Statistical Foundations of Uncertainty Quantification for Inverse Problems
Center for Mathematical Sciences
University of Cambridge, June 19th – 22nd , 2017
Richard Nickl (University of Cambridge)
Markus Reiß (Humboldt Universität zu Berlin)
Andrew Stuart (California Institute of Technology)
Harry van Zanten (University of Amsterdam)
Participation is by invitation only. Please email SFconference2017@dpmms.cam.ac.uk for any queries.
Here is a list of participants and a program.
Scientific Goals: The workshop aims at bringing together leading researchers in the area of statistical inference for inverse problems, to discuss and initiate the development of rigorous mathematical foundations for commonly used `uncertainty quantification’ methodology. The main focus is on the development of objective data-driven measures that can guarantee that algorithms used in statistical inverse problems have actually returned an accurate solution. Traditional statistical methods insist in the construction of `confidence sets’ or `algorithmic certificates’ for the parameters of inferential interest, but in complex parameter spaces such as those encountered in inverse problems, this is often a very difficult task. Alternatively, Bayesian methodology (posterior inference, credible sets, Bayes factors, etc) is frequently used, but even disregarding computational barriers, the objective (frequentist) meaning of posterior based-inferences is largely unclear in such settings. The workshop will try to push forward the frontiers of this research area by combining expertise from a variety of concrete application areas within statistical inverse problems with recent advances on the inferential foundations of non-parametric and high-dimensional statistics. The hope is that a rigorous mathematical paradigm emerges that can serve as a foundation for uncertainty quantification in modern day statistical inverse problems.
This conference is generously funded by the European Research Council. We are also grateful to the Cantab Capital Institute for the Mathematics of Information for further financial support.