Suchergebnis: Katalogdaten im Herbstsemester 2018

Statistik Master Information
Die hier aufgelisteten Lehrveranstaltungen gehören zum Curriculum des Master-Studiengangs Statistik. Die entsprechenden KP gelten nicht als Mobilitäts-KP, auch wenn gewisse Lerneinheiten nicht an der ETH Zürich belegt werden können.
Kernfächer
In der Regel werden die Kernfächer in jedem Themenbereich sowohl in einer mathematisch ausgerichteten als auch in einer anwendungsorientierten Art angeboten. Pro Themenbereich wird jeweils nur eine dieser beiden Arten für das Master-Diplom angerechnet.
Regression
NummerTitelTypECTSUmfangDozierende
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 "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.
Varianzanalyse und Versuchsplanung
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.
Multivariate Statistik
Kein Angebot in diesem Semester.
Zeitreihen und stochastische Prozesse
NummerTitelTypECTSUmfangDozierende
401-4623-00LTime Series AnalysisW6 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
Mathematische Statistik
NummerTitelTypECTSUmfangDozierende
401-3621-00LFundamentals of Mathematical Statistics Information W10 KP4V + 1US. van de Geer
KurzbeschreibungThe course covers the basics of inferential statistics.
Lernziel
401-8623-00LLikelihood Inference (University of Zurich)
Der Kurs muss direkt an der UZH belegt werden.
UZH Modulkürzel: STA402

Beachten Sie die Einschreibungstermine an der UZH: https://www.uzh.ch/cmsssl/de/studies/application/mobilitaet.html
W5 KP3GUni-Dozierende
KurzbeschreibungOverview over the basics of likelihood inference.
Lernziel
Vertiefungs- und Wahlfächer
Statistische und mathematische Fächer
NummerTitelTypECTSUmfangDozierende
401-3601-00LProbability Theory Information
Höchstens eines der drei Bachelor-Kernfächer
401-3461-00L Funktionalanalysis I / Functional Analysis I
401-3531-00L Differentialgeometrie I / Differential Geometry I
401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory
ist im Master-Studiengang Mathematik anrechenbar.
W10 KP4V + 1UA.‑S. Sznitman
KurzbeschreibungBasics of probability theory and the theory of stochastic processes in discrete time
LernzielThis course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned:
Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.
InhaltThis course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned:
Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.
Skriptavailable, will be sold in the course
LiteraturR. Durrett, Probability: Theory and examples, Duxbury Press 1996
H. Bauer, Probability Theory, de Gruyter 1996
J. Jacod and P. Protter, Probability essentials, Springer 2004
A. Klenke, Wahrscheinlichkeitstheorie, Springer 2006
D. Williams, Probability with martingales, Cambridge University Press 1991
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).
401-3612-00LStochastic SimulationW5 KP3GF. Sigrist
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.
401-4619-67LAdvanced Topics in Computational Statistics
Findet dieses Semester nicht statt.
W4 KP2VN. Meinshausen
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.
401-4637-67LOn Hypothesis TestingW4 KP2VF. Balabdaoui
KurzbeschreibungThis course is a review of the main results in decision theory.
LernzielThe 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)
401-4633-00LData Analytics in Organisations and BusinessW5 KP2V + 1UI. Flückiger
KurzbeschreibungOn the end-to-end process of data analytics in organisations & business and how to transform data into insights for fact based decisions. Presentation of the process from the beginning with framing the business problem to presenting the results and making decisions by the use of data analytics. For each topic case studies from the financial service, healthcare and retail sectors will be presented.
LernzielThe goal of this course is to give the students the understanding of the data analytics process in the business world, with special focus on the skills and techniques used besides the technical skills. The student will become familiar with the "business language", current problems and thinking in organisations and business and tools used.
InhaltFraming the Business Problem
Framing the Analytics Problem
Data
Methodology
Model Building
Deployment
Model Lifecycle
Soft Skills for the Statistical/Mathematical Professional
SkriptLecture Notes will be available.
Voraussetzungen / BesonderesPrerequisites: Basic statistics and probability theory and regression
401-6217-00LUsing R for Data Analysis and Graphics (Part II) Information Belegung eingeschränkt - Details anzeigen W1.5 KP1GM. Mächler, M. Tanadini
KurzbeschreibungThe course provides the second part an introduction to the statistical software R for scientists. Topics are data generation and selection, graphical functions, important statistical functions, types of objects, models, programming and writing functions.
Note: This part builds on "Using R... (Part I)", but can be taken independently if the basics of R are already known.
LernzielThe students will be able to use the software R efficiently for data analysis, graphics and simple programming
InhaltThe course provides the second part of an introduction to the statistical software R (https://www.r-project.org/) for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part II of the course builds on part I and covers the following additional topics:
- Elements of the R language: control structures (if, else, loops), lists, overview of R objects, attributes of R objects;
- More on R functions;
- Applying functions to elements of vectors, matrices and lists;
- Object oriented programming with R: classes and methods;
- Tayloring R: options
- Extending basic R: packages

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: www.rstudio.org
SkriptAn Introduction to R. http://stat.ethz.ch/CRAN/doc/contrib/Lam-IntroductionToR_LHL.pdf
Voraussetzungen / BesonderesBasic knowledge of R equivalent to "Using R .. (part 1)" ( = 401-6215-00L ) is a prerequisite for this course.

