Students have a command of concepts of exploratory data analysis such as empirical distributions, histograms, boxplots, statistical summary measures and graphical presentations of data.
They know about concepts and methods of statistical inference such as parameter estimation, confidence intervals and tests of significance.
They know the basic notions of Bayesian statistics and have a command of prior and posterior distribution modeling, predictive distributions and are able to compute Bayes estimates and Bayes credible regions for important probability distributions.
Students know important methods of Multivariate Statistics such as PCA, MANOVA, Discriminant and Factor Analysis, Clustering methods, Correspondence Analysis and Canonical Correlation Analysis and know how to apply these methods.
They have command of building (linear) regression models, estimation of regression coefficients and know how to choose between models.
Students are able to apply the above methods using the statistical programming system R.

Attendance of the course "Information Theory and Probability"

The module covers the following topics/contents:

• Data types and basic tasks of Statistics
• Introduction to the statistical programming language R
• Descriptive Statistics: Barplots, Histograms, Empirical Distribution Functions, Boxplots, QQ-Plots etc.
• Statistical Measures of Location, Scale and Concentration: mean values, median, quantiles, variance, skewness, excess, Lorenz curve, Gini-Index Likelihood function, Estimation methods (method of moments, maximum likelihood estimation), Confidence intervals, Statistical Tests ( for mean, variance, proportions, distributions, nonparametric tests)
• Bayesian Statistics: Bayes rule for probability densities, conjugate priors, Bayes estimates for linear/quadratic and 0-1 loss functions, predictive distributions, Bayes credible regions
• Multiple linear Regression und Least Squares Method, Parameter estimation and Model choice
• Basics of multivariate statistics, multivariate normal distribution, principal component analysis, Clustering procedures, multivariate analysis of variance, Discriminant analysis, Correspondence analysis and Canonical Correlation Analysis

Lecture script as provided in the course (required)
J.K. Blitzstein and J. Hwang: Introduction to Probability. 2nd ed., Chapman and Hall/CRC 2019
M.D. Ugarte, A.F. Militino and A.T. Arnholt: Probability and Statistics with R. 2nd ed., Chapman and Hall 2015
J. Albert and J. Hu: Probability and Bayesian Modeling. Chapman and Hall/CRC 2020
W.K. Härdle and L. Simar: Applied Multivariate Statistical Analysis. 5th ed., Springer 2019

Lectures with integrated exercises

Immanent examination character: presentation, assignment reports, written/oral exam