Suchergebnis: Katalogdaten im Herbstsemester 2018

Mathematik Master Information
Wahlfächer
Für das Master-Diplom in Angewandter Mathematik ist die folgende Zusatzbedingung (nicht in myStudies ersichtlich) zu beachten: Mindestens 15 KP der erforderlichen 28 KP aus Kern- und Wahlfächern müssen aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten stammen.
Wahlfächer aus Bereichen der reinen Mathematik
Auswahl: Algebra, Zahlentheorie, Topologie, diskrete Mathematik, Logik
NummerTitelTypECTSUmfangDozierende
401-3113-68LExponential Sums over Finite Fields Information W8 KP4GE. Kowalski
KurzbeschreibungExponential sums over finite fields arise in many problems of number theory. We will discuss the elementary aspects of the theory (centered on the Riemann Hypothesis for curves, following Stepanov's method) and survey the formalism arising from Deligne's general form of the Riemann Hypothesis over finite fields. We will then discuss various applications, especially in analytic number theory.
LernzielThe goal is to understand both the basic results on exponential sums in one variable, and the general formalism of Deligne and Katz that underlies estimates for much more general types of exponential sums, including the "trace functions" over finite fields.
InhaltExamples of elementary exponential sums
The Riemann Hypothesis for curves and its applications
Definition of trace functions over finite fields
The formalism of the Riemann Hypothesis of Deligne
Selected applications
SkriptLectures notes from various sources will be provided
LiteraturKowalski, "Exponential sums over finite fields, I: elementary methods:
Iwaniec-Kowalski, "Analytic number theory", chapter 11
Fouvry, Kowalski and Michel, "Trace functions over finite fields and their applications"
401-3100-68LIntroduction to Analytic Number Theory Information W8 KP4GI. N. Petrow
KurzbeschreibungThis course is an introduction to classical multiplicative analytic number theory. The main object of study is the distribution of the prime numbers in the integers. We will study arithmetic functions and learn the basic tools for manipulating and calculating their averages. We will make use of generating series and tools from complex analysis.
LernzielThe main goal for the course is to prove the prime number theorem in arithmetic progressions: If gcd(a,q)=1, then the number of primes p = a mod q with p<x is approximately (1/phi(q))*(x/log x), as x tends to infinity, where phi(q) is the Euler totient function.
InhaltDeveloping the necessary techniques and theory to prove the prime number theorem in arithmetic progressions will lead us to the study of prime numbers by Chebyshev's method, to study techniques for summing arithmetic functions by Dirichlet series, multiplicative functions, L-series, characters of a finite abelian group, theory of integral functions, and a detailed study of the Riemann zeta function and Dirichlet's L-functions.
SkriptLecture notes will be provided for the course.
LiteraturMultiplicative Number Theory by Harold Davenport
Multiplicative Number Theory I. Classical Theory by Hugh L. Montgomery and Robert C. Vaughan
Analytic Number Theory by Henryk Iwaniec and Emmanuel Kowalski
Voraussetzungen / BesonderesComplex analysis
Group theory
Linear algebra
Familiarity with the Fourier transform and Fourier series preferable but not required.
401-3059-00LKombinatorik II
Findet dieses Semester nicht statt.
W4 KP2GN. Hungerbühler
KurzbeschreibungDer Kurs Kombinatorik I und II ist eine Einführung in die abzählende Kombinatorik.
LernzielDie Studierenden sind in der Lage, kombinatorische Probleme einzuordnen und die adaequaten Techniken zu deren Loesung anzuwenden.
InhaltInhalt der Vorlesungen Kombinatorik I und II: Kongruenztransformationen der Ebene, Symmetriegruppen von geometrischen Figuren, Eulersche Funktion, Cayley-Graphen, formale Potenzreihen, Permutationsgruppen, Zyklen, Lemma von Burnside, Zyklenzeiger, Saetze von Polya, Anwendung auf die Graphentheorie und isomere Molekuele.
Auswahl: Geometrie
NummerTitelTypECTSUmfangDozierende
401-3057-00LEndliche Geometrien IIW4 KP2GN. Hungerbühler
KurzbeschreibungEndliche Geometrien I, II: Endliche Geometrien verbinden Aspekte der Geometrie mit solchen der diskreten Mathematik und der Algebra endlicher Körper. Inbesondere werden Modelle der Inzidenzaxiome konstruiert und Schliessungssätze der Geometrie untersucht. Anwendungen liegen im Bereich der Statistik, der Theorie der Blockpläne und der Konstruktion orthogonaler lateinischer Quadrate.
LernzielEndliche Geometrien I, II: Die Studierenden sind in der Lage, Modelle endlicher Geometrien zu konstruieren und zu analysieren. Sie kennen die Schliessungssätze der Inzidenzgeometrie und können mit Hilfe der Theorie statistische Tests entwerfen sowie orthogonale lateinische Quadrate konstruieren. Sie sind vertraut mit Elementen der Theorie der Blockpläne.
InhaltEndliche Geometrien I, II: Endliche Körper, Polynomringe, endliche affine Ebenen, Axiome der Inzidenzgeometrie, Eulersches Offiziersproblem, statistische Versuchsplanung, orthogonale lateinische Quadrate, Transformationen endlicher Ebenen, Schliessungsfiguren von Desargues und Pappus-Pascal, Hierarchie der Schliessungsfiguren, endliche Koordinatenebenen, Schiefkörper, endliche projektive Ebenen, Dualitätsprinzip, endliche Möbiusebenen, selbstkorrigierende Codes, Blockpläne
Literatur- Max Jeger, Endliche Geometrien, ETH Skript 1988

