Research Group "Stochastic Algorithms and Nonparametric Statistics"
Seminar "Modern Methods in Applied Stochastics and Nonparametric
Statistics" Winter Semester 2013/14
last reviewed:Oktober 21, 2013, Christine Schneider
15.10.13
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22.10.13
Roland Hildebrand (WIAS Berlin)
Convex optimization and semi-definite relaxations
We provide an overview over semi-definite programming and some of its theoretical aspects and applications. This includes semi-definite representability of robust programs, polynomial optimization, and optimal experiment design in system identification.
29.10.13
Eric Creusen (TU Eindhoven)
Diffusion weighted MRI: enhancement and analysis
Abstract:
05.11.13
No Talk
(Matheon Center Days)
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tba
12.11.13
Michael Tretyakov (University of Nottingham)
Numerical integration of SDEs with nonglobally Lipschitz coefficients
Abstract: The talk will start with introduction to the problem of approximating solutions to regular SDEs which coefficients can grow faster than a linear function at infinity. In particular, the solution to this problem in the case of weak-sense approximations, the concept of rejecting exploding trajectories (CRE), will be recalled. CRE was introduced in [Milstein, Tretyakov SIAM J. Num. An. 2005] and it allows us to apply any usual method of weak approximation to SDEs with nonglobally Lipschitz coefficients. Then more recent results on mean-square SDE approximations in the nonglobally Lipschitz case will be considered including a special balanced-type scheme proposed in [Tretyakov, Zhang SIAM J. Num. An. to appear]. This balanced scheme is apparently the first explicit mean-square approximation for which convergence with order was proved when both drift and diffusion coefficients can grow faster than a linear function at infinity. Some numerical experiments comparing various mean-square schemes convergent in the nonglobally Lipschitz case will also be presented.
19.11.13
Christian Bayer (WIAS Berlin)
On non-asymptotic sequential stopping criteria in
Monte-Carlo simulations
Abstract:
We discuss the choice of the number M of samples needed in a Monte
Carlo simulation such that the error exceeds a tolerance level only
with a prescribed (small) probability. While this problem boils down
to a simple application of the central limit theorem in the asymptotic
situation of M tending to infinity, the situation is much more
delicate for finite, positive error tolerances.
In a first didactic part, we discuss various insights in this problem
from the classical statistical literature. In the second part, we
suggest our own algorithm for choosing M, which is based on some
heuristic error decomposition. We also present some numerical tests,
which seem to indicate that this algorithm achieves a good compromise
between the sought-for accuracy and efficiency of the Monte Carlo
algorithm, even for heavy-tailed distributions.
Based on joint work with Haakon Hoel (KAUST), Erik von Schwerin (EPFL)
and Raul Tempone (KAUST).
07.01.14
Elmar Diederichs
Local Approximation of Topological
Spaces by Primitive Clusters
Abstract:
21.01.14
Maya Zhilova (WIAS Berlin)
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28.01.14
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04.02.14
Andreas Andresen (WIAS Berlin)
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TBA
11.02.14
Niklas Willrich (WIAS Berlin)
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18.02.14
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