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Risk, rare events and extremes

MATH-447

Enseignant(s) :

Davison Anthony C.

Langue:

English

Remarque

Cous donné en alternance tous les deux ans (donné en 2019-20)

Summary

Modelling of rare events, such as stock market crashes, storms and catastrophic structural failures, is important. This course will describe the special models and methods that are relevant to such modelling, including the mathematical bases, statistical tools and applications.

Content

Mathematical bases: behaviour of maxima and threshold exceedances in large samples, both for independent and dependent data. Poisson process modelling.

Statistical methods: modelling using the GEV and GP distributions, for independent and dependent data. Likelihood and Bayesian inference. Non-stationarity. Extremal coefficients. Multivariate extreme-value distributions. Max-stable processes.

Applications: Environmental, financial, and engineering applications. Use of R for extremal modelling.

Learning Prerequisites

Important concepts to start the course

Probability and statistics at the level of second-year bachelor (mathematics), plus further knowledge of statistics and stochastic processes.

Learning Outcomes

By the end of the course, the student must be able to:

Recognize situations where statistical analysis of extrema is appropriate
Manipulate mathematical objects related to the study of extrema
Analyze empirical data on extremes using appropriate statistical methods
Construct appropriate statistical models for extremal data
Interpret such models in terms of underlying phenomena
Infer properties of real systems in terms of probability models for extremes

Teaching methods

Lectures, theoretical and computational exercises in class and at home.

Assessment methods

Mini-project, final exam.

Dans le cas de l¿art. 3 al. 5 du Règlement de section, l¿enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés.

Supervision

Assistants

Yes

Resources

Bibliography

Coles, S. G. (2001) An Introduction to the Statistical Modelling of Extreme Values. Springer.

Beirlant, J, Goegebeur. Y., Teugels. J. and Segers. J. (2004) Statistics of Extremes: Theory and Applications. Wiley.

Dans les plans d'études

Mathématiques - master, 2019-2020, Master semestre 1
- Semestre
  Automne
- Forme de l'examen
  Ecrit
- Crédits
  5
- Matière examinée
  Risk, rare events and extremes
- Cours
  2 Heure(s) hebdo x 14 semaines
- Exercices
  2 Heure(s) hebdo x 14 semaines
Mathématiques - master, 2019-2020, Master semestre 3
- Semestre
  Automne
- Forme de l'examen
  Ecrit
- Crédits
  5
- Matière examinée
  Risk, rare events and extremes
- Cours
  2 Heure(s) hebdo x 14 semaines
- Exercices
  2 Heure(s) hebdo x 14 semaines
Data Science, 2019-2020, Master semestre 1
- Semestre
  Automne
- Forme de l'examen
  Ecrit
- Crédits
  5
- Matière examinée
  Risk, rare events and extremes
- Cours
  2 Heure(s) hebdo x 14 semaines
- Exercices
  2 Heure(s) hebdo x 14 semaines
Data Science, 2019-2020, Master semestre 3
- Semestre
  Automne
- Forme de l'examen
  Ecrit
- Crédits
  5
- Matière examinée
  Risk, rare events and extremes
- Cours
  2 Heure(s) hebdo x 14 semaines
- Exercices
  2 Heure(s) hebdo x 14 semaines
Ingénierie financière, 2019-2020, Master semestre 1
- Semestre
  Automne
- Forme de l'examen
  Ecrit
- Crédits
  5
- Matière examinée
  Risk, rare events and extremes
- Cours
  2 Heure(s) hebdo x 14 semaines
- Exercices
  2 Heure(s) hebdo x 14 semaines
Ingénierie financière, 2019-2020, Master semestre 3
- Semestre
  Automne
- Forme de l'examen
  Ecrit
- Crédits
  5
- Matière examinée
  Risk, rare events and extremes
- Cours
  2 Heure(s) hebdo x 14 semaines
- Exercices
  2 Heure(s) hebdo x 14 semaines
Ingénierie mathématique, 2019-2020, Master semestre 1
- Semestre
  Automne
- Forme de l'examen
  Ecrit
- Crédits
  5
- Matière examinée
  Risk, rare events and extremes
- Cours
  2 Heure(s) hebdo x 14 semaines
- Exercices
  2 Heure(s) hebdo x 14 semaines
Ingénierie mathématique, 2019-2020, Master semestre 3
- Semestre
  Automne
- Forme de l'examen
  Ecrit
- Crédits
  5
- Matière examinée
  Risk, rare events and extremes
- Cours
  2 Heure(s) hebdo x 14 semaines
- Exercices
  2 Heure(s) hebdo x 14 semaines
Mineur en Data science, 2019-2020, Semestre automne
- Semestre
  Automne
- Forme de l'examen
  Ecrit
- Crédits
  5
- Matière examinée
  Risk, rare events and extremes
- Cours
  2 Heure(s) hebdo x 14 semaines
- Exercices
  2 Heure(s) hebdo x 14 semaines

Semaine de référence

	Lu	Ma	Me	Je	Ve
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22

En construction

Cours

Exercice, TP

Projet, autre

légende

Semestre d'automne
Session d'hiver
Semestre de printemps
Session d'été

Cours en français
Cours en anglais
Cours en allemand