- Albrecht Beutelspacher: Einführung in die endliche Geometrie I,II. Bibliographisches Institut 1983

- Margaret Lynn Batten: Combinatorics of Finite Geometries. Cambridge University Press

- Dembowski: Finite Geometries.
401-3111-68LElliptische Kurven und KryptographieW8 KP3V + 1UL. Halbeisen
KurzbeschreibungIm ersten Teil der Vorlesung wird die algebraische Struktur von elliptischen
Kurven behandelt. Insbesondere wird der Satz von Mordell bewiesen. Im zweiten Teil der Vorlesung werden dann Anwendungen elliptischer Kurven in der Kryptographie gezeigt, wie z.B. der Diffie-Hellman-Schluesselaustausch.
LernzielRationale Punkte auf elliptischen Kurven, insbesondere Arithmetik auf elliptischen Kurven, Satz von Mordell, Kongruente Zahlen

Anwendungen der elliptischen Kurven in der Kryptographie, wie zum Beispiel Diffie-Hellman-Schluesselaustausch, Pollard-Rho-Methode
InhaltIm ersten Teil der Vorlesung wird die algebraische Struktur von elliptischen
Kurven behandelt und die Menge der rationalen Punkte auf elliptischen Kurven untersucht. Insbesondere wird mit Hilfe von Saetzen aus der Algebra wie auch aus der projektiven Geometrie gezeigt, dass die Menge der rationalen Punkte auf einer elliptischen Kurven unter einer bestimmten Operation eine endlich erzeugte abelsche Gruppe bildet. Zudem werden elliptische Kurven untersucht, welche mit rationalen, rechtwinkligen Dreiecken mit ganzzahligem Flaecheninhalt zusammenhaengen.

Im zweiten Teil der Vorlesung werden dann Anwendungen elliptischer Kurven in der Kryptographie gezeigt. Solche Anwendungen sind zum Beispiel ein auf
elliptischen Kurven basierendes Kryptosystem oder ein Algorithmus zur Faktorisierung grosser Zahlen.
LiteraturJoseph Silverman, John Tate: "Rational Points on Elliptic Curves", Undergraduate Texts in Mathematics, Springer-Verlag (1992)

