# Search result: Catalogue data in Spring Semester 2019

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. | ||||||

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 | |
---|---|---|---|---|---|---|

401-3622-00L | RegressionDoes not take place this semester. | W | 8 credits | 4G | not available | |

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 | Credits cannot be recognised for both courses 401-3622-00L Regression 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 No offering in this semester yet | ||||||

Multivariate Statistics | ||||||

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

401-6102-00L | Multivariate Statistics | W | 4 credits | 2G | N. Meinshausen | |

Abstract | Multivariate Statistics deals with joint distributions of several random variables. This course introduces the basic concepts and provides an overview over classical and modern methods of multivariate statistics. We will consider the theory behind the methods as well as their applications. | |||||

Objective | After the course, you should be able to: - describe the various methods and the concepts and theory behind them - identify adequate methods for a given statistical problem - use the statistical software "R" to efficiently apply these methods - interpret the output of these methods | |||||

Content | Visualization / Principal component analysis / Multidimensional scaling / The multivariate Normal distribution / Factor analysis / Supervised learning / Cluster analysis | |||||

Lecture notes | None | |||||

Literature | The course will be based on class notes and books that are available electronically via the ETH library. | |||||

Prerequisites / Notice | Target audience: This course is the more theoretical version of "Applied Multivariate Statistics" (401-0102-00L) and is targeted at students with a math background. Prerequisite: A basic course in probability and statistics. Note: The courses 401-0102-00L and 401-6102-00L are mutually exclusive. You may register for at most one of these two course units. | |||||

401-0102-00L | Applied Multivariate Statistics | W | 5 credits | 2V + 1U | F. Sigrist | |

Abstract | Multivariate statistics analyzes data on several random variables simultaneously. This course introduces the basic concepts and provides an overview of classical and modern methods of multivariate statistics including visualization, dimension reduction, supervised and unsupervised learning for multivariate data. An emphasis is on applications and solving problems with the statistical software R. | |||||

Objective | After the course, you are able to: - describe the various methods and the concepts behind them - identify adequate methods for a given statistical problem - use the statistical software R to efficiently apply these methods - interpret the output of these methods | |||||

Content | Visualization, multivariate outliers, the multivariate normal distribution, dimension reduction, principal component analysis, multidimensional scaling, factor analysis, cluster analysis, classification, multivariate tests and multiple testing | |||||

Lecture notes | None | |||||

Literature | 1) "An Introduction to Applied Multivariate Analysis with R" (2011) by Everitt and Hothorn 2) "An Introduction to Statistical Learning: With Applications in R" (2013) by Gareth, Witten, Hastie and Tibshirani Electronic versions (pdf) of both books can be downloaded for free from the ETH library. | |||||

Prerequisites / Notice | This course is targeted at students with a non-math background. Requirements: ========== 1) Introductory course in statistics (min: t-test, regression; ideal: conditional probability, multiple regression) 2) Good understanding of R (if you don't know R, it is recommended that you study chapters 1,2,3,4, and 5 of "Introductory Statistics with R" from Peter Dalgaard, which is freely available online from the ETH library) An alternative course with more emphasis on theory is 401-6102-00L "Multivariate Statistics" (only every second year). 401-0102-00L and 401-6102-00L are mutually exclusive. You can register for only one of these two courses. | |||||

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

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

401-6624-11L | Applied Time Series | W | 5 credits | 2V + 1U | M. Dettling | |

Abstract | The course starts with an introduction to time series analysis (examples, goal, mathematical notation). In the following, descriptive techniques, modeling and prediction as well as advanced topics will be covered. | |||||

Objective | Getting to know the mathematical properties of time series, as well as the requirements, descriptive techniques, models, advanced methods and software that are necessary such that the student can independently run an applied time series analysis. | |||||

Content | The course starts with an introduction to time series analysis that comprises of examples and goals. We continue with notation and descriptive analysis of time series. A major part of the course will be dedicated to modeling and forecasting of time series using the flexible class of ARMA models. More advanced topics that will be covered in the following are time series regression, state space models and spectral analysis. | |||||

