Suchergebnis: Katalogdaten im Herbstsemester 2020

DAS in Data Science Information
Vertiefungen
Statistics
NummerTitelTypECTSUmfangDozierende
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.
401-3612-00LStochastic 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.
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 KP4GP. L. Bühlmann, M. Mächler
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 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.
401-4623-00LTime 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
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