Research Group "Stochastic Algorithms and Nonparametric Statistics"
Seminar "Modern Methods in Applied Stochastics and Nonparametric
Statistics" Summer semester 2011
last reviewed: May, 31, 2011, Christine Schneider, Karsten Tabelow
12.04.2011
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19.04.2011
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26.04.2011
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03.05.2011
Peter Friz (WIAS, TU Berlin)
First meeting - reading group on viscosity theory and related topics
Abstract:
10.05.2011
Natalia Bochkina (WIAS, University Edinburgh)
Consistency and efficiency of the posterior distribution in generalised linear inverse problems
Abstract: I will talk about asymptotic properties of the posterior distribution in linear ill-posed inverse problems with non-Gaussian distribution of errors where regularisation is done via Bayesian modelling with possibly improper prior distribution. In particular, I will discuss behaviour of the posterior distribution when the `true' value of the parameter is on the boundary. (This work is joint with Peter Green, University of Bristol, UK).
17.05.2011
Peter Friz (WIAS, TU Berlin)
Second meeting - reading group on viscosity theory and related topics
Abstract:
24.05.2011
Jianing Zhang (WIAS Berlin)
Lp-solutions of BSDEs with time delayed generators
Abstract: We deal with the theory of BSDEs with time delayed generators introduced by Delong and Imkeller (2010). These BSDEs are characterized by generators which typically depend on the past of the value and the control processes up to current time. Assuming Lipschitz conditions, Delong and Imkeller establish an L2 space characterization of BSDE solutions. We amend this with an Lp space theory and discuss some technical obstacles which have to be overcome to achieve this goal. We then apply our results to study the case of a time delayed backward equation with a Markovian terminal condition and derive representation formulas for the BSDE solution which are analogous to those for BSDEs with standard (non-time delayed) generators. This is a joint work with Gon\ccalo dos Reis (TU Berlin) and Anthony R\'eveillac (HU Berlin).
31.05.2011
John Schoenmakers (WIAS Berlin)
New dual methods for single and multiple exercise options
Abstract:Part I) We recap the dual method of Rogers (2002) / Haugh & Kogan (2004)
and introduce the concept of surely optimal dual martingales. We present
characterization and stability theorems for surely optimal dual
martingales.
Next we outline how this new concept leads to efficient algorithms for
computing
upper bounds for American options.
In particular, in an Ito-Levy framework we develop a regression based
algorithm which allows for computing both upper and lower bounds at
the same time. Moreover, unlike the Andersen & Broadie algorithm, this
algorithm doesn't require nested simulation and is therefore fast.
Part II) In the second part of the talk we extend the dual method to the
multiple stopping problem and we outline an algorithm for the evaluation
of multiple
exercise options such as swing options.
07.06.2011
Marina Bogomolov (Tel-Aviv University)
Hierarchical Testing of Subsets of Hypotheses
Abstract: This talk is based on a joint work with Yoav Benjamini. As the size
of large testing problems encountered in practice keeps increasing,
more of these problems have further structure where the set of
hypotheses can be partitioned into subsets of the hypotheses, and a
discovery of some signal in a subset is of interest on top of the
discovery of a signal in each of the many hypothesis on its own.
Furthermore, the true state of the tested signals tends to be more
similar within these subsets than across the subsets. Examples are
regions in the brain in functional MRI research, sets of genes in
genomic research, or geographical areas in disease outbreaks
monitoring.
The challenges in the analysis of such multiple testing problems
will be discussed, and previous efforts to address them will be
reviewed. We then present a few new methods to control various
aspects of the False Discovery Rate, and discuss their benefits and
limitations.
21.06.2011
Ronnie Loeffen (WIAS Berlin)
Option pricing in affine term structure models via spectral
representations
Abstract: Relying on a result due to Ogura (1970), we provide, under some
conditions, a spectral expansion for the pricing semi-group of one dimensional
affine term structure models. This representation allows us to quickly price
European vanilla options on the corresponding yield or bonds for a whole range
of
strikes and maturities. We present several examples illustrating our approach.
This is joint work with M. Chazal, G. Deelstra and P. Patie (ULB, Brussels).
28.06.2011
Hilmar Mai (HU Berlin)
Efficient estimation for a Lévy-driven SDEs and jump filtering
Abstract:Stochastic differential equations driven by Lévy processes are a popular
tool for stochastic modeling particularly in mathematical finance. When
making inference about the drift component of such models the jumps of
the Lévy noise pose an additional challenge compared to the classical
Gaussian setting. This naturally leads to a jump filtering problem, i.e.
the question if we can disentangle the continuous and the jump component
of the process when it is observed discretely at high frequency.
As a fundamental example we will consider the estimation of the drift of
a Lévy-driven Ornstein-Uhlenbeck process from discrete observations. The
estimator is based on the discretization of the continuous-time
likelihood estimator. Since the likelihood function is a functional of
the unknown continuous part of the process, we use a threshold method to
filter jumps from the data. Then, we prove that under suitable
conditions on the discretization scheme and the jump part of the process
the discretized MLE with jump filtering is asymptotically normal and
efficient in the sense of Hájek-Le Cam.
Finally, we discuss a simulation study to asses the finite sample
behavior of the estimator and demonstrate its practical tractability.
05.07.2011
Stéphane Mallat (CMAP, Ecole Polytechnique)
High Dimensional Classification with Invariant Representations
Abstract: Classification requires finding appropriate metrics to compare signals.
Audio and visual perceptual metrics remain a mystery. They are invariant
to particular groups of transformations such as translations and scaling
and are continuous to deformations relatively to these group actions.
Representations that are both invariant to a group action and Lipschitz
continuous to deformations can linearize classification problems, but
finding them is a challenge.
We introduce a class of non-linear scattering operators which satisfy
these properties. They are computed by cascading modulus operators and
wavelets transforms on the group. For translations, it provides new
representations of stationary processes which discriminate textures
having same power spectrum. A linear PCA classification applied to
scattering representations is shown to provide state of the art
classification results on data bases of images and audio signals.
12.07.2011
Andreas Andresen (HU Berlin)
Schilder's theorem for Hilbert space valued Wiener processes, a sequence space approach
Abstract: A generalization of Ciesielski's isomorphism to a homoeomorphism between Cα ([0,1],H) and (hn) ⊂ H with hn → 0 is used to give an elementary proof of Schilder's theorem for Wiener processes with values in a separable Hilbert space.
