Suchergebnis: Katalogdaten im Herbstsemester 2020

Mathematik Master Information
Wahlfächer
Für das Master-Diplom in Angewandter Mathematik ist die folgende Zusatzbedingung (nicht in myStudies ersichtlich) zu beachten: Mindestens 15 KP der erforderlichen 28 KP aus Kern- und Wahlfächern müssen aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten stammen.
Wahlfächer aus Bereichen der angewandten Mathematik ...
vollständiger Titel:
Wahlfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten
Auswahl: Wahrscheinlichkeitstheorie, Statistik
NummerTitelTypECTSUmfangDozierende
401-4607-70LA Medley of Advanced ProbabilityW4 KP2VW. Werner
KurzbeschreibungWe will review various topics of probability theory, with the goal to provide a short self-contained introduction to each of them, and try to describe the type of ideas and techniques that are used.
Exact topics will include (small bits of) Lévy processes, continuous-state branching processes, large deviation theory, large random matrices.
LernzielThe goal is for each of the topics that will be covered to provide:
- A general introduction to the subject
- An example of one of the main statements, and some of the ideas that go into the proof
- A detailed proof of one statement
Voraussetzungen / BesonderesPrerequisites: Martingales, Markov chains, Brownian motion, stochastic calculus.
401-3628-14LBayesian Statistics
Findet dieses Semester nicht statt.
W4 KP2V
KurzbeschreibungIntroduction to the Bayesian approach to statistics: decision theory, prior distributions, hierarchical Bayes models, empirical Bayes, Bayesian tests and model selection, empirical Bayes, Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods.
LernzielStudents understand the conceptual ideas behind Bayesian statistics and are familiar with common techniques used in Bayesian data analysis.
InhaltTopics that we will discuss are:

Difference between the frequentist and Bayesian approach (decision theory, principles), priors (conjugate priors, noninformative priors, Jeffreys prior), tests and model selection (Bayes factors, hyper-g priors for regression),hierarchical models and empirical Bayes methods, computational methods (Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods)
SkriptA script will be available in English.
LiteraturChristian Robert, The Bayesian Choice, 2nd edition, Springer 2007.

A. Gelman et al., Bayesian Data Analysis, 3rd edition, Chapman & Hall (2013).

Additional references will be given in the course.
Voraussetzungen / BesonderesFamiliarity with basic concepts of frequentist statistics and with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed.
401-0625-01LApplied Analysis of Variance and Experimental DesignW5 KP2V + 1UL. Meier
KurzbeschreibungPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LernzielParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
InhaltPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteraturG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Voraussetzungen / BesonderesThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
401-0649-00LApplied Statistical RegressionW5 KP2V + 1UM. Dettling
KurzbeschreibungThis course offers a practically oriented introduction into regression modeling methods. The basic concepts and some mathematical background are included, with the emphasis lying in learning "good practice" that can be applied in every student's own projects and daily work life. A special focus will be laid in the use of the statistical software package R for regression analysis.
LernzielThe students acquire advanced practical skills in linear regression analysis and are also familiar with its extensions to generalized linear modeling.
InhaltThe course starts with the basics of linear modeling, and then proceeds to parameter estimation, tests, confidence intervals, residual analysis, model choice, and prediction. More rarely touched but practically relevant topics that will be covered include variable transformations, multicollinearity problems and model interpretation, as well as general modeling strategies.

The last third of the course is dedicated to an introduction to generalized linear models: this includes the generalized additive model, logistic regression for binary response variables, binomial regression for grouped data and poisson regression for count data.
SkriptA script will be available.
LiteraturFaraway (2005): Linear Models with R
Faraway (2006): Extending the Linear Model with R
Draper & Smith (1998): Applied Regression Analysis
Fox (2008): Applied Regression Analysis and GLMs
Montgomery et al. (2006): Introduction to Linear Regression Analysis
Voraussetzungen / BesonderesThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software package R, for which an introduction will be held.

