Extreme Value Statistics

Most statistical methods are aimed at characterizing expected values, but in many settings it is the unexpected values, the extremes or outliers, that are of interest - e.g. extreme weather events, rare drug toxicities, or extreme movements in financial markets. This is an introductory course in Extreme Value Statistics, focusing mostly on univariate methods but including some multivariate modelling topics, it will be held on the 2nd and 3rd December 2020. We will cover the theory and associated statistical methods which form a cornerstone of natural hazard risk planning and engineering design safety, and which enable extrapolation to levels beyond those already observed in a dataset. We describe current best practice and step-by-step implementation of methods for calculating high quantiles and associated uncertainties. We address topical challenges arising from non-stationarity in processes. The ideas are illustrated throughout by using detailed worked examples from environmental risk assessment, financial and clinical-safety applications. All of the topics covered are accompanied by hands-on computer tutorials in R, so that participants will carry out themselves a complete set of worked examples throughout the course.

Most statistical methods are aimed at characterizing expected values, but in many settings it is the unexpected values, the extremes or outliers, that are of interest - e.g. extreme weather events, rare drug toxicities, or extreme movements in financial markets. This is an introductory course in Extreme Value Statistics, focusing mostly on univariate methods but including some multivariate modelling topics. We will cover the theory and associated statistical methods which form a cornerstone of natural hazard risk planning and engineering design safety, and which enable extrapolation to levels beyond those already observed in a dataset. We describe current best practice and step-by-step implementation of methods for calculating high quantiles and associated uncertainties. We address topical challenges arising from non-stationarity in processes. The ideas are illustrated throughout by using detailed worked examples from environmental risk assessment, financial and clinical-safety applications. All of the topics covered are accompanied by hands-on computer tutorials in R, so that participants will carry out themselves a complete set of worked examples throughout the course.

Learning Outcomes

By attending this course, attendees can hope to gain the following:

• Solid understanding of the theory and best practice to support their own independent use of Extreme Value Statistics;

• Detailed step-by-step methods for systematic Extreme Value Modelling and computation of high quantiles and extreme values;

• Practical experience of using state of the art software to carry out Extreme Value Analysis for themselves, with a complete set of worked examples and accompanying code.

Topics Covered

• Motivating examples

• Introduction to univariate Extreme Value Theory

• Modelling process maxima and threshold excesses

• Using diagnostic tools for efficient threshold selection

• Addressing non-stationarity by using covariates in EV models

• Dealing with serial dependence in data

• Extensive worked examples from environmental hazard, finance, offshore and clinical trials settings

• Modelling multivariate extreme values

As well as statisticians and quantitative researchers these may include but are not limited to structural design engineers, metocean scientists, offshore engineers, re/insurance natural peril defence planners, environmental consultancies, pharmaceutical companies, clinical trial safety regulators, financial risk managers.

It will assumed that delegates are Statistically literate with degree level statistics or a similar level of experience. This course assumes no previous knowledge of Extreme Value Statistics, but requires a general familiarity with statistical modelling techniques equivalent to undergraduate level statistics. Course workshops will use R, knowledge of which would be an advantage, however this is not a necessity since all required code will be supplied in the accompanying course notes.

Certificate of completion

Digital certificate - Included