Suchergebnis: Katalogdaten im Herbstsemester 2017

Nummer	Titel	Typ	ECTS	Umfang	Dozierende
Mathematik Master
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
401-4607-67L	Schramm-Loewner Evolutions	W	4 KP	2V	W. Werner
Kurzbeschreibung	This course will be an introduction to Schramm-Loewner Evolutions which are natural random planar curve that arise in a number of contexts in probability theory and statistical theory in two dimensions.
Lernziel	The goal of the course is to provide an overview of the definition and the main properties of Schramm-Loewner Evolutions (SLE).
Inhalt	Most of the following items will be covered in the lectures: - Introduction to SLE - Definition of SLE - Phases of SLE, hitting probabilities - How does one prove that an SLE is actually a curve? - Restriction, locality - Relation to loop-soups and the Gaussian Free Field - Some SLEs as scaling limit of lattice models
401-4597-67L	Probability on Transitive Graphs	W	4 KP	2V	V. Tassion
Kurzbeschreibung	In this course, we will present modern topics at the interface between probability and geometric group theory. We will define two random processes on Cayley graphs: the simple random walk and percolation, and discuss their respective behaviors depending on the geometric properties of the underlying group.
Lernziel	Present in an original framework important tools in the study of - random walks: spectral gap, harmonic functions, entropy,... - percolation: uniqueness of the infinite cluster, mass-transport principle,...
Inhalt	In this course, we will present modern topics at the interface between probability and geometric group theory. To every group with a finite generating set, one can associate a graph, called Cayley graph. (For example, the d-dimensional grid is a Cayley graph associated to the group Z^d.) Then, we will define two random processes on Cayley graphs: the simple random walk and percolation, and discuss their respective behaviors depending on the geometric properties of the underlying group. The focus will be on the random processes and their properties, and we will use very few notions of geometric group theory.
Literatur	Probability on trees and network (R. Lyons, Y. Peres)
Voraussetzungen / Besonderes	- Probability Theory - No prerequisite on group theory, all the background will be introduced in class.
401-4619-67L	Advanced Topics in Computational Statistics	W	4 KP	2V	N. Meinshausen
Kurzbeschreibung	This lecture covers selected advanced topics in computational statistics. This year the focus will be on graphical modelling.
Lernziel	Students learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes.
Inhalt	The 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 / Besonderes	We assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics.
401-4637-67L	On Hypothesis Testing	W	4 KP	2V	F. Balabdaoui
Kurzbeschreibung	This course is a review of the main results in decision theory.
Lernziel	The goal of this course is to present a review for the most fundamental results in statistical testing. This entails reviewing the Neyman-Pearson Lemma for simple hypotheses and the Karlin-Rubin Theorem for monotone likelihood ratio parametric families. The students will also encounter the important concept of p-values and their use in some multiple testing situations. Further methods for constructing tests will be also presented including likelihood ratio and chi-square tests. Some non-parametric tests will be reviewed such as the Kolmogorov goodness-of-fit test and the two sample Wilcoxon rank test. The most important theoretical results will reproved and also illustrated via different examples. Four sessions of exercises will be scheduled (the students will be handed in an exercise sheet a week before discussing solutions in class).
Literatur	- Statistical Inference (Casella & Berger) - Testing Statistical Hypotheses (Lehmann and Romano)
401-3628-14L	Bayesian Statistics	W	4 KP	2V	F. Sigrist
Kurzbeschreibung	Introduction to the Bayesian approach to statistics: Decision theory, prior distributions, hierarchical Bayes models, Bayesian tests and model selection, empirical Bayes, computational methods, Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods.
Lernziel	Students understand the conceptual ideas behind Bayesian statistics and are familiar with common techniques used in Bayesian data analysis.
Inhalt	Topics that we will discuss are: Difference between the frequentist and Bayesian approach (decision theory, principles), priors (conjugate priors, Jeffreys priors), tests and model selection (Bayes factors, hyper-g priors in regression),hierarchical models and empirical Bayes methods, computational methods (Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods)
Skript	A script will be available in English.
Literatur	Christian 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 / Besonderes	Familiarity 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.
401-0625-01L	Applied Analysis of Variance and Experimental Design	W	5 KP	2V + 1U	L. Meier
Kurzbeschreibung	Principles 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.
Lernziel	Participants 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.
Inhalt	Principles 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.
Literatur	G. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Voraussetzungen / Besonderes	The 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.
401-0649-00L	Applied Statistical Regression	W	5 KP	2V + 1U	M. Dettling
Kurzbeschreibung	This 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.
Lernziel	The students acquire advanced practical skills in linear regression analysis and are also familiar with its extensions to generalized linear modeling.
Inhalt	The 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.
Skript	A script will be available.
Literatur	Faraway (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 / Besonderes	The 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 "Regression" 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.
401-3627-00L	High-Dimensional Statistics Findet dieses Semester nicht statt.	W	4 KP	2V	P. 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.
Lernziel	Knowledge of methods and basic theory for high-dimensional statistical inference
Inhalt	Lasso 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
Literatur	Peter 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 / Besonderes	Knowledge of basic concepts in probability theory, and intermediate knowledge of statistics (e.g. a course in linear models or computational statistics).
401-4623-00L	Time Series Analysis Findet dieses Semester nicht statt.	W	6 KP	3G	keine Angaben
Kurzbeschreibung	Statistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R.
Lernziel	Understanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R.
Inhalt	This course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations. Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R.
Skript	Not available
Literatur	A list of references will be distributed during the course.
Voraussetzungen / Besonderes	Basic knowledge in probability and statistics
401-3612-00L	Stochastic Simulation Findet dieses Semester nicht statt.	W	5 KP	3G
Kurzbeschreibung	This course provides an introduction to statistical Monte Carlo methods. This includes applications of simulations in various fields (Bayesian statistics, statistical mechanics, operations research, financial mathematics), algorithms for the generation of random variables (accept-reject, importance sampling), estimating the precision, variance reduction, introduction to Markov chain Monte Carlo.
Lernziel	Stochastic simulation (also called Monte Carlo method) is the experimental analysis of a stochastic model by implementing it on a computer. Probabilities and expected values can be approximated by averaging simulated values, and the central limit theorem gives an estimate of the error of this approximation. The course shows examples of the many applications of stochastic simulation and explains different algorithms used for simulation. These algorithms are illustrated with the statistical software R.
Inhalt	Examples of simulations in different fields (computer science, statistics, statistical mechanics, operations research, financial mathematics). Generation of uniform random variables. Generation of random variables with arbitrary distributions (quantile transform, accept-reject, importance sampling), simulation of Gaussian processes and diffusions. The precision of simulations, methods for variance reduction. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC).
Skript	A script will be available in English.
Literatur	P. 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 / Besonderes	Familiarity with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed.

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