Suchergebnis: Katalogdaten im Herbstsemester 2017
Statistik Master Die hier aufgelisteten Lehrveranstaltungen gehören zum Curriculum des Master-Studiengangs Statistik. Die entsprechenden KP gelten nicht als Mobilitäts-KP, auch wenn gewisse Lerneinheiten nicht an der ETH Zürich belegt werden können. | ||||||
Vertiefungs- und Wahlfächer | ||||||
Statistische und mathematische Fächer | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
---|---|---|---|---|---|---|
401-3601-00L | Probability Theory Höchstens eines der drei Bachelor-Kernfächer 401-3461-00L Funktionalanalysis I / Functional Analysis I 401-3531-00L Differentialgeometrie I / Differential Geometry I 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory ist im Master-Studiengang Mathematik anrechenbar. | W | 10 KP | 4V + 1U | A.‑S. Sznitman | |
Kurzbeschreibung | Basics of probability theory and the theory of stochastic processes in discrete time | |||||
Lernziel | 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. | |||||
Inhalt | 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. | |||||
Skript | available, will be sold in the course | |||||
Literatur | 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 Statistics Findet dieses Semester nicht statt. | W | 4 KP | 2V | P. L. Bühlmann | |
Kurzbeschreibung | "High-Dimensional Statistics" deals with modern methods and theory for statistical inference when the number of unknown parameters is of much larger order than sample size. Statistical estimation and algorithms for complex models and aspects of multiple testing will be discussed. | |||||
Lernziel | Knowledge of methods and basic theory for high-dimensional statistical inference | |||||
Inhalt | 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 | |||||
Literatur | 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. | |||||
Voraussetzungen / Besonderes | 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 Findet dieses Semester nicht statt. | W | 5 KP | 3G | ||
Kurzbeschreibung | This course provides an introduction to statistical Monte Carlo methods. This includes applications of simulations in various fields (Bayesian statistics, statistical mechanics, operations research, financial mathematics), algorithms for the generation of random variables (accept-reject, importance sampling), estimating the precision, variance reduction, introduction to Markov chain Monte Carlo. | |||||
Lernziel | Stochastic simulation (also called Monte Carlo method) is the experimental analysis of a stochastic model by implementing it on a computer. Probabilities and expected values can be approximated by averaging simulated values, and the central limit theorem gives an estimate of the error of this approximation. The course shows examples of the many applications of stochastic simulation and explains different algorithms used for simulation. These algorithms are illustrated with the statistical software R. | |||||
Inhalt | Examples of simulations in different fields (computer science, statistics, statistical mechanics, operations research, financial mathematics). Generation of uniform random variables. Generation of random variables with arbitrary distributions (quantile transform, accept-reject, importance sampling), simulation of Gaussian processes and diffusions. The precision of simulations, methods for variance reduction. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC). | |||||
Skript | A script will be available in English. | |||||
Literatur | 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). | |||||
Voraussetzungen / Besonderes | Familiarity with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed. | |||||
401-4619-67L | Advanced Topics in Computational Statistics | W | 4 KP | 2V | N. Meinshausen | |
Kurzbeschreibung | This lecture covers selected advanced topics in computational statistics. This year the focus will be on graphical modelling. | |||||
Lernziel | Students learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes. | |||||
Inhalt | 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 | |||||
Voraussetzungen / Besonderes | 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 KP | 2V + 1U | I. Flückiger | |
Kurzbeschreibung | 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. | |||||
Lernziel | 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. | |||||
Inhalt | Framing the Business Problem Framing the Analytics Problem Data Methodology Model Building Deployment Model Lifecycle Soft Skills for the Statistical/Mathematical Professional | |||||
Skript | Lecture Notes will be available. | |||||
Voraussetzungen / Besonderes | Prerequisites: Basic statistics and probability theory and regression | |||||
401-6217-00L | Using R for Data Analysis and Graphics (Part II) | W | 1.5 KP | 1G | A. Drewek, M. Mächler | |
