Vorlesung: Bayes-Modellierung

Topics of the course are:

• The Bayesian Approach
• Bayesian Computation (Numerical integration, Monte Carlo inference, Markov Chain Monte Carlo)
• Bayesian Decision Theory

The course is given in English.

Prerequisites: Understanding of statistical inference concepts and probality theory as e.g. given by the B.Sc. courses Stochastics and Statistics in the (Bio)Mathematics program. This includes univariate and multivariate normal distributions, expectations, maximum likelihood theory, statistical hypothesis testing.

Programming: We will use R and Stan / CmdStanR. In principle CmdStan can also be used from Python.

Intended audience: M.Sc. students in Mathematics, Biomathematics and Data Science. Students of other study directions are also welcome, but check the prerequisites.

• Carlin, B.P. and T.A. Louis (2009). Bayesian Methods for Data Analysis. 3rd edition. Chapman and Hall/CRC Press

• McElreath R. (2020), Statistical Rethinking, 2nd edition, CRC Press.

• Gelman et al. (2013), Bayesian Data Analysis, 3rd edition, Chapman & Hall/CRC. Free edition for non-commercial purposes!

• Bayes'scher Ansatz für statistische Modellierung und Inferenz (Priori- und Posteriori-Verteilung, Punktschätzer, Variabilität)
• Computerintensive Methoden in der Bayes-Inferenz (asymptotische Methoden, Markov Chain Monte Carlo)
• Bayes-Modellierung (Regression, hierarchische Modelle, dynamische Modelle, Modellvergleiche)
• Statistische Entscheidungsprobleme (Nutzenfunktion, Bayes-Risk, Optimalität, sequentielle Entscheidungen)

B.Sc. Mathematik mit Informatik

B.Sc. Mathematik

M.Sc. Mathematik 

M.Sc. Biomathematik