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

Prerequisites / Notice | The course starts with an introduction to time series analysis that comprises of examples and goals. We continue with notation and descriptive analysis of time series. A major part of the course will be dedicated to modeling and forecasting of time series using the flexible class of ARMA models. More advanced topics that will be covered in the following are time series regression, state space models and spectral analysis. | |||||

Mathematical Statistics No offering in this semester yet | ||||||

Specialization Areas and Electives | ||||||

Statistical and Mathematical Courses | ||||||

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

401-4632-15L | Causality | W | 4 credits | 2G | C. Heinze-Deml | |

Abstract | In statistics, we are used to search for the best predictors of some random variable. In many situations, however, we are interested in predicting a system's behavior under manipulations. For such an analysis, we require knowledge about the underlying causal structure of the system. In this course, we study concepts and theory behind causal inference. | |||||

Objective | After this course, you should be able to - understand the language and concepts of causal inference - know the assumptions under which one can infer causal relations from observational and/or interventional data - describe and apply different methods for causal structure learning - given data and a causal structure, derive causal effects and predictions of interventional experiments | |||||

Prerequisites / Notice | Prerequisites: basic knowledge of probability theory and regression | |||||

401-3632-00L | Computational Statistics | W | 8 credits | 3V + 1U | M. H. Maathuis | |

Abstract | We discuss modern statistical methods for data analysis, including methods for data exploration, prediction and inference. We pay attention to algorithmic aspects, theoretical properties and practical considerations. The class is hands-on and methods are applied using the statistical programming language R. | |||||

Objective | The student obtains an overview of modern statistical methods for data analysis, including their algorithmic aspects and theoretical properties. The methods are applied using the statistical programming language R. | |||||

Content | See the class website | |||||

Prerequisites / Notice | At least one semester of (basic) probability and statistics. Programming experience is helpful but not required. | |||||

401-3602-00L | Applied Stochastic Processes | W | 8 credits | 3V + 1U | V. Tassion | |

Abstract | Poisson processes; renewal processes; Markov chains in discrete and in continuous time; some applications. | |||||

Objective | Stochastic processes are a way to describe and study the behaviour of systems that evolve in some random way. In this course, the evolution will be with respect to a scalar parameter interpreted as time, so that we discuss the temporal evolution of the system. We present several classes of stochastic processes, analyse their properties and behaviour and show by some examples how they can be used. The main emphasis is on theory; in that sense, "applied" should be understood to mean "applicable". | |||||

Literature | R. N. Bhattacharya and E. C. Waymire, "Stochastic Processes with Applications", SIAM (2009), available online: http://epubs.siam.org/doi/book/10.1137/1.9780898718997 R. Durrett, "Essentials of Stochastic Processes", Springer (2012), available online: http://link.springer.com/book/10.1007/978-1-4614-3615-7/page/1 M. Lefebvre, "Applied Stochastic Processes", Springer (2007), available online: http://link.springer.com/book/10.1007/978-0-387-48976-6/page/1 S. I. Resnick, "Adventures in Stochastic Processes", Birkhäuser (2005) | |||||

Prerequisites / Notice | Prerequisites are familiarity with (measure-theoretic) probability theory as it is treated in the course "Probability Theory" (401-3601-00L). | |||||

401-3642-00L | Brownian Motion and Stochastic Calculus | W | 10 credits | 4V + 1U | W. Werner | |

Abstract | This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. | |||||

Objective | This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. | |||||

Lecture notes | Lecture notes will be distributed in class. | |||||

Literature | - J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016). - I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991). - D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer (2005). - L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, vol. 1 and 2, Cambridge University Press (2000). - D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer (2006). | |||||

Prerequisites / Notice | Familiarity with measure-theoretic probability as in the standard D-MATH course "Probability Theory" will be assumed. Textbook accounts can be found for example in - J. Jacod, P. Protter, Probability Essentials, Springer (2004). - R. Durrett, Probability: Theory and Examples, Cambridge University Press (2010). | |||||

