Suchergebnis: Katalogdaten im Herbstsemester 2019

DAS in Data Science Information
Vertiefungen
Statistics
NummerTitelTypECTSUmfangDozierende
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 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.
401-3612-00LStochastic Simulation
Findet dieses Semester nicht statt.
W5 KP3G
KurzbeschreibungThis 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.
LernzielStochastic 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.
InhaltExamples 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).
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 / BesonderesFamiliarity with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed.
401-3621-00LFundamentals of Mathematical Statistics Information W10 KP4V + 1US. van de Geer
KurzbeschreibungThe course covers the basics of inferential statistics.
Lernziel
401-3622-00LStatistical Modelling Information W8 KP4GC. Heinze-Deml
KurzbeschreibungIn der Regression wird die Abhängigkeit einer zufälligen Response-Variablen von anderen Variablen untersucht. Wir betrachten die Theorie der linearen Regression mit einer oder mehreren Ko-Variablen, hoch-dimensionale lineare Modelle, nicht-lineare Modelle und verallgemeinerte lineare Modelle, Robuste Methoden, Modellwahl und nicht-parametrische Modelle.
LernzielEinführung in Theorie und Praxis eines umfassenden und vielbenutzten Teilgebiets der Statistik, unter Berücksichtigung neuerer Entwicklungen.
InhaltIn der Regression wird die Abhängigkeit einer beobachteten quantitativen Grösse von einer oder mehreren anderen (unter Berücksichtigung zufälliger Fehler) untersucht. Themen der Vorlesung sind: Einfache und multiple Regression, Theorie allgemeiner linearer Modelle, Hoch-dimensionale Modelle, Ausblick auf nichtlineare Modelle. Querverbindungen zur Varianzanalyse, Modellsuche, Residuenanalyse; Einblicke in Robuste Regression. Durchrechnung und Diskussion von Anwendungsbeispielen.
SkriptVorlesungsskript
Voraussetzungen / BesonderesThis is the course unit with former course title "Regression".
Credits cannot be recognised for both courses 401-3622-00L Statistical Modelling and 401-0649-00L Applied Statistical Regression in the Mathematics Bachelor and Master programmes (to be precise: one course in the Bachelor and the other course in the Master is also forbidden).
401-3628-14LBayesian StatisticsW4 KP2VF. Sigrist
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.
401-4623-00LTime Series Analysis
Findet dieses Semester nicht statt.
W6 KP3GN. Meinshausen
KurzbeschreibungStatistical 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.
LernzielUnderstanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R.
InhaltThis 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.
SkriptNot available
LiteraturA list of references will be distributed during the course.
Voraussetzungen / BesonderesBasic knowledge in probability and statistics
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