# Search result: Catalogue data in Autumn Semester 2020

Statistics Master 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 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-0649-00L | Applied Statistical Regression | W | 5 credits | 2V + 1U | M. Dettling | |

Abstract | 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. | |||||

Objective | The students acquire advanced practical skills in linear regression analysis and are also familiar with its extensions to generalized linear modeling. | |||||

Content | 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. | |||||

Lecture notes | A script will be available. | |||||

Literature | 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 | |||||

Prerequisites / Notice | 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 "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. | |||||

401-3622-00L | Statistical Modelling | W | 8 credits | 4G | P. L. Bühlmann, M. Mächler | |

Abstract | In 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. | |||||

Objective | Introduction into theory and practice of a broad and popular area of statistics, from a modern viewpoint. | |||||

Content | In 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 notes | Lecture notes | |||||

Prerequisites / Notice | This 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 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-0625-01L | Applied Analysis of Variance and Experimental Design | W | 5 credits | 2V + 1U | L. Meier | |

Abstract | 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. | |||||

Objective | 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. | |||||

Content | 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. | |||||

Literature | G. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000. | |||||

Prerequisites / Notice | 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. | |||||

Multivariate Statistics No course offerings in this semester. | ||||||

Time Series and Stochastic Processes | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-4623-00L | Time Series Analysis | W | 6 credits | 3G | F. Balabdaoui | |

Abstract | The 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. | |||||

Objective | The 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. | |||||

Content | This 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 | |||||

Literature | The main reference for this course is the book "Introduction to Time Series and Forecasting", by P. J. Brockwell and R. A. Davis | |||||

Prerequisites / Notice | Basic knowledge in probability and statistics | |||||

Mathematical Statistics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3621-00L | Fundamentals of Mathematical Statistics | W | 10 credits | 4V + 1U | S. van de Geer | |

Abstract | The course covers the basics of inferential statistics. | |||||

Objective | ||||||

401-8623-00L | Likelihood 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». | W | 5 credits | 3G | University lecturers | |

Abstract | Overview over the basics of likelihood inference. | |||||

Objective | ||||||

Specialization Areas and Electives | ||||||

Statistical and Mathematical Courses | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3601-00L | Probability Theory 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. | W | 10 credits | 4V + 1U | A.‑S. Sznitman | |

Abstract | Basics of probability theory and the theory of stochastic processes in discrete time | |||||

Objective | This 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. | |||||

Content | This 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 notes | available in electronic form. | |||||

Literature | R. 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 | |||||

401-3627-00L | High-Dimensional StatisticsDoes not take place this semester. | W | 4 credits | 2V | P. 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. | |||||

Objective | Knowledge of methods and basic theory for high-dimensional statistical inference | |||||

Content | 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 | |||||

Literature | 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. | |||||

Prerequisites / Notice | Knowledge of basic concepts in probability theory, and intermediate knowledge of statistics (e.g. a course in linear models or computational statistics). | |||||

401-3612-00L | Stochastic Simulation | W | 5 credits | 3G | F. Sigrist | |

Abstract | This 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. | |||||

Objective | Students 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. | |||||

Content | Examples 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 notes | A script will be available in English. | |||||

Literature | 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). | |||||

Prerequisites / Notice | It 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. | |||||

401-4619-67L | Advanced Topics in Computational StatisticsDoes not take place this semester. | W | 4 credits | 2V | not available | |

Abstract | This lecture covers selected advanced topics in computational statistics. This year the focus will be on graphical modelling. | |||||

Objective | Students learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes. | |||||

Content | 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 | |||||

Prerequisites / Notice | We assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics. | |||||

401-4633-00L | Data Analytics in Organisations and Business | W | 5 credits | 2V + 1U | I. Flückiger | |

Abstract | On 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. | |||||

Objective | The 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. | |||||

Content | Framing the Business Problem Framing the Analytics Problem Data Methodology Model Building Deployment Model Lifecycle Soft Skills for the Statistical/Mathematical Professional | |||||

Lecture notes | Lecture Notes will be available. | |||||

Prerequisites / Notice | Prerequisites: Basic statistics and probability theory and regression | |||||

401-6217-00L | Using R for Data Analysis and Graphics (Part II) | W | 1.5 credits | 1G | M. Mächler | |

Abstract | The 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. | |||||

Objective | The students will be able to use the software R efficiently for data analysis, graphics and simple programming | |||||

Content | The 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 notes | An Introduction to R. Link | |||||

Prerequisites / Notice | Basic 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. | |||||

401-0627-00L | Smoothing and Nonparametric Regression with Examples | W | 4 credits | 2G | S. Beran-Ghosh | |

Abstract | Starting 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. | |||||

Objective | The 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. | |||||

Content | Rough 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 notes | Brief 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. | |||||

Literature | References: - 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 / Notice | Prerequisites: A background in Linear Algebra, Calculus, Probability & Statistical Inference including Estimation and Testing. | |||||

447-6221-00L | Nonparametric Regression 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. | W | 1 credit | 1G | M. Mächler | |

Abstract | This 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. | |||||

Objective | Knowledge 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. | |||||

447-6233-00L | Spatial Statistics 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. | W | 1 credit | 1G | A. J. Papritz | |

Abstract | In 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. | |||||

Objective | The 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. | |||||

Content | After 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 notes | Slides, descriptions of the problems for the data analyses and worked-out solutions to them will be provided. | |||||

Literature | P.J. Diggle & P.J. Ribeiro Jr. 2007. Model-based Geostatistics. Springer | |||||

447-6245-00L | Data Mining 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. | W | 1 credit | 1G | M. Mächler | |

Abstract | Block 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 notes | The block course is based on (German language) lecture notes. | |||||

Prerequisites / Notice | The 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!). | |||||

447-6257-00L | Repeated Measures | W | 1 credit | 1G | L. Meier | |

Abstract | Generation 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. | |||||

Objective | Participants will gain the ability of recognizing repeated measures and to analyze them adequately. They will know how to deal with pseudoreplicates. | |||||

447-6191-00L | Statistical Analysis of Financial Data | W | 2 credits | 1G | M. Dettling, A. F. Ruckstuhl | |

Abstract | Distributions 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. | |||||

Objective | Getting to know the typical properties of financial data and appropriate statistical models, incl. the corresponding functions in R. | |||||

447-6289-00L | Sampling Surveys | W | 2 credits | 1G | B. Hulliger | |

Abstract | The 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. | |||||

Objective | Knowledge 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 notes | Introduction to the statistical methods of survey research | |||||

401-3628-14L | Bayesian StatisticsDoes not take place this semester. | W | 4 credits | 2V | ||

Abstract | Introduction 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. | |||||

Objective | Students understand the conceptual ideas behind Bayesian statistics and are familiar with common techniques used in Bayesian data analysis. | |||||

Content | Topics 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 notes | A script will be available in English. | |||||

Literature | 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. | |||||

Prerequisites / Notice | 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. |

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