I am Junior Professor in Applied Mathematics with Specialism in Risk and Uncertainty Quantification at the Freie Universität Berlin and Research Group Leader for Uncertainty Quantification at the Zuse Institute Berlin. I have wide interests in uncertainty quantification the broad sense, understood as the meeting point of numerical analysis, applied probability and statistics, and scientific computation. On this site you will find information about how to contact me, my research, publications, and teaching activities.
It is a pleasure to announce that Luc Bonnet will be joining the UQ research group for a three-month visit funded by the German Academic Exchange Service (DAAD), with effect from 1 September 2019. He will be working on the application of optimal uncertainty quantification methodology to problems in aerodynamics and aircraft design.
The 2020 SIAM conference on Uncertainty Quantification (UQ20) will take place from 24 to 27 March 2020, on the Garching campus (near Munich) of the Technical University of Munich (TUM), Germany. UQ20 is being organised in cooperation with the GAMM Activity Group on UQ.
More information about the scientific programme will be added in due course, but the following scientists are already confirmed as plenary speakers:
- David M. Higdon, Virginia Polytechnic Institute and State University, USA
- George Em Karniadakis, Brown University, USA
- Frances Y. Kuo, University of New South Wales, Australia
- Youssef M. Marzouk, Massachusetts Institute of Technology, USA
- Anthony Nouy, École Centrale de Nantes, France
- Elaine Spiller, Marquette University, USA
- Claudia Tebaldi, The Joint Global Change Research Institute, USA
- Karen Veroy-Grepl, RWTH Aachen University, Germany
Esfandiar Nava-Yazdani, Christoph von Tycowicz, Hans-Christian Hege, and I have just uploaded an updated preprint of our work “Geodesic analysis in Kendall's shape space with epidemiological applications” (previously entitled “A shape trajectories approach to longitudinal statistical analysis”) to the arXiv. This work is part of the ECMath / MATH+ project CH-15 “Analysis of Empirical Shape Trajectories”.
Abstract. We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall's shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example application we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone.
I have just uploaded a preprint of “Comments on the article ‘A Bayesian conjugate gradient method’” to the arXiv. This note discusses the recent paper “A Bayesian conjugate gradient method” in Bayesian Analysis by Jon Cockayne, Chris Oates, Ilse Ipsen, and Mark Girolami, and is an invitation to a rejoinder from the authors.
Abstract. The recent article “A Bayesian conjugate gradient method” by Cockayne, Oates, Ipsen, and Girolami proposes an approximately Bayesian iterative procedure for the solution of a system of linear equations, based on the conjugate gradient method, that gives a sequence of Gaussian/normal estimates for the exact solution. The purpose of the probabilistic enrichment is that the covariance structure is intended to provide a posterior measure of uncertainty or confidence in the solution mean. This note gives some comments on the article, poses some questions, and suggests directions for further research.
This Summer Semester 2019, I will offer a course in the mathematics of Inverse Problems at the Freie Universität Berlin. The course load will be 2+2 SWS and the course will be a valid selection for the Numerik IV and Stochastic IV modules.
Inverse problems, meaning the recovery of parameters or states in a mathematcial model that best match some observed data, are ubiquitous in applied sciences. This course will provide an introduction to the deterministic (variational) and stochastic (Bayesian) theories of inverse problems in function spaces.
- Examples of inverse problems in mathematics and physical sciences
- Preliminaries from functional analysis
- Preliminaries from probability theory
- Linear inverse problems and variational regularisation
- Bayesian regularisation of inverse problems
- Monte Carlo methods for Bayesian problems
For further details see the KVV page.