401-6228-00L | Programming with R for Reproducible Research | W | 1 credit | 1G | M. Mächler | |

Abstract | Deeper understanding of R: Function calls, rather than "commands". Reproducible research and data analysis via Sweave and Rmarkdown. Limits of floating point arithmetic. Understanding how functions work. Environments, packages, namespaces. Closures, i.e., Functions returning functions. Lists and [mc]lapply() for easy parallelization. Performance measurement and improvements. | |||||

Objective | ||||||

Content | See https://stat.ethz.ch/education/semesters/ss2014/Progr_R3 | |||||

Lecture notes | Material available from https://stat.ethz.ch/education/semesters/ss2014/Progr_R3 | |||||

Literature | Norman Matloff (2011) The Art of R Programming - A tour of statistical software design. no starch press, San Francisco. on stock at Polybuchhandlung (CHF 42.-). | |||||

Prerequisites / Notice | R Knowledge on the same level as after *both* parts of the ETH lecture 401-6217-00L Using R for Data Analysis and Graphics Link | |||||

401-4627-00L | Empirical Process Theory with Applications in Statistics and Machine Learning | W | 4 credits | 2V | S. van de Geer | |

Abstract | Empirical process theory provides a rich toolbox for studying the properties of empirical risk minimizers, such as least squares and maximum likelihood estimators, support vector machines, etc. | |||||

Objective | ||||||

Content | In this series of lectures, we will start with considering exponential inequalities, including concentration inequalities, for the deviation of averages from their mean. We furthermore present some notions from approximation theory, because this enables us to assess the modulus of continuity of empirical processes. We introduce e.g., Vapnik Chervonenkis dimension: a combinatorial concept (from learning theory) of the "size" of a collection of sets or functions. As statistical applications, we study consistency and exponential inequalities for empirical risk minimizers, and asymptotic normality in semi-parametric models. We moreover examine regularization and model selection. | |||||

401-3629-00L | Quantitative Risk Management | W | 4 credits | 2V + 1U | P. Cheridito | |

Abstract | This course introduces methods from probability theory and statistics that can be used to model financial risks. Topics addressed include loss distributions, risk measures, extreme value theory, multivariate models, copulas, dependence structures and operational risk. | |||||

Objective | The goal is to learn the most important methods from probability theory and statistics used in financial risk modeling. | |||||

Content | 1. Introduction 2. Basic Concepts in Risk Management 3. Empirical Properties of Financial Data 4. Financial Time Series 5. Extreme Value Theory 6. Multivariate Models 7. Copulas and Dependence 8. Operational Risk | |||||

Lecture notes | Course material is available on https://people.math.ethz.ch/~patrickc/qrm | |||||

Literature | Quantitative Risk Management: Concepts, Techniques and Tools AJ McNeil, R Frey and P Embrechts Princeton University Press, Princeton, 2015 (Revised Edition) http://press.princeton.edu/titles/10496.html | |||||

Prerequisites / Notice | The course corresponds to the Risk Management requirement for the SAA ("Aktuar SAV Ausbildung") as well as for the Master of Science UZH-ETH in Quantitative Finance. | |||||

401-4658-00L | Computational Methods for Quantitative Finance: PDE Methods | W | 6 credits | 3V + 1U | L. Herrmann, K. Kirchner | |

Abstract | Introduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB programming and knowledge of numerical mathematics at ETH BSc level. | |||||

Objective | Introduce the main methods for efficient numerical valuation of derivative contracts in a Black Scholes as well as in incomplete markets due Levy processes or due to stochastic volatility models. Develop implementation of pricing methods in MATLAB. Finite-Difference/ Finite Element based methods for the solution of the pricing integrodifferential equation. | |||||

