Mathematical Statistics (BM)
Collegejaar:  20172018 

Studiegidsnummer:  4373MATST 
Docent(en): 

Voertaal:  Engels 
Blackboard:  Ja 
EC:  6 
Niveau:  400 
Periode:  Semester 1 
 Wel Keuzevak
 Wel Contractonderwijs
 Wel Exchange
 Wel Study Abroad
 Geen Avondonderwijs
 Wel AlaCarte en Aanschuifonderwijs
 Geen Honours Class
Description
In statistics, we estimate/reconstruct objects from data. Given a noisy image for example, the aim is to reconstruct the underlying true image.
A first course in statistics typically deals with reconstruction of finite dimensional parameters, such as the mean or the standard deviation of a distribution. For many interesting applications, however, we want to assume as little as possible about the true underlying objects. Taking a fixed number of parameters is then not appropriate. Instead this should be modelled by assuming a highdimensional or even infinite dimensional parameter space. To reconstruct an image, for instance, we can think of it as a twodimensional function and take as a parameter space a function class.
The mathematical theory of complex statistical models has been developed largely during the past years but remains a topic of active research with many challenging open problems. One of the nice features is that there is a notion of optimality and estimators (reconstruction methods) can be constructed that (nearly) achieve this optimal behaviour.
Course objectives
In the course we give a mathematical introduction to this field. The course is based on lecture notes that will be made available after the lectures. We start with a short introduction of mathematical prerequisites. We then discuss general estimation methods and derive rate optimal bounds for the statistical estimation risk. To illustrate the mathematical theory we discuss applications in biology, image reconstruction and finance. One lecture will be devoted to the statistical theory of neural networks.
References
Tsybakov, A.: Introduction to nonparametric statistics. Springer, 2009.
available from: http://link.springer.com/book/10.1007%2Fb13794
Johnstone, I.: Gaussian estimation: Sequence and wavelet models. Lecture notes.
available from: http://statweb.stanford.edu/~imj/GE061113.pdf
Prerequisites
The course requires tools from different areas in mathematics such as measure theory and function spaces. We briefly introduce these concepts at the beginning of the lecture. An introduction to mathematical statistics, measure theory and functional analysis is nevertheless helpful but not required.
Assessment method
Weekly homework assignments with math problems (1/3) and a final exam (2/3).
Depending on the number of students the final exam will be oral or written.
Registration
Via blackboard.
To be able to obtain a grade and the ECTS for the course, sign up for the (re)exam in uSis ten calendar days before the actual (re)exam will take place. Note, the student is expected to participate actively in all activities of the program and therefore uses and registers for the first exam opportunity.
Exchange and Study Abroad students, please see the Prospective students website for information on how to apply.
Contact information
In case of further question, please contact directly
schmidthieber@math.leidenuniv.nl
The course is also open to 3rd year bachelor students.
Maakt deel uit van  Soort opleiding  Semester  Blok 

Mathematics  Master  1  
Wiskunde  Bachelor  1 