Fagplan – ETH Zürich
401-3632-00L Computational Statistics (10 cred.) : Beregningskrevende stokastiske
metoder
Abstract
Objective
Content
"Computational Statistics" deals with modern methods of data analysis (aka "data
science") for prediction and inference. An overview of existing methodology is
provided and also by the exercises, the student is taught to choose among possible
models and about their algorithms and to validate them using graphical methods and
simulation based approaches.
Getting to know modern methods of data analysis for prediction and inference.
Learn to choose among possible models and about their algorithms.
Validate them using graphical methods and simulation based approaches.
Course Synopsis:
multiple regression, nonparametric methods for regression and classification (kernel
estimates, smoothing splines, regression and classification trees, additive models,
projection pursuit, neural nets, ridging and the lasso, boosting). Problems of
interpretation, reliable prediction and the curse of dimensionality are dealt with using
resampling, bootstrap and cross validation.
Details are available via http://stat.ethz.ch/education/ .
Exercises will be based on the open-source statistics software R (http://www.Rproject.org/). Emphasis will be put on applied problems. Active participation in the
exercises is strongly recommended.
More details are available via the webpage http://stat.ethz.ch/education/ (->
"Computational Statistics").
lecture notes are available online; see
Lecture notes
http://stat.ethz.ch/education/ (-> "Computational Statistics").
Literature
(see the link above, and the lecture notes)
Prerequisites / Basic "applied" mathematical calculus and linear algebra.
Notice
At least one semester of (basic) probability and statistics.
401-8628-00L Survival Analysis (University of Zurich) (3 cred): Levetidsanalyse
The analysis of survival times, or in more general terms, the analysis
of time to event variables is concerned with models for censored
observations. Because we cannot always wait until the event of interest
Abstract
actually happens, the methods discussed here are required for an
appropriate handling of incomplete observations where we only know that
the event of interest did not happen within ...
Objective
During the course, we will study the most important methods and models
for censored data, including
- general concepts of censoring,
- simple summary statistics,
Content
- estimation of survival curves,
- frequentist inference for two and more groups, and
- regression models for censored observations
!!!
Tilbys av universitetet, må søke spesielt om opptak til faget
701-0104-00L Statistical Modelling of Spatial Data(3 cred.) : Romlig statistikk
In environmental sciences one often deals with spatial data. When analysing
such data the focus is either on exploring their structure (dependence on
Abstract
explanatory variables, autocorrelation) and/or on spatial prediction. The
course provides an introduction to geostatistical methods that are useful for
such purposes.
The course will provide an overview of the basic concepts and stochastic
models that are commonly used to model spatial data. In addition, the
Objective
participants will learn a number of geostatistical techniques and acquire some
familiarity with software that is useful for analysing spatial data.
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
Content
spatial patterns by regression, modelling autocorrelation by variogram;
kriging: mean-square prediction of spatial data) will be taught. The lectures
will be complemented by data analyses that the participants have to do
themselves.
Lecture material, descriptions of the problems for the data analyses and
worked out solutions to them will be provided. The course material is
Lecture notes
available from an Ilias repository that can be accessed by the URL
http://group.ilias-app2.let.ethz.ch/36743 .
Literature
P.J. Diggle & P.J. Ribeiro Jr. 2007. Model-based Geostatistics. Springer
From spring semester 2014 onwards, admission to the course requires the
proof that the participants have successfully passed the exams of the courses
Prerequisites / 401-6215-00L Using R for Data Analysis and Graphics (Part I) and 401Notice
0649-00L Applied Statistical Regression (Part 1) or have equivalent
qualifications. Course material in English will be provided and the course will
be taught in English if participants are not sufficiently fluent in German.
252-0526-00L Statistical Learning Theory (4 credits): Maskinlæring
The course covers advanced methods of statistical learning :
PAC learning and statistical learning theory;variational methods and
Abstract optimization, e.g., maximum entropy techniques, information bottleneck,
deterministic and simulated annealing; clustering for vectorial, histogram and
relational data; model selection; graphical models.
The course surveys recent methods of statistical learning. The fundamentals of
Objective machine learning as presented in the course "Introduction to Machine Learning"
are expanded and in particular, the theory of statistical learning is discussed.
# Boosting: A state-of-the-art classification approach that is sometimes used as an
alternative to SVMs in non-linear classification.
# 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.
# Statistical learning theory: How can we measure the quality of a classifier? Can
we give any guarantees for the prediction error?
# 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
Content
# 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.
# Reinforcement learning: The problem of learning through interaction with an
environment which changes. To achieve optimal behavior, we have to base
decisions not only on the current state of the environment, but also on how we
expect it to develop in the future.
Lecture
notes
no script; transparencies of the lectures will be made available.
Duda, Hart, Stork: Pattern Classification, Wiley Interscience, 2000.
Hastie, Tibshirani, Friedman: The Elements of Statistical Learning, Springer,
Literature 2001.
L. Devroye, L. Gyorfi, and G. Lugosi: A probabilistic theory of pattern
recognition. Springer, New York, 1996
Prerequisites /
Notice
Requirements:
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.
401-4658-00L Computational Methods for Quantitative Finance: PDE Methods (6 cred)
Abstract
Objective
Content
Lecture notes
Introduction to principal methods of option pricing. Emphasis on PDE-based
methods. Prerequisite MATLAB programming
and knowledge of numerical mathematics at ETH BSc level.
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.
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.
There will be english, typed lecture notes as well as MATLAB software for
registered participants in the course.
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.
Literature
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.
Prerequisites / The 2009 title of this course unit was "Computational Methods for
Notice
Quantitative Finance II: Finite Element and Finite Difference Methods".