Content | 1. Review of option pricing. Wiener and Levy price process models. Deterministic, local and stochastic volatility models. 2. Finite Difference Methods for option pricing. Relation to bi- and multinomial trees. European contracts. 3. Finite Difference methods for Asian, American and Barrier type contracts. 4. Finite element methods for European and American style contracts. 5. Pricing under local and stochastic volatility in Black-Scholes Markets. 6. Finite Element Methods for option pricing under Levy processes. Treatment of integrodifferential operators. 7. Stochastic volatility models for Levy processes. 8. Techniques for multidimensional problems. Baskets in a Black-Scholes setting and stochastic volatility models in Black Scholes and Levy markets. 9. Introduction to sparse grid option pricing techniques. | |||||

Lecture notes | There will be english, typed lecture notes as well as MATLAB software for registered participants in the course. | |||||

Literature | R. Cont and P. Tankov : Financial Modelling with Jump Processes, Chapman and Hall Publ. 2004. Y. Achdou and O. Pironneau : Computational Methods for Option Pricing, SIAM Frontiers in Applied Mathematics, SIAM Publishers, Philadelphia 2005. D. Lamberton and B. Lapeyre : Introduction to stochastic calculus Applied to Finance (second edition), Chapman & Hall/CRC Financial Mathematics Series, Taylor & Francis Publ. Boca Raton, London, New York 2008. J.-P. Fouque, G. Papanicolaou and K.-R. Sircar : Derivatives in financial markets with stochastic volatility, Cambridge Univeristy Press, Cambridge, 2000. N. Hilber, O. Reichmann, Ch. Schwab and Ch. Winter: Computational Methods for Quantitative Finance, Springer Finance, Springer, 2013. | |||||

401-2284-00L | Measure and Integration | W | 6 credits | 3V + 2U | J. Teichmann | |

Abstract | Introduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces | |||||

Objective | Basic acquaintance with the abstract theory of measure and integration | |||||

Content | Introduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces | |||||

Lecture notes | https://people.math.ethz.ch/~lang/mi.pdf | |||||

Literature | - D. A. Salamon, Measure and Integration, EMS 2016 - W. Rudin, Real and Complex Analysis, McGraw-Hill 1987 - P. R. Halmos, Measure Theory, Springer 1950 | |||||

401-3903-11L | Geometric Integer Programming | W | 6 credits | 2V + 1U | R. Weismantel, J. Paat, M. Schlöter | |

Abstract | Integer programming is the task of minimizing a linear function over all the integer points in a polyhedron. This lecture introduces the key concepts of an algorithmic theory for solving such problems. | |||||

Objective | The purpose of the lecture is to provide a geometric treatment of the theory of integer optimization. | |||||

Content | Key topics are: - lattice theory and the polynomial time solvability of integer optimization problems in fixed dimension, - the theory of integral generating sets and its connection to totally dual integral systems, - finite cutting plane algorithms based on lattices and integral generating sets. | |||||

Lecture notes | not available, blackboard presentation | |||||

Literature | Bertsimas, Weismantel: Optimization over Integers, Dynamic Ideas 2005. Schrijver: Theory of linear and integer programming, Wiley, 1986. | |||||

Prerequisites / Notice | "Mathematical Optimization" (401-3901-00L) | |||||

401-4904-00L | Combinatorial Optimization | W | 6 credits | 2V + 1U | R. Zenklusen | |

Abstract | Combinatorial Optimization deals with efficiently finding a provably strong solution among a finite set of options. This course discusses key combinatorial structures and techniques to design efficient algorithms for combinatorial optimization problems. We put a strong emphasis on polyhedral methods, which proved to be a powerful and unifying tool throughout combinatorial optimization. | |||||

Objective | The goal of this lecture is to get a thorough understanding of various modern combinatorial optimization techniques with an emphasis on polyhedral approaches. Students will learn a general toolbox to tackle a wide range of combinatorial optimization problems. | |||||

Content | Key topics include: - Polyhedral descriptions; - Combinatorial uncrossing; - Ellipsoid method; - Equivalence between separation and optimization; - Design of efficient approximation algorithms for hard problems. | |||||