The course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
https://moodle-app2.let.ethz.ch/course/view.php?id=1145
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
401-0627-00LSmoothing and Nonparametric Regression with ExamplesW4 KP2GS. Beran-Ghosh
KurzbeschreibungStarting with an overview of selected results from parametric inference, kernel smoothing will be introduced along with some asymptotic theory, optimal bandwidth selection, data driven algorithms and some special topics. Examples from environmental research will be used for motivation, but the methods will also be applicable elsewhere.
LernzielThe students will learn about methods of kernel smoothing and application of concepts to data. The aim will be to build sufficient interest in the topic and intuition as well as the ability to implement the methods to various different datasets.
InhaltRough Outline:

- Parametric estimation methods: selection of important results
o Maximum likelihood, Method of Least squares: regression & diagnostics

- Nonparametric curve estimation
o Density estimation, Kernel regression, Local polynomials, Bandwidth selection
o Selection of special topics (as time permits, we will cover as many topics as possible) such as rapid change points, mode estimation, robust smoothing, partial linear models, etc.

- Applications: potential areas of applications will be discussed such as, change assessment, trend and surface estimation, probability and quantile curve estimation, and others.
SkriptBrief summaries or outlines of some of the lecture material will be posted at https://www.wsl.ch/en/employees/ghosh.html.

NOTE: The posted notes will tend to be just sketches whereas only the in-class lessons will contain complete information.

LOG IN: In order to have access to the posted notes, you will need the course user id & the password. These will be given out on the first day of the lectures.
LiteraturReferences:
- Statistical Inference, by S.D. Silvey, Chapman & Hall.
- Regression Analysis: Theory, Methods and Applications, by A. Sen and M. Srivastava, Springer.
- Density Estimation, by B.W. Silverman, Chapman and Hall.
- Kernel Smoothing, by M.P. Wand and M.C. Jones, Chapman and Hall.
- Local polynomial modelling and its applications, by J. Fan and I. Gijbels, Chapman & Hall.
- Nonparametric Simple Regression, by J. Fox, Sage Publications.
- Applied Smoothing Techniques for Data Analysis: the Kernel Approach With S-Plus Illustrations, by A.W. Bowman, A. Azzalini, Oxford University Press.
- Kernel Smoothing: Principles, Methods and Applications, by S. Ghosh, Wiley.

Additional references will be given out in the lectures.
Voraussetzungen / BesonderesPrerequisites: A background in Linear Algebra, Calculus, Probability & Statistical Inference including Estimation and Testing.
447-6221-00LNichtparametrische Regression Belegung eingeschränkt - Details anzeigen
Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an kanzlei@ethz.ch. Die Kanzlei wird anschliessend die Belegung vornehmen.
W1 KP1GM. Mächler
KurzbeschreibungFokus ist die nichtparametrische Schätzung von Wahrscheinlichkeitsdichten und Regressionsfunktionen. Diese neueren Methoden verzichten auf einschränkende Modellannahmen wie 'lineare Funktion'. Sie benötigen eine Gewichtsfunktion und einen Glättungsparameter. Schwerpunkt ist eine Dimension, mehrere Dimensionen und Stichproben von Kurven werden kurz behandelt. Übungen am Computer.
LernzielKenntnisse der Schätzung von Wahrscheinlichkeitsdichten und Regressionsfunktionen mittels verschiedener statistischer Methoden.
Verständnis für die Wahl der Gewichtsfunktion und des Glättungsparameters, auch automatisch.
Praktische Anwendung auf Datensätze am Computer.
447-6233-00LSpatial Statistics Belegung eingeschränkt - Details anzeigen
Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an kanzlei@ethz.ch. Die Kanzlei wird anschliessend die Belegung vornehmen.
W1 KP1GA. J. Papritz
KurzbeschreibungIn many research fields, spatially referenced data are collected. When analysing such data the focus is either on exploring their structure (dependence on explanatory variables, autocorrelation) and/or on spatial prediction. The course provides an introduction to geostatistical methods that are useful for such purposes.
LernzielThe course will provide an overview of the basic concepts and stochastic models that are commonly used to model spatial data. In addition, the participants will learn a number of geostatistical techniques and acquire some familiarity with software that is useful for analysing spatial data.
InhaltAfter an introductory discussion of the types of problems and the kind of data that arise in environmental research, an introduction into linear geostatistics (models: stationary and intrinsic random processes, modelling large-scale spatial patterns by regression, modelling autocorrelation by variogram; kriging: mean-square prediction of spatial data) will be taught. The lectures will be complemented by data analyses that the participants have to do themselves.
SkriptSlides, descriptions of the problems for the data analyses and worked-out solutions to them will be provided.
LiteraturP.J. Diggle & P.J. Ribeiro Jr. 2007. Model-based Geostatistics. Springer
447-6245-00LData-Mining Information Belegung eingeschränkt - Details anzeigen
Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an kanzlei@ethz.ch. Die Kanzlei wird anschliessend die Belegung vornehmen.
W1 KP1GM. Mächler
KurzbeschreibungBlock über "Prognoseprobleme", bzw. "Supervised Learning"

