Numerische Methoden zur Datenanalyse
Numerical Methods for Data Analysis

You will learn many different techniques for generating (pseudo) random numbers according to arbitrary probability distributions, as well as numerical techniques for implementing them.  This module will also familiarize you with advanced techniques for solving high-dimensional integrals, performing optimization and regression tasks and for simulating physical situations.

After successful completion of this module, the student is able

• to apply different techniques for generating (pseudo) random numbers according to arbitrary probability distributions.
• to know and apply Monte Carlo based integration techniques such as accept/reject, sample mean, importance sampling and stratified sampling.
• to understand the fundamentals of random walks.
• to use Markov Chain Monte Carlo techniques for sampling from distributions.
• to use simulated annealing techniques to solve optimization problems.

The student will be expected to program algorithms and produce graphical output. Access to a computer and practical knowledge of a computing language is necessary.

This module consists of a lecture and an exercise class. The lectures will present the learning content (in English).  Examples will be drawn from a range of physics areas.  A number of exercises will be assigned that the students will be expected to solve over the course of the semester and submit in a written report. 

A recitation session will precede the lectures, where students will present their solutions to the exercises and where further examples will be presented.

Presentation, blackboard. Lecture notes will be provided. You will need access to a computer.

• C.P. Robert & G. Casella: Monte Carlo Statistical Methods, 2nd Edition, Springer Verlag, (2004)
• W.R. Gilks, S. Richardson & D.J. Spiegelhalter: Markov Chain Monte Carlo in Practice, Chapman and Hall/CRC, (1996)
• R.Y. Rubinstein & D.P. Kroese: Simulation and the Monte Carlo Method, Wiley-Interscience, (2007)
• N.J. Giordano and H. Nakanishi: Computational Physics, 2nd Edition, Pearson, (2006)
• W.H. Press, B.P. Flannery, S.A. Teukolsky & W.T. Vetterling: Numerical Recipes. The Art of Scientific Computing, Cambridge Universitty Press, (1989)

Das Erreichen der im Abschnitt Lernergebnisse dargestellten Kompetenzen mindestens in der dort angegebenen Erkenntnisstufe wird exemplarisch durch eine von den Studierenden selbständig zu bearbeitende Abschlusspräsentation überprüft. Die Leistung der Studierenden wird an Hand der Präsentation der Ergebnisse und einer anschließenden Diskussion bewertet. Die Prüfung hat eine Dauer von insgesamt 25 Minuten.