Workshop on

**Statistical
Foundations of Uncertainty Quantification for Inverse Problems**

Center for Mathematical Sciences

University
of Cambridge, June 19^{th}
– 22^{nd
},
2017

**Scientific Organisers**

*Richard
Nickl (University of Cambridge)*

*Markus
Rei**ß*
*(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.

A list of participants and further information will be posted soon.

*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.