Kurzbeschreibung | 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. | |||||
Lernziel | The students will be able to use the software R efficiently for data analysis. | |||||
Inhalt | The course provides the second part of an introduction to the statistical software R 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 | |||||
Skript | An Introduction to R. Link | |||||
Voraussetzungen / Besonderes | 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 Please login (with your ETH (or other University) username+password) at Link Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration. | |||||
401-4637-67L | On Hypothesis Testing | W | 4 KP | 2V | F. Balabdaoui | |
Kurzbeschreibung | This course is a review of the main results in decision theory. | |||||
Lernziel | The goal of this course is to present a review for the most fundamental results in statistical testing. This entails reviewing the Neyman-Pearson Lemma for simple hypotheses and the Karlin-Rubin Theorem for monotone likelihood ratio parametric families. The students will also encounter the important concept of p-values and their use in some multiple testing situations. Further methods for constructing tests will be also presented including likelihood ratio and chi-square tests. Some non-parametric tests will be reviewed such as the Kolmogorov goodness-of-fit test and the two sample Wilcoxon rank test. The most important theoretical results will reproved and also illustrated via different examples. Four sessions of exercises will be scheduled (the students will be handed in an exercise sheet a week before discussing solutions in class). | |||||
Literatur | - Statistical Inference (Casella & Berger) - Testing Statistical Hypotheses (Lehmann and Romano) | |||||
401-0627-00L | Smoothing and Nonparametric Regression with Examples | W | 4 KP | 2G | S. Beran-Ghosh | |
Kurzbeschreibung | Starting with an overview of selected results from parametric inference, kernel smoothing (including local polynomials) 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. | |||||
Lernziel | 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. | |||||
Inhalt | Rough Outline: - Parametric estimation methods: selection of important results o Maximum likelihood o 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. | |||||
Skript | Brief summaries or outlines of some of the lecture material will be posted at Link (click on "ETH Course" in the left panel). 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. | |||||
Literatur | 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. - Kernel Smoothing, by M.P. Wand and M.C. Jones, Chapman and Hall. - Local polynomial modelling and its applications, by J. Fan and I. Gijbels, Chapman & Hall. - Nonparametric Simple Regression, by J. Fox, Sage Publications. - Applied Smoothing Techniques for Data Analysis: the Kernel Approach With S-Plus Illustrations, by A.W. Bowman, A. Azzalini, Oxford University Press. Additional references will be given out in the lectures. | |||||
Voraussetzungen / Besonderes | Prerequisites: A background in Linear Algebra, Calculus, Probability & Statistical Inference including Estimation and Testing. | |||||
401-6201-00L | Nonparametric and Resampling Methods Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an Link. Die Kanzlei wird anschliessend die Belegung vornehmen. | W | 2 KP | 2G | L. Meier, D. Kuonen | |
Kurzbeschreibung | Nonparametric tests, randomization tests, jackknife and bootstrap, as well as asymptotic properties of estimators. | |||||
Lernziel | For classical parametric models there exist optimal statistical estimators and test statistics whose distributions can often be determined exactly. The methods covered in this course allow for finding statistical procedures for more general models and to derive exact or approximate distributions of complicated estimators and test statistics. | |||||
Inhalt | Nonparametric tests, randomization tests, jackknife and bootstrap, as well as asymptotic properties of estimators. | |||||
Voraussetzungen / Besonderes | This course is part of the programme for the certificate and diploma in Advanced Studies in Applied Statistics. It is given every second year in the winter semester break. | |||||
401-6221-00L | Nichtparametrische Regression Findet dieses Semester nicht statt. Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an Link. Die Kanzlei wird anschliessend die Belegung vornehmen. | W | 1 KP | 1G | ||
Kurzbeschreibung | Fokus ist die nichtparametrische Schätzung von Wahrscheinlichkeitsdichten und Regressionsfunktionen. Diese neueren Methoden verzichten auf einschränkende Modellannahmen wie 'lineare Funktion'. Sie benötigen eine Gewichtsfunktion und einen Glättungsparameter. Schwerpunkt ist eine Dimension, mehrere Dimensionen und Stichproben von Kurven werden kurz behandelt. Übungen am Computer. | |||||