Ian Blake, Gadiel Seroussi, Nigel Smart: "Elliptic Curves in Cryptography",
Lecture Notes Series 265, Cambridge University Press (2004)
Voraussetzungen / BesonderesVoraussgesetzt werden Algebra I und Grundbegriffe der projektiven Geometrie.
Auswahl: Analysis
NummerTitelTypECTSUmfangDozierende
401-4115-00LIntroduction to Geometric Measure TheoryW6 KP3VU. Lang
KurzbeschreibungIntroduction to Geometric Measure Theory from a metric viewpoint. Contents: Lipschitz maps, differentiability, area and coarea formula, rectifiable sets, introduction to the (de Rham-Federer-Fleming) theory of currents, currents in metric spaces after Ambrosio-Kirchheim, normal currents, relation to BV functions, slicing, compactness theorem for integral currents and applications.
Lernziel
InhaltExtendability and differentiability of Lipschitz maps, metric differentiability, rectifiable sets, approximate tangent spaces, area and coarea formula, brief survey of the (de Rham-Federer-Fleming) theory of currents, currents in metric spaces after Ambrosio-Kirchheim, currents with finite mass and normal currents, relation to BV functions, rectifiable and integral currents, slicing, compactness theorem for integral currents and applications.
Literatur- Pertti Mattila, Geometry of Sets and Measures in Euclidean Spaces, 1995
- Herbert Federer, Geometric Measure Theory, 1969
- Leon Simon, Introduction to Geometric Measure Theory, 2014, Link
- Luigi Ambrosio and Bernd Kirchheim, Currents in metric spaces, Acta math. 185 (2000), 1-80
- Urs Lang, Local currents in metric spaces, J. Geom. Anal. 21 (2011), 683-742
401-4463-62LFourier Analysis in Function Space TheoryW4 KP2VT. Rivière
KurzbeschreibungIn the most important part of the course, we will present the notion of Singular Integrals and Calderón-Zygmund theory as well as its application to the analysis of linear elliptic operators.
Lernziel
InhaltDuring the first lectures we will review the theory of tempered distributions and their Fourier transforms. We will go in particular through the notion of Fréchet spaces, Banach-Steinhaus for Fréchet spaces etc. We will then apply this theory to the Fourier characterization of Hilbert-Sobolev spaces.
In the second part of the course we will study fundamental pro­perties of the Hardy-Littlewood Maximal Function in relation with L^p spaces. We will then make a digression through the notion of Marcinkiewicz weak L^p spaces and Lorentz spaces. At this occa­sion we shall give in particular a proof of Aoki-Rolewicz theorem on the metrisability of quasi-normed spaces. We will introduce the preduals to the weak L^p spaces, the Lorentz L^{p',1} spaces as well as the general L^{p,q} spaces and show some applications of these dualities such as the improved Sobolev embeddings.
In the third part of the course, the most important one, we will present the notion of Singular Integrals and Calderón-Zygmund theory as well as its application to the analysis of linear elliptic operators.
This theory will naturally bring us, via the so called Littlewood-Paley decomposition, to the Fourier characterization of classical Hilbert and non Hilbert Function spaces which is one of the main goals of this course.
If time permits we shall present the notion of Paraproduct, Para­compositions and the use of Littlewood-Paley decomposition for estimating products and general non-linearities. We also hope to cover fundamental notions from integrability by compensation theory such as Coifman-Rochberg-Weiss commutator estimates and some of its applications to the analysis of PDE.
Literatur1) Elias M. Stein, "Singular Integrals and Differentiability Proper­ties of Functions" (PMS-30) Princeton University Press.
2) Javier Duoandikoetxea, "Fourier Analysis" AMS.
3) Loukas Grafakos, "Classical Fourier Analysis" GTM 249 Springer.
4) Loukas Grafakos, "Modern Fourier Analysis" GTM 250 Springer.
Voraussetzungen / BesonderesNotions from ETH courses in Measure Theory, Functional Analysis I and II (Fun­damental results in Banach and Hilbert Space theory, Fourier transform of L^2 Functions)
Auswahl: Weitere Gebiete
NummerTitelTypECTSUmfangDozierende
401-3502-68LReading Course Belegung eingeschränkt - Details anzeigen
DIE BELEGUNG ERFOLGT DURCH DAS STUDIENSEKRETARIAT.

