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Tuesday, 17.01.2017, 10.15 Uhr (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Prof. Dr. T. Sullivan, FU Berlin:
Well-posedness of Bayesian inverse problems -- Stable priors on quasi-Banach spaces
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The Bayesian perspective on inverse problems has attracted much mathematical attention in recent years, and particular attention has been paid to Bayesian inverse problems (BIPs) in which the parameter to be inferred lies in an infinite-dimensional space, a typical example being a scalar or tensor field coupled to some observed data via an ordinary or partial differential equation. Numerical solution of such infinite-dimensional BIPs must necessarily be performed in an approximate manner on a finite-dimensional subspace, but it is profitable to delay discretisation to the last possible moment and consider the original infinite-dimensional problem as the primary object of study, since infinite-dimensional well-posedness results and algorithms descend to any finite-dimensional subspace in a discretisation-independent way, whereas careless early discretisation may lead to a sequence of well-posed finite-dimensional BIPs or algorithms whose stability properties degenerate as the discretisation dimension increases. This presentation will give an introduction to the framework of well-posed BIPs in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451-559, 2010) and others. Recently, this framework has been extended to the case of a heavy-tailed prior measure in the family of stable distributions, such as an infinite-dimensional Cauchy distribution, for which polynomial moments are infinite or undefined. It is shown that analogues of the Karhunen-Loeve expansion for square-integrable random variables can be used to sample such measures on quasi-Banach spaces. Furthermore, under weaker regularity assumptions than those used to date, the Bayesian posterior measure is shown to depend Lipschitz continuously in the Hellinger and total variation metrics upon perturbations of the misfit function and observed data.

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization

Host
WIAS Berlin
Tuesday, 17.01.2017, 15.00 Uhr (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. M. Maurelli, WIAS Berlin:
A mean field SDE with Neumann boundary conditions
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
Wednesday, 18.01.2017, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Dr. A. Naumov, Lomonosov Moscow State University, Russische Föderation:
Bootstrap confidence sets for spectral projectors of sample covariance
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Let X_1, ... ,X_n be i.i.d. sample in R^p with zero mean and the covariance matrix S. The problem of recovering the projector onto the eigenspace of S from these observations naturally arises in many applications. Recent technique from [Koltchinskii and Lounici, 2015b] helps to study the asymptotic distribution of the distance in the Frobenius norm between the true projector P_r on the subspace of the r th eigenvalue and its empirical counterpart hatP_r in terms of the effective trace of S. This paper offers a bootstrap procedure for building sharp condence sets for the true projector P_r from the given data. This procedure does not rely on the asymptotic distribution of P_r - hatP_r _2 and its moments, it applies for small or moderate sample size n and large dimension p . The main result states the validity of the proposed procedure for nite samples with an explicit error bound on the error of bootstrap approximation. This bound involves some new sharp results on Gaussian comparison and Gaussian anti-concentration in high dimension. Numeric results confirm a nice performance of the method in realistic examples.

Host
WIAS Berlin
Universität Potsdam
SFB 649: Ökonomisches Risiko
Humboldt-Universität zu Berlin
Wednesday, 18.01.2017, 15.15 Uhr (WIAS-ESH)
BERLINER OBERSEMINAR Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar)
Dr. H. Hardering, Technische Universität Dresden:
Gradient flows in Riemannian manifolds space discretization by geodesic finite elements
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
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Further Informations
Berliner Oberseminar ``Nichtlineare Partielle Differentialgleichungen'' (Langenbach Seminar)

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Thursday, 19.01.2017, 09.00 Uhr (WIAS-406)
Halbleiterseminar
M. Kantner, WIAS:
Modeling of single-photon sources on a device level
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Further Informations
Halbleiterseminar

Host
WIAS Berlin
Thursday, 19.01.2017, 11.00 Uhr (WIAS-406)
Analysis-Stochastik-Seminar
Dr. M. Heida, WIAS Berlin:
Stochastic two-scale convergence (part III)
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Further Informations
Analysis-Stochastik-Seminar

Host
WIAS Berlin
Thursday, 19.01.2017, 16.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Modelle der Photonik
F. Bierbüsse, Humboldt-Universität zu Berlin:
Solitary solutions of the short pulse equation for a defocusing nonlinearity
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
Humboldt-Universität zu Berlin
WIAS Berlin