Lernziel | Kenntnisse der Schätzung von Wahrscheinlichkeitsdichten und Regressionsfunktionen mittels verschiedener statistischer Methoden. Verständnis für die Wahl der Gewichtsfunktion und des Glättungsparameters, auch automatisch. Praktische Anwendung auf Datensätze am Computer. | |||||
401-6233-00L | Spatial Statistics Findet dieses Semester nicht statt. Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an Link. Die Kanzlei wird anschliessend die Belegung vornehmen. | W | 1 KP | 1G | ||
Kurzbeschreibung | 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. | |||||
Lernziel | 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. | |||||
Inhalt | 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. | |||||
Skript | Slides, descriptions of the problems for the data analyses and worked-out solutions to them will be provided. | |||||
Literatur | P.J. Diggle & P.J. Ribeiro Jr. 2007. Model-based Geostatistics. Springer | |||||
263-5200-00L | Data Mining: Learning from Large Data Sets | W | 4 KP | 2V + 1U | A. Krause, Y. Levy | |
Kurzbeschreibung | Many scientific and commercial applications require insights from massive, high-dimensional data sets. This courses introduces principled, state-of-the-art techniques from statistics, algorithms and discrete and convex optimization for learning from such large data sets. The course both covers theoretical foundations and practical applications. | |||||
Lernziel | Many scientific and commercial applications require us to obtain insights from massive, high-dimensional data sets. In this graduate-level course, we will study principled, state-of-the-art techniques from statistics, algorithms and discrete and convex optimization for learning from such large data sets. The course will both cover theoretical foundations and practical applications. | |||||
Inhalt | Topics covered: - Dealing with large data (Data centers; Map-Reduce/Hadoop; Amazon Mechanical Turk) - Fast nearest neighbor methods (Shingling, locality sensitive hashing) - Online learning (Online optimization and regret minimization, online convex programming, applications to large-scale Support Vector Machines) - Multi-armed bandits (exploration-exploitation tradeoffs, applications to online advertising and relevance feedback) - Active learning (uncertainty sampling, pool-based methods, label complexity) - Dimension reduction (random projections, nonlinear methods) - Data streams (Sketches, coresets, applications to online clustering) - Recommender systems | |||||
Voraussetzungen / Besonderes | Prerequisites: Solid basic knowledge in statistics, algorithms and programming. Background in machine learning is helpful but not required. | |||||
401-6245-00L | Data-Mining Findet dieses Semester nicht statt. Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an Link. Die Kanzlei wird anschliessend die Belegung vornehmen. | W | 1 KP | 1G | ||
Kurzbeschreibung | Block über "Prognoseprobleme", bzw. "Supervised Learning" Teil 1, Klassifikation: logistische Regression, Lineare/Quadratische Diskriminanzanalyse, Bayes-Klassifikator; additive & Baummodelle, weitere flexible ("nichtparametrische") Methoden. Teil 2, Flexible Vorhersage: Additive Modelle, MARS, Y-Transformations-Modelle (ACE,AVAS); Projection Pursuit Regression (PPR), Neuronale Netze. | |||||
Lernziel | ||||||
Inhalt | Aus dem weiten Feld des "Data Mining" behandeln wir in diesem Block nur sogenannte "Prognoseprobleme", bzw. "Supervised Learning". Teil 1, Klassifikation, repetiert logistische Regression und Lineare / Quadratische Diskriminanzanalyse (LDA/QDA), und erweitert diese (im Rahmen des "Bayes-Klassifikators") auf (generalisierte) additive ("GAM") und Baummodelle ("CART"), und (summarisch/kurz) auf weitere flexible ("nichtparametrische") Methoden. Teil 2, Flexible Vorhersage (kontinuierliche oder Klassen-Zielvariable) umfasst Additive Modelle, MARS, Y-Transformations-Modelle (ACE, AVAS); Projection Pursuit Regression (PPR), Neuronale Netze. | |||||
Skript | Grundlage des Kurses ist das Skript. | |||||
Voraussetzungen / Besonderes | Die Uebungen werden ausschliesslich mit der (Free, open source) Software "R" (Link) durchgeführt, womit am Schluss auch eine "Schnellübung" als Schlussprüfung stattfindet. | |||||
401-6289-00L | Stichproben-Erhebungen Findet dieses Semester nicht statt. Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an Link. Die Kanzlei wird anschliessend die Belegung vornehmen. | W | 2 KP | 1G | ||
Kurzbeschreibung | Die Elemente einer Stichproben-Erhebung werden erklärt. Die wichtigsten klassischen Stichprobenpläne (Einfach und geschichtete Zufallsstichprobe) mit ihren Schätzern sowie Schätzverfahren mit Hilfsinformationen und der Horvitz-Thompson Schätzer werden eingeführt. Datenaufbereitung, Antwortausfälle und deren Behandlung, Varianzschätzungen sowie Analysen von Stichprobendaten werden diskutiert. | |||||