Bitte schicken Sie ein E-Mail an das Studiensekretariat D-MATH <Link> mit folgenden Angaben:
1) welchen Reading Course (60, 90, 120 Arbeitsstunden entsprechend 2, 3, 4 ECTS-Kreditpunkten) Sie belegen möchten;
2) in welchem Semester;
3) für welchen Studiengang;
4) Ihr Name und Vorname;
5) Ihre Studierenden-Nummer;
6) der Name und Vorname des Betreuers/der Betreuerin des Reading Courses.
W2 KP4AProfessor/innen
KurzbeschreibungIn diesem Reading Course wird auf Eigeninitiative und auf individuelle Vereinbarung mit einem Dozenten/einer Dozentin hin ein Stoff durch eigenständiges Literaturstudium erarbeitet.
Lernziel
401-3503-68LReading Course Belegung eingeschränkt - Details anzeigen
DIE BELEGUNG ERFOLGT DURCH DAS STUDIENSEKRETARIAT.

Bitte schicken Sie ein E-Mail an das Studiensekretariat D-MATH <Link> mit folgenden Angaben:
1) welchen Reading Course (60, 90, 120 Arbeitsstunden entsprechend 2, 3, 4 ECTS-Kreditpunkten) Sie belegen möchten;
2) in welchem Semester;
3) für welchen Studiengang;
4) Ihr Name und Vorname;
5) Ihre Studierenden-Nummer;
6) der Name und Vorname des Betreuers/der Betreuerin des Reading Courses.
W3 KP6AProfessor/innen
KurzbeschreibungIn diesem Reading Course wird auf Eigeninitiative und auf individuelle Vereinbarung mit einem Dozenten/einer Dozentin hin ein Stoff durch eigenständiges Literaturstudium erarbeitet.
Lernziel
401-3504-68LReading Course Belegung eingeschränkt - Details anzeigen
DIE BELEGUNG ERFOLGT DURCH DAS STUDIENSEKRETARIAT.

Bitte schicken Sie ein E-Mail an das Studiensekretariat D-MATH <Link> mit folgenden Angaben:
1) welchen Reading Course (60, 90, 120 Arbeitsstunden entsprechend 2, 3, 4 ECTS-Kreditpunkten) Sie belegen möchten;
2) in welchem Semester;
3) für welchen Studiengang;
4) Ihr Name und Vorname;
5) Ihre Studierenden-Nummer;
6) der Name und Vorname des Betreuers/der Betreuerin des Reading Courses.
W4 KP9AProfessor/innen
KurzbeschreibungIn diesem Reading Course wird auf Eigeninitiative und auf individuelle Vereinbarung mit einem Dozenten/einer Dozentin hin ein Stoff durch eigenständiges Literaturstudium erarbeitet.
Lernziel
401-0000-00LCommunication in MathematicsW1 KP1VW. Merry
KurzbeschreibungDon't hide your Next Great Theorem behind bad writing.

This course teaches fundamental communication skills in mathematics: how to write clearly and how to structure mathematical content for different audiences, from theses, to preprints, to personal statements in applications.
LernzielKnowing how to present written mathematics in a structured and clear manner.
InhaltTopics covered include:

- How to write a thesis (more generally, a mathematics paper).
- Elementary LaTeX skills and language conventions.
- How to write a personal statement for Masters and PhD applications.
SkriptFull lecture notes will be made available on my website:

Link
Voraussetzungen / BesonderesThere are no formal mathematical prerequisites.
Wahlfächer aus Bereichen der angewandten Mathematik ...
vollständiger Titel:
Wahlfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten
Auswahl: Numerische Mathematik
NummerTitelTypECTSUmfangDozierende
401-4657-00LNumerical Analysis of Stochastic Ordinary Differential Equations Information
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
W6 KP3V + 1UA. Jentzen, L. Yaroslavtseva
KurzbeschreibungCourse on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.
LernzielThe aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.
InhaltGeneration of random numbers
Monte Carlo methods for the numerical integration of random variables
Stochastic processes and Brownian motion
Stochastic ordinary differential equations (SODEs)
Numerical approximations of SODEs
Applications to computational finance: Option valuation
SkriptLecture notes are available as a PDF file: see Learning materials.
LiteraturP. Glassermann:
Monte Carlo Methods in Financial Engineering.
Springer-Verlag, New York, 2004.

P. E. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations.
Springer-Verlag, Berlin, 1992.
Voraussetzungen / BesonderesPrerequisites:

Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.

a) mandatory courses:
Elementary Probability,
Probability Theory I.

b) recommended courses:
Stochastic Processes.

Start of lectures: Wednesday, September 19, 2018.

