Part of the ENBIS-22 Trondheim conference.
By Arvid Naess, Dept of Mathematical Sciences, NTNU, Trondheim, Norway
This short course aims at developing the ability to carry out an extreme value analysis on the basis of observed or simulated time histories arising from random processes observed e.g as a result of environmental phenomena. Rational methodologies that make it possible to predict extremes of e.g. wind speeds, wave heights, water levels in rivers, rainfalls etc. are clearly highly desirable, as they would be in many other areas. The emphasis will be on the prediction of extremes in short-term, stationary environmental conditions. However, because of its importance, the prediction of long-term extremes will also be discussed
The course schedule will consist of four 45 minutes lectures with three 15 minutes breaks for refreshments and coffee/tea. The first lecture starts at 9:15, and the last ends at 13:00.
Course specifics: The course will start with a discussion of the commonly adopted approaches to extreme value prediction, which, even in applications, have very often been based on asymptotic results. This is done either by assuming that epochal extremes, e.g. three hours extreme values, are distributed according to the generalized (asymptotic) extreme value distribution with unknown parameters to be estimated on the basis of the observed data. Or, it is assumed that the exceedances above high thresholds follow a generalized (asymptotic) Pareto distribution with parameters to be estimated from the data. The major problem with such approaches is that the asymptotic extreme value theory itself cannot be used in practice to decide to what extent it is applicable for the observed data, which are hardly asymptotic. Hence, the assumption that an asymptotic extreme value distribution is the appropriate distribution for the observed data is based more or less on faith or convenience. Fortunately, we now have recourse to the so-called ACER method, which will serve as a complimentary toolbox to the asymptotic approach. The ACER method can provide us with a nonparametric replica of the extreme value distribution inherent in the data. This allows us to use the obtained information as a diagnostic tool for investigating the basis for e.g. applying asymptotic distributions. The ACER approach may also be used instead of the asymptotic distributions for extreme value prediction. The ACER approach can also be used on nonstationary time series, which is essential for long term analyses. The methods will be discussed in detail and illustrated by several examples.
Course material: Course slides and computer program with user’s guide.
Short biography of Professor Arvid Naess
Arvid Naess has been a Professor of Structural Engineering since 1987 and a Professor of Statistics since 2001 at the Norwegian University of Science and Technology. He works on a wide range of problems related to stochastic dynamics of structures and structural safety and reliability, where extreme value statistics is an important element. Professor Naess has published more than 250 scientific papers and lectured at conferences and universities worldwide. He is an associate editor of many international journals. He is a recipient of the Alfred M Freudenthal medal from ASCE, and is an elected Fellow of ASME, ASCE and SEI. He is also an elected member of The Royal Norwegian Society of Sciences and Letters and The Norwegian Academy of Technical Sciences.