Teil 1, Klassifikation: logistische Regression, Lineare/Quadratische Diskriminanzanalyse, Bayes-Klassifikator; additive & Baummodelle, weitere flexible ("nichtparametrische") Methoden.

Teil 2, Flexible Vorhersage: Additive Modelle, MARS, Y-Transformations-Modelle (ACE,AVAS); Projection Pursuit Regression (PPR), Neuronale Netze.
Lernziel
InhaltAus dem weiten Feld des "Data Mining" behandeln wir in diesem Block nur sogenannte "Prognoseprobleme", bzw. "Supervised Learning".

Teil 1, Klassifikation, repetiert logistische Regression und Lineare / Quadratische Diskriminanzanalyse (LDA/QDA), und erweitert diese (im Rahmen des "Bayes-Klassifikators") auf (generalisierte) additive ("GAM") und Baummodelle ("CART"), und (summarisch/kurz) auf weitere flexible ("nichtparametrische") Methoden.

Teil 2, Flexible Vorhersage (kontinuierliche oder Klassen-Zielvariable) umfasst Additive Modelle, MARS, Y-Transformations-Modelle (ACE, AVAS); Projection Pursuit Regression (PPR), Neuronale Netze.
SkriptGrundlage des Kurses ist das Skript.
Voraussetzungen / BesonderesDie Uebungen werden ausschliesslich mit der (Free, open source) Software "R"
(http://www.r-project.org) durchgeführt, womit am Schluss auch eine "Schnellübung" als Schlussprüfung stattfindet.
447-6257-00LWiederholte Messungen Belegung eingeschränkt - Details anzeigen
Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an kanzlei@ethz.ch. Die Kanzlei wird anschliessend die Belegung vornehmen.
W1 KP1GL. Meier
KurzbeschreibungEntstehung und Strukturen von wiederholten Messungen. Planung und Durchführung entsprechender Studien. Within- und Between-sujects Faktoren. Häufige Kovarianz-Strukturen. Statistische Analysemethoden: Graphische Darstellung, Summary statistics approach, univariate und multivariate Varianzanalyse, gemischtes lineares Modell.
LernzielBefähigung zur Erkennung und adäquaten statistischen Auswertung von wiederholten Messungen. Korrekter Umgang mit Pseudoreplikaten.
SkriptEs wird ein Skript abgegeben.
447-6191-00LStatistical Analysis of Financial Data Belegung eingeschränkt - Details anzeigen
Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an kanzlei@ethz.ch. Die Kanzlei wird anschliessend die Belegung vornehmen.
W2 KP1GM. Dettling, A. F. Ruckstuhl
KurzbeschreibungDistributions for financial data. Volatility models: ARCH- and GARCH models. Value at risk and expected shortfall. Portfolio theory: minimum-variance portfolio, efficient frontier, Sharpe’s ratio. Factor models: capital asset pricing model, macroeconomic factor models, fundamental factor model. Copulas: Basic theory, Gaussian and t-copulas, archimedean copulas, calibration of copulas.
LernzielGetting to know the typical properties of financial data and appropriate statistical models, incl. the corresponding functions in R.
447-6289-00LStichproben-Erhebungen Belegung eingeschränkt - Details anzeigen
Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an kanzlei@ethz.ch. Die Kanzlei wird anschliessend die Belegung vornehmen.
W2 KP1GB. Hulliger
KurzbeschreibungDie Elemente einer Stichproben-Erhebung werden erklärt. Die wichtigsten klassischen Stichprobenpläne (Einfach und geschichtete Zufallsstichprobe) mit ihren Schätzern sowie Schätzverfahren mit Hilfsinformationen und der Horvitz-Thompson Schätzer werden eingeführt. Datenaufbereitung, Antwortausfälle und deren Behandlung, Varianzschätzungen sowie Analysen von Stichprobendaten werden diskutiert.
LernzielKenntnis der Elemente und des Ablaufs einer Stichprobenerhebung. Verständnis für das Paradigma der Zufallsstichproben. Kenntnis der einfachen und geschichteten Stichproben-Strategien und Fähigkeit die entsprechenden Methoden anzuwenden. Kenntnis von weiterführenden Methoden für Schätzverfahren, Datenaufbereitung und Analysen.
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, Bayesian tests and model selection, empirical Bayes, computational methods, 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, 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)
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.
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