreme value analysis using incomplete data. The first examines very long human lifetimes, and the second looks at large insurance claims—both showing that meaningful analysis of extremes is still possible even when some information is missing.
Pre-order your copy