In the Mathematics Bachelor and Master programmes, the two course units 401-0649-00L "Applied Statistical Regression" and 401-3622-00L "Statistical Modelling" are mutually exclusive. Registration for the examination of one of these two course units is only allowed if you have not registered for the examination of the other course unit.
401-4521-70LGeometric Tomography - Uniqueness, Statistical Reconstruction and Algorithms Information Belegung eingeschränkt - Details anzeigen W4 KP2VJ. Hörrmann
KurzbeschreibungSelf-contained course on the theoretical aspects of the reconstruction of geometric objects from tomographic projection and section data.
LernzielIntroduction to geometric tomography and understanding of various theoretical aspects of reconstruction problems.
InhaltThe problem of reconstruction of an object from geometric information like X-ray data is a classical inverse problem on the overlap between applied mathematics, statistics, computer science and electrical engineering. We focus on various aspects of the problem in the case of prior shape information on the reconstruction object. We will answer questions on uniqueness of the reconstruction and also cover statistical and algorithmic aspects.
LiteraturR. Gardner: Geometric Tomography
F. Natterer: The Mathematics of Computerized Tomography
A. Rieder: Keine Probleme mit inversen Problemen
Voraussetzungen / BesonderesA sound mathematical background in geometry, analysis and probability is required though a repetition of relevant material will be included. The ability to understand and write mathematical proofs is mandatory.
401-4607-59LPercolation Theory Information W4 KP2VV. Tassion
KurzbeschreibungAn introduction to the percolation theory.
LernzielPercolation theory has many applications and is one of the most famous model to
describe phase transition phenomena in physics. One reason for this success is
the variety of mathematical tools, which allows for a precise and rigorous
description of the models. The objective of this course is to gain familiarity
with the methods of the percolation theory and to learn some of its important
results. The students will develop their background and intuition in
probability, and the course is particularly recommended to students with
additional interests in physics or graph theory.
InhaltDefinition of percolation. Standard tools: FKG, BK inequalities, Mixing
property, Russo's formula. Sharpness of the phase transition. Correlation
length and interpretations. Uniqueness of the infinite cluster. Critical
percolation in dimension 2. Supercritical percolation in dimension d>2,
Grimmett-Marstrand Theorem and consequences.
LiteraturB. Bollobas, O. Riordan: Percolation, CUP 2006
G. Grimmett: Percolation 2ed, Springer 1999
Voraussetzungen / BesonderesPreliminaries:
401-2604-00L Probability and Statistics (mandatory)
401-3601-00L Probability Theory (recommended)
401-4619-67LAdvanced Topics in Computational Statistics
Findet dieses Semester nicht statt.
W4 KP2Vkeine Angaben
KurzbeschreibungThis lecture covers selected advanced topics in computational statistics. This year the focus will be on graphical modelling.
LernzielStudents learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes.
InhaltThe main focus will be on graphical models in various forms:
Markov properties of undirected graphs; Belief propagation; Hidden Markov Models; Structure estimation and parameter estimation; inference for high-dimensional data; causal graphical models
Voraussetzungen / BesonderesWe assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics.
401-3627-00LHigh-Dimensional Statistics
Findet dieses Semester nicht statt.
W4 KP2VP. L. Bühlmann
Kurzbeschreibung"High-Dimensional Statistics" deals with modern methods and theory for statistical inference when the number of unknown parameters is of much larger order than sample size. Statistical estimation and algorithms for complex models and aspects of multiple testing will be discussed.
LernzielKnowledge of methods and basic theory for high-dimensional statistical inference
InhaltLasso and Group Lasso for high-dimensional linear and generalized linear models; Additive models and many smooth univariate functions; Non-convex loss functions and l1-regularization; Stability selection, multiple testing and construction of p-values; Undirected graphical modeling
LiteraturPeter Bühlmann and Sara van de Geer (2011). Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer Verlag.
ISBN 978-3-642-20191-2.
Voraussetzungen / BesonderesKnowledge of basic concepts in probability theory, and intermediate knowledge of statistics (e.g. a course in linear models or computational statistics).
401-4623-00LTime Series AnalysisW6 KP3GF. Balabdaoui
KurzbeschreibungThe course offers an introduction into analyzing times series, that is observations which occur in time. The material will cover Stationary Models, ARMA processes, Spectral Analysis, Forecasting, Nonstationary Models, ARIMA Models and an introduction to GARCH models.
LernzielThe goal of the course is to have a a good overview of the different types of time series and the approaches used in their statistical analysis.
InhaltThis course treats modeling and analysis of time series, that is random variables which change in time. As opposed to the i.i.d. framework, the main feature exibited by time series is the dependence between successive observations.

The key topics which will be covered as:

Stationarity
Autocorrelation
Trend estimation
Elimination of seasonality
Spectral analysis, spectral densities
Forecasting
ARMA, ARIMA, Introduction into GARCH models
LiteraturThe main reference for this course is the book "Introduction to Time Series and Forecasting", by P. J. Brockwell and R. A. Davis
Voraussetzungen / BesonderesBasic knowledge in probability and statistics
401-3612-00LStochastic SimulationW5 KP3GF. Sigrist
KurzbeschreibungThis course introduces statistical Monte Carlo methods. This includes applications of stochastic simulation in various fields (statistics, statistical mechanics, operations research, financial mathematics), generating uniform and arbitrary random variables (incl. rejection and importance sampling), the accuracy of methods, variance reduction, quasi-Monte Carlo, and Markov chain Monte Carlo.
LernzielStudents know the stochastic simulation methods introduced in this course. Students understand and can explain these methods, show how they are related to each other, know their weaknesses and strengths, apply them in practice, and proof key results.
InhaltExamples of simulations in different fields (statistics, statistical mechanics, operations research, financial mathematics). Generation of uniform random variables. Generation of random variables with arbitrary distributions (including rejection sampling and importance sampling), simulation of multivariate normal variables and stochastic differential equations. The accuracy of Monte Carlo methods. Methods for variance reduction and quasi-Monte Carlo. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC). Algorithms introduced in the course are illustrated with the statistical software R.
SkriptA script will be available in English.
LiteraturP. Glasserman, Monte Carlo Methods in Financial Engineering.
Springer 2004.

B. D. Ripley. Stochastic Simulation. Wiley, 1987.

Ch. Robert, G. Casella. Monte Carlo Statistical Methods.
Springer 2004 (2nd edition).
Voraussetzungen / BesonderesIt is assumed that students have had an introduction to probability theory and statistics (random variables, joint and conditional distributions, law of large numbers, central limit theorem, basics of measure theory).

The course resources (including script, slides, exercises) will be provided via the Moodle online learning platform.
  •  Seite  1  von  1