Lecture notes | Lecture notes will be available online. | |||||

Literature | - Bernhard Korte, Jens Vygen: Combinatorial Optimization. 5th edition, Springer, 2012. - Alexander Schrijver: Combinatorial Optimization: Polyhedra and Efficiency, Springer, 2003. This work has 3 volumes. | |||||

Prerequisites / Notice | Prior exposure to Linear Programming can greatly help the understanding of the material. We therefore recommend that students interested in Combinatorial Optimization get familiarized with Linear Programming before taking this lecture. | |||||

261-5110-00L | Optimization for Data Science | W | 8 credits | 3V + 2U + 2A | B. Gärtner, D. Steurer | |

Abstract | This course teaches an overview of modern optimization methods, with applications in particular for machine learning and data science. | |||||

Objective | Understanding the theoretical and practical aspects of relevant optimization methods used in data science. Learning general paradigms to deal with optimization problems arising in data science. | |||||

Content | This course teaches an overview of modern optimization methods, with applications in particular for machine learning and data science. In the first part of the course, we will discuss how classical first and second order methods such as gradient descent and Newton's method can be adapated to scale to large datasets, in theory and in practice. We also cover some new algorithms and paradigms that have been developed specifically in the context of data science. The emphasis is not so much on the application of these methods (many of which are covered in other courses), but on understanding and analyzing the methods themselves. In the second part, we discuss convex programming relaxations as a powerful and versatile paradigm for designing efficient algorithms to solve computational problems arising in data science. We will learn about this paradigm and develop a unified perspective on it through the lens of the sum-of-squares semidefinite programming hierarchy. As applications, we are discussing non-negative matrix factorization, compressed sensing and sparse linear regression, matrix completion and phase retrieval, as well as robust estimation. | |||||

Prerequisites / Notice | As background, we require material taught in the course "252-0209-00L Algorithms, Probability, and Computing". It is not necessary that participants have actually taken the course, but they should be prepared to catch up if necessary. | |||||

252-0526-00L | Statistical Learning Theory | W | 7 credits | 3V + 2U + 1A | J. M. Buhmann | |

Abstract | The course covers advanced methods of statistical learning : Statistical learning theory;variational methods and optimization, e.g., maximum entropy techniques, information bottleneck, deterministic and simulated annealing; clustering for vectorial, histogram and relational data; model selection; graphical models. | |||||

Objective | The course surveys recent methods of statistical learning. The fundamentals of machine learning as presented in the course "Introduction to Machine Learning" are expanded and in particular, the theory of statistical learning is discussed. | |||||

Content | # Theory of estimators: How can we measure the quality of a statistical estimator? We already discussed bias and variance of estimators very briefly, but the interesting part is yet to come. # Variational methods and optimization: We consider optimization approaches for problems where the optimizer is a probability distribution. Concepts we will discuss in this context include: * Maximum Entropy * Information Bottleneck * Deterministic Annealing # Clustering: The problem of sorting data into groups without using training samples. This requires a definition of ``similarity'' between data points and adequate optimization procedures. # Model selection: We have already discussed how to fit a model to a data set in ML I, which usually involved adjusting model parameters for a given type of model. Model selection refers to the question of how complex the chosen model should be. As we already know, simple and complex models both have advantages and drawbacks alike. # Statistical physics models: approaches for large systems approximate optimization, which originate in the statistical physics (free energy minimization applied to spin glasses and other models); sampling methods based on these models | |||||

Lecture notes | A draft of a script will be provided; transparencies of the lectures will be made available. | |||||

Literature | Hastie, Tibshirani, Friedman: The Elements of Statistical Learning, Springer, 2001. L. Devroye, L. Gyorfi, and G. Lugosi: A probabilistic theory of pattern recognition. Springer, New York, 1996 | |||||

Prerequisites / Notice | Requirements: knowledge of the Machine Learning course basic knowledge of statistics, interest in statistical methods. It is recommended that Introduction to Machine Learning (ML I) is taken first; but with a little extra effort Statistical Learning Theory can be followed without the introductory course. | |||||

636-0702-00L | Statistical Models in Computational Biology | W | 6 credits | 2V + 1U + 2A | N. Beerenwinkel | |

