Content of this course are copula based models for multivariate data. The first part establishes basic theory, introduces selected copula families, measures of association, dependence concepts and stochastic orderings. Second part of the course will be devoted to parametric and semiparametric copula estimation and to testing goodness-of-fit and independence.

This course yields a mathematical introduction into the theory of extremes. Besides a derivationof the Fisher-Tippett theorem for sample maxima, it is also shown how the theory of point pro-cesses yields a methodological basis for the Peaks Over Threshold method. Some examplesof statistical data analysis for the modelling of extremes will also be discussed.

This is a basic course on categorical data analysis. The aim is to cover standard techniques for the analysis of categorical data, like presence or absence of a disease, size of a company or number of losses incurred within a period of time. We discuss theoretical properties of the models covered, statistical inference and model diagnostics, examples on real data and software illustrations in R.