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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


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