# Search result: Catalogue data in Spring Semester 2020

Mathematics Master | ||||||

Electives For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields. | ||||||

Electives: Applied Mathematics and Further Application-Oriented Fields ¬ | ||||||

Selection: Probability Theory, Statistics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-4605-20L | Selected Topics in Probability | W | 4 credits | 2V | A.‑S. Sznitman | |

Abstract | This course will discuss some questions of current interest in probability theory. Among examples of possible subjects are for instance topics in random media, large deviations, random walks on graphs, branching random walks, random trees, percolation, concentration of measures, large random matrices, stochastic calculus, stochastic partial differential equations. | |||||

Objective | This course will discuss some questions of current interest in probability theory. Among examples of possible subjects are for instance topics in random media, large deviations, random walks on graphs, branching random walks, random trees, percolation, concentration of measures, large random matrices, stochastic calculus, stochastic partial differential equations. | |||||

Prerequisites / Notice | Lecture Probability Theory. | |||||

401-4626-00L | Advanced Statistical Modelling: Mixed Models | W | 4 credits | 2V | M. Mächler | |

Abstract | Mixed Models = (*| generalized| non-) linear Mixed-effects Models, extend traditional regression models by adding "random effect" terms. In applications, such models are called "hierarchical models", "repeated measures" or "split plot designs". Mixed models are widely used and appropriate in an aera of complex data measured from living creatures from biology to human sciences. | |||||

Objective | - Becoming aware how mixed models are more realistic and more powerful in many cases than traditional ("fixed-effects only") regression models. - Learning to fit such models to data correctly, critically interpreting results for such model fits, and hence learning to work the creative cycle of responsible statistical data analysis: "fit -> interpret & diagnose -> modify the fit -> interpret & ...." - Becoming aware of computational and methodological limitations of these models, even when using state-of-the art software. | |||||

Content | The lecture will build on various examples, use R and notably the `lme4` package, to illustrate concepts. The relevant R scripts are made available online. Inference (significance of factors, confidence intervals) will focus on the more realistic *un*balanced situation where classical (ANOVA, sum of squares etc) methods are known to be deficient. Hence, Maximum Likelihood (ML) and its variant, "REML", will be used for estimation and inference. | |||||

Lecture notes | We will work with an unfinished book proposal from Prof Douglas Bates, Wisconsin, USA which itself is a mixture of theory and worked R code examples. These lecture notes and all R scripts are made available from Link | |||||

Literature | (see web page and lecture notes) | |||||

Prerequisites / Notice | - We assume a good working knowledge about multiple linear regression ("the general linear model') and an intermediate (not beginner's) knowledge about model based statistics (estimation, confidence intervals,..). Typically this means at least two classes of (math based) statistics, say 1. Intro to probability and statistics 2. (Applied) regression including Matrix-Vector notation Y = X b + E - Basic (1 semester) "Matrix calculus" / linear algebra is also assumed. - If familiarity with [R](Link) is not given, it should be acquired during the course (by the student on own initiative). | |||||

401-4627-00L | Empirical Process Theory and Applications | 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. | |||||

401-4632-15L | 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 | |||||

401-6102-00L | Multivariate StatisticsDoes not take place this semester. | W | 4 credits | 2G | not available | |

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. | |||||

401-4604-20L | NCCR SwissMAP – Master Class in Mathematical Physics: Minicourse "Percolation Theory" | W | 2 credits | 2G | V. Tassion | |

Abstract | ||||||

Objective | ||||||

Literature | "Percolation" by Geoffrey Grimmett. " Introduction to percolation theory" Lecture notes by H. Duminil-Copin. | |||||

Prerequisites / Notice | Probability Theory |

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