Search result: Catalogue data in Autumn Semester 2020

Statistics Master Information
The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.
Master Studies (Programme Regulations 2014)
Core Courses
In each subject area, the core courses offered are normally mathematical as well as application-oriented in content. For each subject area, only one of these is recognised for the Master degree.
Regression
NumberTitleTypeECTSHoursLecturers
401-0649-00LApplied Statistical RegressionW5 credits2V + 1UM. Dettling
AbstractThis 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.
ObjectiveThe students acquire advanced practical skills in linear regression analysis and are also familiar with its extensions to generalized linear modeling.
ContentThe 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.
Lecture notesA script will be available.
LiteratureFaraway (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
Prerequisites / NoticeThe 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.
401-3622-00LStatistical Modelling Information W8 credits4GP. L. Bühlmann, M. Mächler
AbstractIn regression, the dependency of a random response variable on other variables is examined. We consider the theory of linear regression with one or more covariates, high-dimensional linear models, nonlinear models and generalized linear models, robust methods, model choice and nonparametric models. Several numerical examples will illustrate the theory.
ObjectiveIntroduction into theory and practice of a broad and popular area of statistics, from a modern viewpoint.
ContentIn 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.
Lecture notesLecture notes
Prerequisites / NoticeThis 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).
Analysis of Variance and Design of Experiments
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental DesignW5 credits2V + 1UL. Meier
AbstractPrinciples 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.
ObjectiveParticipants 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.
ContentPrinciples 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.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe 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 Statistics
No course offerings in this semester.
Time Series and Stochastic Processes
NumberTitleTypeECTSHoursLecturers
401-4623-00LTime Series AnalysisW6 credits3GF. Balabdaoui
AbstractThe 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.
ObjectiveThe 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.
ContentThis 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
LiteratureThe main reference for this course is the book "Introduction to Time Series and Forecasting", by P. J. Brockwell and R. A. Davis
Prerequisites / NoticeBasic knowledge in probability and statistics
Mathematical Statistics
NumberTitleTypeECTSHoursLecturers
401-3621-00LFundamentals of Mathematical Statistics Information W10 credits4V + 1US. van de Geer
AbstractThe course covers the basics of inferential statistics.
Objective
401-8623-00LLikelihood Inference (University of Zurich)
No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH.
UZH Module Code: STA402

Mind the enrolment deadlines at UZH:
Link

The two core courses Fundamentals of Mathematical Statistics (401-3621-00L) and Likelihood Inference (401-8623-00L) are similar in content. Therefore only one of them can be recognised towards the Master’s degree in Statistics (Programme Regulations 2020) in the core course area «Mathematical Statistics».
W5 credits3GUniversity lecturers
AbstractOverview over the basics of likelihood inference.
Objective
Specialization Areas and Electives
Statistical and Mathematical Courses
NumberTitleTypeECTSHoursLecturers
401-3601-00LProbability Theory Information
At most one of the three course units (Bachelor Core Courses)
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics. In this case, you cannot change the category assignment by yourself in myStudies but must take contact with the Study Administration Office (Link) after having received the credits.
W10 credits4V + 1UA.‑S. Sznitman
AbstractBasics of probability theory and the theory of stochastic processes in discrete time
ObjectiveThis 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.
ContentThis 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.
Lecture notesavailable in electronic form.
LiteratureR. 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
Does not take place this semester.
W4 credits2VP. L. Bühlmann
Abstract"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.
ObjectiveKnowledge of methods and basic theory for high-dimensional statistical inference
ContentLasso 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
LiteraturePeter Bühlmann and Sara van de Geer (2011). Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer Verlag.
ISBN 978-3-642-20191-2.
Prerequisites / NoticeKnowledge 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 credits3GF. Sigrist
AbstractThis 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.
ObjectiveStudents 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.
ContentExamples 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.
Lecture notesA script will be available in English.
LiteratureP. 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).
Prerequisites / NoticeIt 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.
401-4619-67LAdvanced Topics in Computational Statistics
Does not take place this semester.
W4 credits2Vnot available
AbstractThis lecture covers selected advanced topics in computational statistics. This year the focus will be on graphical modelling.
ObjectiveStudents learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes.
ContentThe 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
Prerequisites / NoticeWe assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics.
401-4633-00LData Analytics in Organisations and BusinessW5 credits2V + 1UI. Flückiger
AbstractOn 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.
ObjectiveThe 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.
ContentFraming the Business Problem
Framing the Analytics Problem
Data
Methodology
Model Building
Deployment
Model Lifecycle
Soft Skills for the Statistical/Mathematical Professional
Lecture notesLecture Notes will be available.
Prerequisites / NoticePrerequisites: Basic statistics and probability theory and regression
401-6217-00LUsing R for Data Analysis and Graphics (Part II) Restricted registration - show details W1.5 credits1GM. Mächler
AbstractThe 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.
ObjectiveThe students will be able to use the software R efficiently for data analysis, graphics and simple programming
ContentThe course provides the second part of an introduction to the statistical software R (Link) 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: Link
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeBasic 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.
Subscribing via Mystudies should *automatically* make you
a student participant of the Moodle course of this lecture, which is at

Link

ALL material is available on this moodle page.
401-0627-00LSmoothing and Nonparametric Regression with Examples Information W4 credits2GS. Beran-Ghosh
AbstractStarting 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.
ObjectiveThe 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.
ContentRough 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.
Lecture notesBrief summaries or outlines of some of the lecture material will be posted at Link.