Abstract | The course offers an introduction to graphical models and their application to complex biological systems. Graphical models combine a statistical methodology with efficient algorithms for inference in settings of high dimension and uncertainty. The unifying graphical model framework is developed and used to examine several classical and topical computational biology methods. | |||||

Objective | The goal of this course is to establish the common language of graphical models for applications in computational biology and to see this methodology at work for several real-world data sets. | |||||

Content | Graphical models are a marriage between probability theory and graph theory. They combine the notion of probabilities with efficient algorithms for inference among many random variables. Graphical models play an important role in computational biology, because they explicitly address two features that are inherent to biological systems: complexity and uncertainty. We will develop the basic theory and the common underlying formalism of graphical models and discuss several computational biology applications. Topics covered include conditional independence, Bayesian networks, Markov random fields, Gaussian graphical models, EM algorithm, junction tree algorithm, model selection, Dirichlet process mixture, causality, the pair hidden Markov model for sequence alignment, probabilistic phylogenetic models, phylo-HMMs, microarray experiments and gene regulatory networks, protein interaction networks, learning from perturbation experiments, time series data and dynamic Bayesian networks. Some of the biological applications will be explored in small data analysis problems as part of the exercises. | |||||

Lecture notes | no | |||||

Literature | - Airoldi EM (2007) Getting started in probabilistic graphical models. PLoS Comput Biol 3(12): e252. doi:10.1371/journal.pcbi.0030252 - Bishop CM. Pattern Recognition and Machine Learning. Springer, 2007. - Durbin R, Eddy S, Krogh A, Mitchinson G. Biological Sequence Analysis. Cambridge university Press, 2004 | |||||

701-0104-00L | Statistical Modelling of Spatial Data | W | 3 credits | 2G | A. J. Papritz | |

Abstract | In environmental sciences one often deals with spatial data. 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 analyses. | |||||

Objective | The course will provide an overview of the basic concepts and stochastic models that are used to model spatial data. In addition, participants will learn a number of geostatistical techniques and acquire familiarity with R software that is useful for analyzing 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 linear 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 solutions to them will be provided. | |||||

Literature | P.J. Diggle & P.J. Ribeiro Jr. 2007. Model-based Geostatistics. Springer. Bivand, R. S., Pebesma, E. J. & Gómez-Rubio, V. 2013. Applied Spatial Data Analysis with R. Springer. | |||||

Prerequisites / Notice | Familiarity with linear regression analysis (e.g. equivalent to the first part of the course 401-0649-00L Applied Statistical Regression) and with the software R (e.g. 401-6215-00L Using R for Data Analysis and Graphics (Part I), 401-6217-00L Using R for Data Analysis and Graphics (Part II)) are required for attending the course. | |||||

401-6222-00L | Robust and Nonlinear Regression Does not take place this semester. | W | 2 credits | 1V + 1U | ||

Abstract | In a first part, the basic ideas of robust fitting techniques are explained theoretically and practically using regression models and explorative multivariate analysis. The second part addresses the challenges of fitting nonlinear regression functions and finding reliable confidence intervals. | |||||

Objective | Participants are familiar with common robust fitting methods for the linear regression models as well as for exploratory multivariate analysis and are able to assess their suitability for the data at hand. They know the challenges that arise in fitting of nonlinear regression functions, and know the difference between classical and profile based methods to determine confidence intervals. They can apply the discussed methods in practise by using the statistics software R. | |||||

Content | Robust fitting: influence function, breakdown point, regression M-estimation, regression MM-estimation, robust inference, covariance estimation with high breakdown point, application in principal component analysis and linear discriminant analysis. Nonlinear regression: the nonlinear regression model, estimation methods, approximate tests and confidence intervals, estimation methods, profile t plot, profile traces, parameter transformation, prediction and calibration | |||||

Lecture notes | Lecture notes are available | |||||

Prerequisites / Notice | It is a block course on three Mondays in June |

- Page 1 of 2 All