Date of the End-of-Semester examination: Wednesday, December 19, 2018, 13:00-15:00; students must arrive before 12:30 at ETH HG E 19.
Room for the End-of-Semester examination: ETH HG E 19.

Exam inspection: Tuesday, February 26, 2019,
12:00-13:00 at HG D 7.2.
Please bring your legi.
401-4785-00LMathematical and Computational Methods in PhotonicsW8 KP4GH. Ammari
KurzbeschreibungThe aim of this course is to review new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods used to address challenging problems in nanophotonics. The emphasis will be on analyzing plasmon resonant nanoparticles, super-focusing & super-resolution of electromagnetic waves, photonic crystals, electromagnetic cloaking, metamaterials, and metasurfaces
LernzielThe field of photonics encompasses the fundamental science of light propagation and interactions in complex structures, and its technological applications.

The recent advances in nanoscience present great challenges for the applied and computational mathematics community. In nanophotonics, the aim is to control, manipulate, reshape, guide, and focus electromagnetic waves at nanometer length scales, beyond the resolution limit. In particular, one wants to break the resolution limit by reducing the focal spot and confine light to length scales that are significantly smaller than half the wavelength.

Interactions between the field of photonics and mathematics has led to the emergence of a multitude of new and unique solutions in which today's conventional technologies are approaching their limits in terms of speed, capacity and accuracy. Light can be used for detection and measurement in a fast, sensitive and accurate manner, and thus photonics possesses a unique potential to revolutionize healthcare. Light-based technologies can be used effectively for the very early detection of diseases, with non-invasive imaging techniques or point-of-care applications. They are also instrumental in the analysis of processes at the molecular level, giving a greater understanding of the origin of diseases, and hence allowing prevention along with new treatments. Photonic technologies also play a major role in addressing the needs of our ageing society: from pace-makers to synthetic bones, and from endoscopes to the micro-cameras used in in-vivo processes. Furthermore, photonics are also used in advanced lighting technology, and in improving energy efficiency and quality. By using photonic media to control waves across a wide band of wavelengths, we have an unprecedented ability to fabricate new materials with specific microstructures.

The main objective in this course is to report on the use of sophisticated mathematics in diffractive optics, plasmonics, super-resolution, photonic crystals, and metamaterials for electromagnetic invisibility and cloaking. The book merges highly nontrivial multi-mathematics in order to make a breakthrough in the field of mathematical modelling, imaging, and optimal design of optical nanodevices and nanostructures capable of light enhancement, and of the focusing and guiding of light at a subwavelength scale. We demonstrate the power of layer potential techniques in solving challenging problems in photonics, when they are combined with asymptotic analysis and the elegant theory of Gohberg and Sigal on meromorphic operator-valued functions.

In this course we shall consider both analytical and computational matters in photonics. The issues we consider lead to the investigation of fundamental problems in various branches of mathematics. These include asymptotic analysis, spectral analysis, mathematical imaging, optimal design, stochastic modelling, and analysis of wave propagation phenomena. On the other hand, deriving mathematical foundations, and new and efficient computational frameworks and tools in photonics, requires a deep understanding of the different scales in the wave propagation problem, an accurate mathematical modelling of the nanodevices, and fine analysis of complex wave propagation phenomena. An emphasis is put on mathematically analyzing plasmon resonant nanoparticles, diffractive optics, photonic crystals, super-resolution, and metamaterials.
401-4357-68LOn Deep Artificial Neural Networks and Partial Differential Equations Information W4 KP2GA. Jentzen
KurzbeschreibungIn this lecture we rigorously analyse approximation capacities of deep artificial neural networks and prove that deep artificial neural networks do overcome the curse of dimensionality in the numerical approximation of solutions of partial differential equations (PDEs).
LernzielThe aim of this course is to teach the students a decent knowledge on deep artificial neural networks and their approximation capacities.
InhaltIn recent years deep artificial neural networks (DNNs) have very successfully been used in numerical simulations for a series of computational problems ranging from computer vision, image classification, speech recognition, and natural language processing to computational advertisement. Such numerical simulations indicate that deep artificial neural networks seem to admit the fundamental power to overcome the curse of dimensionality when approximating the high-dimensional functions appearing in the above named applications. In this lecture we rigorously analyse approximation capacities of deep artificial neural networks and prove that deep artificial neural networks do overcome the curse of dimensionality in the numerical approximation of solutions of partial differential equations (PDEs). In particular, this course includes (i) a rigorous mathematical introduction to artificial neural networks, (ii) an introduction to some partial differential equations, and (iii) results on approximation capacities of deep artificial neural networks.
SkriptLecture notes will be available as a PDF file.
LiteraturRelated literature:

* Arnulf Jentzen, Diyora Salimova, and Timo Welti,
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients.
arXiv:1809.07321 (2018), 48 pages. Available online at [Link].

