Lecture: Fr, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, every other week, various dates
05.09.
Teacher: Johannes Brutsche
Assistant: Dario Kieffer
Language: in German
After gaining an insight into the basics and various methods and questions of stochastics and probability theory in the Stochastics I lecture, this lecture will mainly focus on statistical topics, especially those that are relevant for students studying to become secondary school teachers. However, the lecture can also be a (hopefully) useful supplement and a good basis for later attendance of the course lecture ‘Mathematical Statistics’ for students in the B.Sc. in Mathematics with an interest in stochastics.
After clarifying the term ‘statistical model’, methods for constructing estimators (e.g. maximum likelihood principle, method of moments) and quality criteria for these (reliability of expectations, consistency) are discussed. Confidence intervals and hypothesis tests are also introduced. Linear models are considered as further applications and, if time permits, other statistical methods. The properties of exponential families and multivariate normal distributions, which are useful for many test and estimation methods, are also introduced.
Linear Algebra I+II and Analysis I+II
Elementary Probabilty Theory (2HfB21, MEH21)
Elementary Probability Theory II (MEdual24)
Compulsory Elective in Mathematics (BSc21)
Lecture: Do, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: David Criens
Assistant: Dario Kieffer
Language: in English
The class of Markov chains is an important class of (discrete-time) stochastic processes that are used frequently to model for example the spread of infections, queuing systems or switches of economic scenarios. Their main characteristic is the Markov property, which roughly means that the future depends on the past only through the current state. In this lecture we provide the mathematical foundation of the theory of Markov chains. In particular, we learn about path properties, such as recurrence and transience, state classifications and discuss convergence to the equilibrium. We also study extensions to continuous time. On the way we discuss applications to biology, queuing systems and resource management. If the time allows, we also take a look at Markov chains with random transition probabilities, so-called random walks in random environment, which is a prominent model in the field of random media.
Required: Elementary Probability Theory~I \ Recommended: Analysis~III, Probability Theory~I
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Projektseminar: Nonparametric Maximum Likelihood Estimation
Teacher: Angelika Rohde
Assistant: Dario Kieffer
Seminar: Statistical Learning for Imbalanced Data Sets
Di, 14-16h, , online
Teacher: Angelika Rohde
Assistant: Dario Kieffer
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Projektseminar: Statistical Learning
Teacher: Angelika Rohde
Assistant: Dario Kieffer
Di, 10-12h, SR 127, Ernst-Zermelo-Str. 1
Teacher: Angelika Rohde
Assistant: Dario Kieffer
Compulsory Elective in Mathematics (BSc21)