820965689 20S 2SWS VO Computational Statistics [MA3402]   Hilfe Logo

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Computational Statistics [MA3402] 
Sommersemester 2020
... alle LV-Personen
Zentrum Mathematik
Zuordnungen: 1 
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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.
MA1401 Introduction to Probability, MA2402 Basic Statistics, MA2404 Markov Chains, Softwarekenntnisse in R
After successful completion of the module the students are able to derive and implement statistical algorithms and use statistical software.
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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.
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