Register  -  Login
Program - Short Course 2011

Monday, July 18 

8’15 a.m.
Opening and Introduction Lectures.
Welcome by Vittorio Severino - President of "Ordine degli Ingegneri Provincia di Caserta"

Copula function in Environmental Applications
Salvatore Grimaldi
11’00 – 12’00 a.m.
Univariate Extreme Value theory. Order statistics, Extreme Value theory, return period, risk
Instructor: Francesco Serinaldi

Afternoon Lab.
2’00 – 6’00 p.m. 
Introduction to “R” statistical software. Importing and exporting data. Graphical representations of a time series. Exporting a graph. Writing, compiling and executing a script. Examples. Using the help-on-line. Routine application for univariate frequency analysis. 
Instructor: Francesco Serinaldi

Tuesday, July 19

Morning Lectures  
9’00 – 12’00 a.m.
Motivations: practical usefulness of copulas (examples). Introduction: definition, basic features, Sklar's Theorem and its inversion. Special copulas: Fréchet-Hoeffding bounds, Survival copulas, Archimedean copulas, Archimedean Alpha- and Beta-families; Asymmetry and exchangeability. Measures of Association: bivariate Kendall's Tau, Spearman's Rho, Blamqvist's Beta; generalization to the multivariate case; Pickand's dependence function. Dependence and conditioning: copulas and conditional probabilities; conditional mixtures; Invariance properties of copulas; Probability Integral Transform and simulation; copulas and derived distributions. Multivariate Return Periods: level layers: sub-, super-, and critical events; Multivariate Kendall's measure; event-based Multivariate Return Period; Multivariate Kendall's Return Period; calculation of most likely critical Multivariate design events.
Instructor: Gianfausto Salvadori
Afternoon Lab.
2’00 – 6’00 p.m.
The “R” package for copulas. Exploratory data analysis; calculation of Measures of Association: Kendall's Tau and Spearman's Rho; Graphical representation of copulas (pseudo-observation plots); Random sample generation via copulas and simulation.
Instructors: Ivan Kojadinovic & Francesco Serinaldi

Wednesday, July 20

Morning Lectures
9’00 – 12’00 a.m.

HOUR 1 (Instructor: Gianfausto Salvadori)

Multivariate Extreme Value theory.
Extreme Value copulas: basic definitions and characterizations; Extreme Value copulas of convex linear combinations and mixtures; Extreme Value copulas: special constructions (extra-parametrization techniques); Multivariate Extreme Value Return Periods.

HOURS 2 & 3 (Instructor: Ivan Kojadinovic)
Fitting copulas. Multivariate families of copulas (Elliptical, Archimedean, Nested, Meta-...); Tail dependence; Multivariate independence tests; Tests of extremeness; Estimation of parameters; Goodness-of-fit procedures.
Afternoon Lab.
2’00 – 6’00 p.m.
Likelihood based methods (EML, CML, IFM), Method of Moments' based estimations (Kendall's Tau and Spearman's Rho)
Instructors: Ivan Kojadinovic & Francesco Serinaldi  

Thrusday, July 21

Morning Lectures
9’00-12’00 a.m.

Hydrological applications of copulas.
Modeling the temporal structure of storms; Derivation of the Antecedent Moisture Condition from the temporal structure of storms; Modeling flood hydrograph and spillway safety control; Distribution of derived variables; Construction of multivariate conditional models; Calculation of multivariate return periods; Calculation of multivariate design events.

Instructor: Carlo De Michele
(and other potential lectures to be defined)

Afternoon Lab.
2’00 – 6’00 p.m.
Tests of independence; Tests of extremeness; Goodness of fit tests.
Instructors: Ivan Kojadinovic & Francesco Serinaldi 

Friday, July 22

9’00-12’00 a.m.

Discussion of students' projects.


15’00 p.m.

Final students' Projects presentations



Ministero dell'Ambiente e della Tutela del Territorio e del Mare

Institute for Environmental Protection and Research

 Honors Center of Italian Universities - H2CU 
Sapienza University of Rome

University of Tuscia,
Viterbo, Italy


News  Archive  
2017 IAHS - Abstract submission deadline: 6 March 2017
Monday, February 20, 2017

Read More    (10293 reads)
Short Course COPULA'17
Saturday, January 07, 2017

Read More    (11848 reads)
2017 EVAN Conference
Monday, December 05, 2016

Read More    (12100 reads)
2017 EGU General Assembly
Thursday, December 01, 2016

Read More    (11936 reads)
2017 IAHS General Assembly
Thursday, December 01, 2016

Read More    (14223 reads)
STAHY Best Paper Award 2016
Friday, June 17, 2016

Read More    (18043 reads)
STAHY 2016 - abstract submission deadline: May 18!!
Tuesday, May 03, 2016

Read More    (18838 reads)

Privacy Statement  |  Terms Of Use  |  Copyright 2007 - STAHY.ORG