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.
LiteratureReferences:
- 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.
- 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.
Prerequisites / NoticePrerequisites: A background in Linear Algebra, Calculus, Probability & Statistical Inference including Estimation and Testing.
447-6221-00LNonparametric Regression Restricted registration - show details
Special Students "University of Zurich (UZH)" in the Master Program in Biostatistics at UZH cannot register for this course unit electronically. Forward the lecturer's written permission to attend to the Registrar's Office. Alternatively, the lecturer may also send an email directly to Link. The Registrar's Office will then register you for the course.
W1 credit1GM. Mächler
AbstractThis course focusses on nonparametric estimation of probability densities and regression functions. These recent methods allow modelling without restrictive assumptions such as 'linear function'. These smoothing methods require a weight function and a smoothing parameter. Focus is on one dimension, higher dimensions and samples of curves are treated briefly. Exercises at the computer.
ObjectiveKnowledge on estimation of probability densities and regression functions via various statistical methods.
Understanding of the choice of weight function and of the smoothing parameter, also done automatically.
Practical application on data sets at the computer.
447-6233-00LSpatial Statistics Restricted registration - show details
Special Students "University of Zurich (UZH)" in the Master Program in Biostatistics at UZH cannot register for this course unit electronically. Forward the lecturer's written permission to attend to the Registrar's Office. Alternatively, the lecturer may also send an email directly to Link. The Registrar's Office will then register you for the course.
W1 credit1GA. J. Papritz
AbstractIn 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.
ObjectiveThe 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.
ContentAfter 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.
Lecture notesSlides, descriptions of the problems for the data analyses and worked-out solutions to them will be provided.
LiteratureP.J. Diggle & P.J. Ribeiro Jr. 2007. Model-based Geostatistics. Springer
447-6245-00LData Mining Information Restricted registration - show details
Special Students "University of Zurich (UZH)" in the Master Program in Biostatistics at UZH cannot register for this course unit electronically. Forward the lecturer's written permission to attend to the Registrar's Office. Alternatively, the lecturer may also send an email directly to Link. The Registrar's Office will then register you for the course.
W1 credit1GM. Mächler
AbstractBlock course only on prediction problems, aka "supervised learning".

Part 1, Classification: logistic regression, linear/quadratic discriminant analysis, Bayes classifier; additive and tree models; further flexible ("nonparametric") methods.

Part 2, Flexible Prediction: additive models, MARS, Y-Transformation models (ACE,AVAS); Projection Pursuit Regression (PPR), neural nets.
Objective
Content"Data Mining" is a large field from which in this block course, we only treat so called prediction problems, aka "supervised learning".

Part 1, Classification, recalls logistic regression and linear / quadratic discriminant analysis (LDA/QDA) and extends these (in the framework of 'Bayes classifier") to (generalized) additive (GAM) and tree models (CART), and further
mentions other flexible ("nonparametric") methods.

Part 2, Flexible Prediction (of continuous or "class" response/target) contains additive models, MARS, Y-Transformation models (ACE, AVAS); Projection Pursuit Regression (PPR), neural nets.
Lecture notesThe block course is based on (German language) lecture notes.
Prerequisites / NoticeThe exercises are done exlusively with the (free, open source) software "R"
(Link). A final exam will also happen at the computers, using R (and your brains!).
447-6257-00LRepeated Measures Restricted registration - show details
Special Students "University of Zurich (UZH)" in the Master Program in Biostatistics at UZH cannot register for this course unit electronically. Forward the lecturer's written permission to attend to the Registrar's Office. Alternatively, the lecturer may also send an email directly to Link. The Registrar's Office will then register you for the course.
W1 credit1GL. Meier
AbstractGeneration and structure of repeated measures. Planning and realization of corresponding studies. Within- and between-subjects factors. Common covariance structures. Statistical analyses: graphical methods, summary statistics approach, univariate and multivariate ANOVA, linear mixed effects models.
ObjectiveParticipants will gain the ability of recognizing repeated measures and to analyze them adequately. They will know how to deal with pseudoreplicates.
447-6191-00LStatistical Analysis of Financial Data Restricted registration - show details
Special Students "University of Zurich (UZH)" in the Master Program in Biostatistics at UZH cannot register for this course unit electronically. Forward the lecturer's written permission to attend to the Registrar's Office. Alternatively, the lecturer may also send an email directly to Link. The Registrar's Office will then register you for the course.
W2 credits1GM. Dettling, A. F. Ruckstuhl
AbstractDistributions 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.
ObjectiveGetting to know the typical properties of financial data and appropriate statistical models, incl. the corresponding functions in R.
447-6289-00LSampling Surveys Restricted registration - show details
Special Students "University of Zurich (UZH)" in the Master Program in Biostatistics at UZH cannot register for this course unit electronically. Forward the lecturer's written permission to attend to the Registrar's Office. Alternatively, the lecturer may also send an email directly to Link. The Registrar's Office will then register you for the course.
W2 credits1GB. Hulliger
AbstractThe elements of a sample survey are explained. The most important classical sample designs (simple random sampling and stratified random sampling) with their estimation procedures and the use of auxiliary information including the Horvitz-Thompson estimator are introduced. Data preparation, non-response and its treatment, variance estimation and analysis of survey data is discussed.
ObjectiveKnowledge of the Elements and the process of a sample survey. Understanding of the paradigm of random samples. Knowledge of simple random samplinig and stratified random sampling and capability to apply the corresponding methods. Knowledge of further methods of sampling and estimation as well as data preparation and analysis.
Lecture notesIntroduction to the statistical methods of survey research
401-3628-14LBayesian Statistics
Does not take place this semester.
W4 credits2V
AbstractIntroduction 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.
ObjectiveStudents understand the conceptual ideas behind Bayesian statistics and are familiar with common techniques used in Bayesian data analysis.
ContentTopics 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)
Lecture notesA script will be available in English.
LiteratureChristian 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.
Prerequisites / NoticeFamiliarity 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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