Lernziel | Kenntnis der Elemente und des Ablaufs einer Stichprobenerhebung. Verständnis für das Paradigma der Zufallsstichproben. Kenntnis der einfachen und geschichteten Stichproben-Strategien und Fähigkeit die entsprechenden Methoden anzuwenden. Kenntnis von weiterführenden Methoden für Schätzverfahren, Datenaufbereitung und Analysen. | |||||
401-3628-14L | Bayesian Statistics | W | 4 KP | 2V | F. Sigrist | |
Kurzbeschreibung | Introduction to the Bayesian approach to statistics: Decision theory, prior distributions, hierarchical Bayes models, Bayesian tests and model selection, empirical Bayes, computational methods, Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods. | |||||
Lernziel | Students understand the conceptual ideas behind Bayesian statistics and are familiar with common techniques used in Bayesian data analysis. | |||||
Inhalt | Topics that we will discuss are: Difference between the frequentist and Bayesian approach (decision theory, principles), priors (conjugate priors, Jeffreys priors), tests and model selection (Bayes factors, hyper-g priors in regression),hierarchical models and empirical Bayes methods, computational methods (Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods) | |||||
Skript | A script will be available in English. | |||||
Literatur | 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. | |||||
Voraussetzungen / Besonderes | 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. | |||||
401-6273-00L | Bayes-Methoden Findet dieses Semester nicht statt. Fachstudierende "Universität Zürich (UZH)" im Master-Studiengang Biostatistik von der UZH können diese Lerneinheit nicht direkt in myStudies belegen. Leiten Sie die schriftliche Teilnahmebewilligung des Dozenten an die Kanzlei weiter. Als Einverständnis gilt auch ein direktes E-Mail des Dozenten an Link. Die Kanzlei wird anschliessend die Belegung vornehmen. | W | 2 KP | 2G | ||
Kurzbeschreibung | Die Bayes-Statistik ist deshalb attraktiv, da sie ermöglicht, Entscheidungen unter Ungewissheit zu treffen, wo die klassische frequentische Statistik versagt! Der Kurs vermittelt einen Einstieg in die Bayes-Statistik, ist mathematisch nur moderat anspruchsvoll, verlangt aber ein gewisses Umdenken, das nicht unterschätzt werden darf. | |||||
Lernziel | ||||||
Inhalt | Bedingte Wahrscheinlichkeit; Bayes-Inferenz (konjugierte Verteilungen, HPD-Bereiche, lineare und empirische Verfahren), Bestimmung der a-posteriori Verteilung durch Simulation (Markov Chain Monte-Carlo mit R2Winbugs), Einführung in mehrstufige hierarchische Modelle. | |||||
Literatur | Gelman A., Carlin J.B., Stern H.S. and D.B. Rubin, Bayesian Data Analysis, Chapman and Hall, 2nd Edition, 2004. Kruschke, J.K., Doing Bayesian Data Analysis, Elsevier2011. | |||||
Voraussetzungen / Besonderes | Voraussetzung: Statistische Grundkenntnisse ; Kenntnis von R. | |||||
401-3913-01L | Mathematical Foundations for Finance | W | 4 KP | 3V + 2U | M. Schweizer, E. W. Farkas | |
Kurzbeschreibung | First introduction to main modelling ideas and mathematical tools from mathematical finance | |||||
Lernziel | This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It mainly aims at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced course) may also find this of interest.. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs. | |||||
Inhalt | Topics to be covered include - financial market models in finite discrete time - absence of arbitrage and martingale measures - valuation and hedging in complete markets - basics about Brownian motion - stochastic integration - stochastic calculus: Itô's formula, Girsanov transformation, Itô's representation theorem - Black-Scholes formula | |||||
Skript | Lecture notes will be sold at the beginning of the course. | |||||
Literatur | Lecture notes will be sold at the beginning of the course. Additional (background) references are given there. | |||||
Voraussetzungen / Besonderes | Prerequisites: Results and facts from probability theory as in the book "Probability Essentials" by J. Jacod and P. Protter will be used freely. Especially participants without a direct mathematics background are strongly advised to familiarise themselves with those tools before (or very quickly during) the course. (A possible alternative to the above English textbook are the (German) lecture notes for the standard course "Wahrscheinlichkeitstheorie".) For those who are not sure about their background, we suggest to look at the exercises in Chapters 8, 9, 22-25, 28 of the Jacod/Protter book. If these pose problems, you will have a hard time during the course. So be prepared. | |||||
401-3901-00L | Mathematical Optimization | W | 11 KP | 4V + 2U | R. Weismantel | |
Kurzbeschreibung | Mathematical treatment of diverse optimization techniques. | |||||
