Computational Statistics

Module MA3402

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2011/2

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

available module versions
SS 2012WS 2011/2

Basic Information

MA3402 is a semester module in English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


Computational statistics methods are required when analyzing complex data structures. In this course you will learn the basics of recent computational statistics methods such as Markov Chain Monte Carlo (MCMC) methods, EM algorithm and the bootstrap. Emphasis will be given to basic theory and applications. In particular the following topics will be covered: Random variable generation: discrete, continuous, univariate, multivariate, resampling. Bayesian inference: posterior distribution, hierarchical models, Markov chains, stationary and limiting distributions, Markov Chain Monte Carlo Methods (MCMC): Gibbs sampling, Metropolis-Hastings algorithm, implementation, convergence diagnostics, software for MCMC, Model adequacy and model choice. EM Algorithm: Theory, EM in exponential family, computation of standard errors. Bootstrap and Jacknife methods: empirical distribution and plug-in, bootstrap estimate of standard errors, jacknife and relationship to bootstrap, confidence intervals based on bootstrap percentiles and extensions.

Learning Outcome

After successful completion of the module the students are able to derive and implement statistical algorithms and use statistical software.


MA1401 Introduction to Probability, MA2402 Basic Statistics, MA2404 Markov Chains, Softwarekenntnisse in R/ Splus

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Computational Statistics Czado, C.
Leitung/Koordination: Kraus, D.
Donnerstag, 10:15–11:45
sowie einzelne oder verschobene Termine
UE 1 Computational Statistics (Exercise Session) Czado, C. Kraus, D. Termine in Gruppen

Learning and Teaching Methods

lecture, exercise course, self-study assignments




Gamerman, D. and Lopes, H.F. (2006): Markov Chain Monte Carlo. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman & Hall/CRC, New York. Tanner, M. A. (1996): Tools for Statistical Inference, 3rd ed. Springer-Verlag, Berlin. Efron, B., Tibshirani, R.J. (1993): An introduction to the bootstrap. Chapman & Hall, London. Chernick, M.R. (1999): Bootstrap methods: a practitioner's guide. Wiley, New York. Gelman, A., Carlin, J.B., Stern H.S. and Rubin, D.B. (2004): Bayesian Data Analysis. Chapman & Hall, London. Rizzo, M (2008): Statistical computing with R, Chapman & Hall/CRC, New York.

Module Exam

Description of exams and course work

The module examination is based on a written exam (60 minutes). Students have to know basic methods of computational statistics and show their ability to develop and implement statistic algorithms under time pressure in a comprehensible way. They can adequately use statistical software.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

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