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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Forschungsseminar Mathematische Statistik

Für den Bereich Statistik

G. Blanchard, M. Reiß, V. Spokoiny, W. Härdle



Weierstrass-Institut für Angewandte Analysis und Stochastik
Mohrenstrasse 39
10117 Berlin



mittwochs, 10.00 - 12.30 Uhr



17. Oktober 2018
Mark Podolskij (Aarhus)
Statistical inference for fractional models
Abstract: In recent years, fractional and moving average type models have gained popularity in economics and finance. Most popular examples include fractional Brownian/stable motion, rough volatility models and Hawkes processes. In this talk we will review some existing estimation methods and present new theoretical results.
24. Oktober 2018
Eugene Stepanov (St.-Petersburg and Pisa)
Hybrid control in a model from molecular biology: between continuous and discrete
Abstract: The central argument of the talk will be the rather modern concept in automated control: hybrid controls through finite state machines in continuous dynamical models.It will be shown that hybrid systems present a highly complicated dynamics. Then a class of largely open problems arizing from molecular biology will be presented and studied, where the hybrid system comes out from a extraordinarily simple and completely classical models based on ODEs without any discrete object incorporated.
31. Oktober 2018
07. November 2018
14. November 2018
Jürgen Pilz (Klagenfurt Universität)
The interplay between random field models for Bayesian spatial prediction and the design of computer experiments
Abstract: In the first part of my talk, I will give an overview of recent work with my colleagues G. Spoeck and H. Kazianka in the area of Bayesian spatial prediction and design [1]-[5]. The Bayesian approach not only offers more flexibility in modeling but also allows us to deal with uncertain distribution parameters, and it leads to more realistic estimates for the predicted variances. Moreover, I will demonstrate how to apply copula methodology to Bayesian spatial modeling and use it to derive predictive distributions. I will also report on recent results for determining objective priors for the crucial nugget and range parameters of the widely used Matern-family of covariance functions. Briefly, I will also consider the problem of choosing an "optimal" spatial design, i.e. finding an optimal spatial configuration of the observation sites minimizing the total mean squared error of prediction over an area of interest. Our results will be illustrated by modeling environmental phenomena and designing a hyrogeological monitoring network in Upper Austria. In the second part of my talk I will report on modifying and transferring spatial random field models to make them accessible to the analysis of complex computer code. Over the last three decades, the design of computer experiments has rapidly developed as a statistical discipline at the intersection of the wellestablished theories of DoE, stochastic processes, stochastic simulation and statistical parameter estimation, with the aim of approximating complex computer models to reproduce the behaviour of engineering, physical, biological, environmental and social science processes. We will focus on the use of Gaussian Processes (GP's) for the approximation of computer models, thereby stepping from simple parametric setups to using GP’s as basis functions of additive models. Then we discuss the numerical problems associated with the estimation of the model parameters, in particular, the second-order (variance and correlation) parameters. To overcome these problems I will highlight joint recent work with my colleague N. Vollert [6] using Bayesian regularization, based on objective (reference) priors for the parameters. Finally, we will consider design problems associated with the search for numerical robustness of the estimation procedures. We illustrate our findings by modeling the magnetic field of a magnetic linear position detection system as used in the automotive industry.
[1] H. Kazianka and J. Pilz: Bayesian spatial modeling and interpolation using copulas. Computers & Geosciences 37(3): 310-319, 2011
[2] H. Kazianka and J. Pilz: Objective Bayesian analysis of spatial data taking account of nugget andrange parameters. The Canadian Journal of Statistics 40(2): 304-327, 2012
[3] J. Pilz, H. Kazianka and G. Spoeck: Some advances in Bayesian spatial prediction and sampling design. Spatial Statistics 1: 65-81, 2012
[4] G. Spoeck and J. Pilz: Spatial sampling design based on spectral approximations of the errorprocess. In: Spatio-temporal design: Advances in Efficient Data Acquisition (W.G. Mueller and J. Mateu, Eds.), Wiley, New York 2013, 72-102
[5] G. Spoeck and J. Pilz: Simplifying objective functions and avoiding stochastic search algorithms in spatial sampling design. Front. Environ. Sci. 3:39: 1-22, 2015
[6] N. Vollert, M. Ortner and J. Pilz: Robust Additive Gaussian Process Models Using ReferencePriors and Cut-Off-Designs. To appear in: Applied Mathematical Modelling (2019), https://doi.org/10.1016/j.apm.2018.07.050
21. November 2018
Markus Bibinger (U Marburg)
Statistical analysis of path properties of volatility
Abstract: In this talk, we review recent contributions on statistical theory to infer path properties of volatility. The interest is in the latent volatility of an Itô semimartingale, the latter being discretely observed over a fixed time horizon. We consider tests to discriminate continuous paths from paths with volatility jumps. Both a local test for jumps at specified times and a global test for jumps over the whole observation interval are discussed. We establish consistency and optimality properties under infill asymptotics, also for observations with additional additive noise. Recently, there is high interest in the smoothness regularity of the volatility process as conflicting models are proposed in the literature. To address this point, we consider inference on the Hurst exponent of fractional stochastic volatility processes. Even though the regularity of the volatility determines optimal spot volatility estimation methods, forecasting techniques and the volatility persistence, identifiability is an unsolved question in high-frequency statistics. We discuss a first approach which can reveal if path properties are stable over time or changing. Eventually, we discuss some recent considerations and conjectures on this open question. The related easier problem of inference on the Hurst exponent from direct discrete observations of a fractional Brownian motion is also visited.
28. November 2018
Melanie Schienle (KIT)
05. Dezember 2018
Matthias Löffler (Cambridge)
Spectral thresholding for Markov chain transition operators
Abstract: We consider estimation of the transition operator P of a Markov chain and its transition density p where the eigenvalues of P are assumed to decay exponentially fast. This is for instance the case for periodised multi-dimensional diffusions observed in low frequency. We investigate the performance of a spectral hard thresholded Galerkin-type estimator for P and p, discarding most of the estimated eigenpairs. Our main contribution is that we show its statistical optimality by establishing matching minimax upper and lower bounds in L^2-loss. Particularly, the effect of the dimension d on the nonparametric rate improves from 2d to d.
12. Dezember 2018
Botond Szabo (Leiden)
19. Dezember 2018
09. Januar 2019
Frank Werner (Göttingen)
16. Januar 2019
Mathias Trabs (U Hamburg)
23. Januar 2019
30. Januar 2019
Jean Pierre Florens (Toulouse)
06. Februar 2019
Christian Clason (Essen)
13. Febuar 2019
Albert Cohen (Paris)

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Frau Andrea Fiebig

Mail: fiebig@mathematik.hu-berlin.de
Telefon: +49-30-2093-5860
Fax:        +49-30-2093-5848
Humboldt-Universität zu Berlin
Institut für Mathematik
Unter den Linden 6
10099 Berlin, Germany