Lernziel | Advanced optimization theory and algorithms. | |||||
Inhalt | 1) Linear optimization: The geometry of linear programming, the simplex method for solving linear programming problems, Farkas' Lemma and infeasibility certificates, duality theory of linear programming. 2) Nonlinear optimization: Lagrange relaxation techniques, Newton method and gradient schemes for convex optimization. 3) Integer optimization: Ties between linear and integer optimization, total unimodularity, complexity theory, cutting plane theory. 4) Combinatorial optimization: Network flow problems, structural results and algorithms for matroids, matchings, and, more generally, independence systems. | |||||
Literatur | 1) D. Bertsimas & R. Weismantel, "Optimization over Integers". Dynamic Ideas, 2005. 2) A. Schrijver, "Theory of Linear and Integer Programming". John Wiley, 1986. 3) D. Bertsimas & J.N. Tsitsiklis, "Introduction to Linear Optimization". Athena Scientific, 1997. 4) Y. Nesterov, "Introductory Lectures on Convex Optimization: a Basic Course". Kluwer Academic Publishers, 2003. 5) C.H. Papadimitriou, "Combinatorial Optimization". Prentice-Hall Inc., 1982. | |||||
Voraussetzungen / Besonderes | Linear algebra. | |||||
401-6282-00L | Statistical Analysis of High-Throughput Genomic and Transcriptomic Data (University of Zurich) Der Kurs muss direkt an der UZH belegt werden. UZH Modulkürzel: STA426 Beachten Sie die Einschreibungstermine an der UZH: Link | W | 5 KP | 3G | H. Rehrauer, M. Robinson | |
Kurzbeschreibung | A range of topics will be covered, including basic molecular biology, genomics technologies and in particular, a wide range of statistical and computational methods that have been used in the analysis of DNA microarray and high throughput sequencing experiments. | |||||
Lernziel | -Understand the fundamental "scientific process" in the field of Statistical Bioinformatics -Be equipped with the skills/tools to preprocess genomic data (Unix, Bioconductor, mapping, etc.) and ensure reproducible research (Sweave) -Have a general knowledge of the types of data and biological applications encountered with microarray and sequencing data -Have the general knowledge of the range of statistical methods that get used with microarray and sequencing data -Gain the ability to apply statistical methods/knowledge/software to a collaborative biological project -Gain the ability to critical assess the statistical bioinformatics literature -Write a coherent summary of a bioinformatics problem and its solution in statistical terms | |||||
Inhalt | Lectures will include: microarray preprocessing; normalization; exploratory data analysis techniques such as clustering, PCA and multidimensional scaling; Controlling error rates of statistical tests (FPR versus FDR versus FWER); limma (linear models for microarray analysis); mapping algorithms (for RNA/ChIP-seq); RNA-seq quantification; statistical analyses for differential count data; isoform switching; epigenomics data including DNA methylation; gene set analyses; classification | |||||
Skript | Lecture notes, published manuscripts | |||||
Voraussetzungen / Besonderes | Prerequisites: Basic knowlegde of the programming language R, sufficient knowledge in statistics Former course title: Statistical Methods for the Analysis of Microarray and Short-Read Sequencing Data | |||||
401-8625-00L | Clinical Biostatistics (University of Zurich) Der Kurs muss direkt an der UZH belegt werden. UZH Modulkürzel: STA404 Beachten Sie die Einschreibungstermine an der UZH: Link | W | 5 KP | 4G | Uni-Dozierende | |
Kurzbeschreibung | Discussion of the different statistical methods that are used in clinical research. | |||||
Lernziel | ||||||
Inhalt | Discussion of the different statistical methods that are used in clinical research. Among other subjects the following will be introduced: sample size calculation, randomization and blinding, analysis of clinical trials (parallel groups design, analysis of covariance, crossover design, equivalence studies), intention-to-treat analysis, multiple testing, group sequential methods, adaptive designs, diagnostic studies, and agreement studies. | |||||
Literatur | - Matthews, J. N. S. (2006). Introduction to Randomized Controlled Clinical Trials. Chapman & Hall/CRC Texts in Statistical Science. - Cook, T. D. and DeMets, L. D. (2008). Introduction to Statistical Methods for Clinical Trials. Chapman & Hall/CRC Texts in Statistical Science. - Pepe, M. (2003). The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press. - Schumacher, M. and Schulgen, G. (2008). Methodik klinischer Studien. Springer, Berlin. | |||||
Voraussetzungen / Besonderes | Basic knowlegde of the programming language R, sufficient knowledge in calculus, linear algebra, probability, statistics |
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