Support vector machines and kernel methods for classification;EM algorithm;Unsupervised learning and clustering algorithms

We discuss modern statistical methods for data analysis, including methods for data exploration, prediction and inference. We pay attention to algorithmic aspects, theoretical properties and practical considerations. The class is hands-on and methods are applied using the statistical programming language R.

"High-Dimensional Statistics" deals with modern methods and theory for statistical inference when the number of unknown parameters is of much larger order than sample size. Statistical estimation and algorithms for complex models and aspects of multiple testing will be discussed.

Introduction to basic methods and fundamental concepts of statistics and probability theory for practicioners in natural sciences. The concepts will be illustrated with some real data examples and applied using the statistical software R.

Regression studies the dependence of a random response variable on other variables. We consider the theory and application of linear regression with one or more covariates. Various extensions such as nonlinear models, generalized linear models, nonparametric models, robust methods, and model selection are discussed.

In regression, the dependency of a random response variable on other variables is examined. We consider the theory of linear regression with one or more covariates, high-dimensional linear models, nonlinear models and generalized linear models, model choice and nonparametric models. Several numerical examples will illustrate the theory.

Introduction to basic methods and fundamental concepts of statistics and probability theory for non-mathematicians. The concepts are presented on the basis of some descriptive examples.

Einführung in die Grundlagen der Statistik, Wahrscheinlichkeitstheorie und Modellierung von Unsicherheiten im Zusammenhang mit Entscheidungsfindungen im Ingenieurwesen. Die Schwerpunkte liegen im Erstellen wahrscheinlichkeitstheoretischer Modelle, im Testen von Hypothesen und in der Überprüfung der Modelle.

The following concepts are covered: probabilities, random variables, probability distributions, joint and conditional probabilities and distributions, law of large numbers, central limit theorem, descriptive statistics, statistical inference, parameter estimation, confidence intervals, statistical tests, two-sample tests, linear regression.

Causality is dealing with fundamental questions about cause and effect. The student seminar covers statistical and mathematical aspects of causality ranging from fundamental formalization of concepts to practical algorithms and methods.

No description available.

The course offers an introduction into analyzing times series, that is observations which occur in time. The material will cover Stationary Models, ACVF and ACF, Estimation of trend and seasonal component, Linear processes, ARMA processes, Forecasting and estimation of a missing value, the Innovation Algorithm.