Veranstaltungen

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Mittwoch, 18.07.2018, 10:00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. J. van Waaij, Humboldt Universität zu Berlin:
Adaptive nonparametric Bayesian methods for SDEs
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We consider continuous time observations (Xt_0le tle T of the SDE dXt = Theta(Xt)dt + dWt: Our goal is estimating the unknown drift function Theta. Due to their numerical advantages, Bayesian methods are often used for this. In this talk I discuss optimal rates of convergence for these methods. I will start with an introduction to Bayesian methods for SDEs and what sufficient con- ditions are for posterior convergence. I show that the sufficient conditions are satisfied for the Gaussian process prior, which leads to optimal convergence rates, provided the smoothness of Theta matches the smootness of the Gaussian process. Adaptivity can be obtained by equipping the hyperparameter(s) of the Gaussian process prior with an additional prior. We discuss several choices for such hyperparameters. A new promising approach to obtain adaptivity is empirical Bayes. Here the optimal hyperparameters for the Gaussian process prior are first esti- mated from the data and then the prior with those hyperparameters plugged- in is used for the inference. This talk is based on van Waaij, 2018 and joint work with Frank van der Meulen (TU Delft), Moritz Schauer (Leiden University) and Harry van Zanten (University of Amsterdam).

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Donnerstag, 26.07.2018, 15:00 Uhr (WIAS-406)
FG Stochastische Systeme mit Wechselwirkung
Prof. A. Drewitz, Universität zu Köln:
Phase transitions in some percolation models with long-range correlations on general graphs
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
We consider two fundamental percolation models with long-range correlations on reasonably general and well-behaved transient graphs: The Gaussian free field and (the vacant set) of Random Interlacements. Both models have been the subject of intensive research during the last years and decades, on $Z^d$ as well as on some more general graphs. We consider their percolation phase transition and investigate a couple of interesting properties of their critical parameters, in particular the existence of a phase transition. This talk is based on joint works with A. Prevost (Koeln) and P.-F. Rodriguez (Los Angeles).

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FG 5 Seminar

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WIAS Berlin