* Philipp Grohs, Fabian Hornung, Arnulf Jentzen, and Philippe von Wurstemberger,
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations.
arXiv:1809.02362 (2018), 124 pages. Available online at [Link].

* Andrew R. Barron,
Universal approximation bounds for superpositions of a sigmoidal function.
IEEE Trans. Inform. Theory 39 (1993), no. 3, 930--945.
Voraussetzungen / BesonderesPrerequisites:
Analysis I and II, Elementary Probability Theory, and Measure Theory
401-4503-68LReading Course: Reduced Basis MethodsW4 KP2GR. Hiptmair
KurzbeschreibungReduced Basis Methods (RBM) allow the efficient repeated numerical soluton of parameter depedent differential equations, which arise, e.g., in PDE-constrained optimization, optimal control, inverse problems, and uncertainty quantification. This course introduces the mathematical foundations of RBM and discusses algorithmic and implementation aspects.
Lernziel* Knowledge about the main principles underlying RBMs
* Familiarity with algorithms for the construction of reduced bases
* Knowledge about the role of and techniques for a posteriori error estimation.
* Familiarity with some applications of RBMs.
LiteraturMain reference:
Hesthaven, Jan S.; Rozza, Gianluigi; Stamm, Benjamin, Certified reduced basis methods for parametrized partial differential equations. SpringerBriefs in Mathematics, 2016

Supplementary reference:
Quarteroni, Alfio; Manzoni, Andrea; Negri, Federico, Reduced basis methods for partial differential equations. An introduction. Unitext 92, Springer, Cham, 2016.
Voraussetzungen / BesonderesThis is a reading course, which will closely follow the book by J. Hesthaven, G. Rozza and B. Stamm. Participants are expected to study particular sections of the book every week, which will then be discussed during the course sessions.
Auswahl: Wahrscheinlichkeitstheorie, Statistik
NummerTitelTypECTSUmfangDozierende
401-4607-68LTopics on the Gaussian Free FieldW4 KP2VW. Werner
KurzbeschreibungWe will discuss various aspects and properties of the Gaussian Free Field.
Lernziel
InhaltTopics discussed will include:
- Discrete and continuous Gaussian Free Field
- Local sets.
- Relation to loop-soups.
- Uniform spanning trees.
401-4611-68LRegularity StructuresW6 KP3VJ. Teichmann
KurzbeschreibungWe develop the main tools of Martin Hairer's theory of regularity structures to solve singular stochastic partial differential equations in a pathwise way or addtionally by re-normalization techniques.
Lernziel
401-4619-67LAdvanced Topics in Computational Statistics
Findet dieses Semester nicht statt.
W4 KP2VN. Meinshausen
KurzbeschreibungThis lecture covers selected advanced topics in computational statistics. This year the focus will be on graphical modelling.
LernzielStudents learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes.
InhaltThe 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 / BesonderesWe assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics.
401-3628-14LBayesian Statistics
Findet dieses Semester nicht statt.
W4 KP2V
KurzbeschreibungIntroduction 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.
LernzielStudents understand the conceptual ideas behind Bayesian statistics and are familiar with common techniques used in Bayesian data analysis.
InhaltTopics 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)
SkriptA script will be available in English.
LiteraturChristian 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 / BesonderesFamiliarity 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.
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 KP2V + 1UL. Meier
KurzbeschreibungPrinciples 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.
LernzielParticipants 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.
InhaltPrinciples 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.
LiteraturG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Voraussetzungen / BesonderesThe 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.
  •  Seite  1  von  3 Nächste Seite Letzte Seite     Alle