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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 SS 2019 (current)

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

available module versions
SS 2019SS 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

Content

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, expectation-maximization (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

Upon completion of the module, students
- know how discrete and continuous random variables/vectors are generated using statistical software
- understand Bayesian principles, such as prior, posterior distributions
- understand the theory of MCMC algorithms from selected examples
- are able to construct MCMC algorithms to simulate from the posterior distributions and to assess convergence of MCMC simulations
- know how to use Bootstrap and Jacknife methods to estimate standard errors of estimators
- know how to apply the EM algorithm to missing data problems.

Preconditions

MA1401 Introduction to Probability, MA2402 Basic Statistics, MA2404 Markov Chains, Softwarekenntnisse in R/ Splus
Bachelor 2019: MA0009 Introduction to Probability and Statistics,
MA2404 Markov Chains, Softwarekenntnisse in R/ Splus

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

lecture, exercise course, self-study assignments
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.

Media

blackboard

Literature

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

The exam may be repeated at the end of the semester.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title
TimeLocationInfoRegistration
Computational Statistics
Mon, 2019-07-29, 13:30 till 14:30 MW: 0001
till 2019-06-30 (cancelation of registration till 2019-07-22)
Mon, 2019-10-07, 15:30 till 16:30 Interims I: 101
till 2019-09-23 (cancelation of registration till 2019-09-30)
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