Uncertainty Quantification in Complex, Nonparametric Statistical Models

Description and Aim

Uncertainty quantification plays a central role in applications of statistics to applied sciences such as physics, astronomy, geophysics, epidemiology, genomics, etc. If one cannot quantify the accuracy of a statistical procedure, a researcher has no information about the validity of the inferences drawn from a particular method given a data set. A rigorous, probabilistic description of statistical uncertainty quantification can be based on the classical notion of a `confidence set', and its frequency interpretation in the large sample/small noise limit. While the last decade has seen remarkable progress in the mathematical theory of statistical confidence sets in contemporary nonparametric and high-dimensional models, a gap remains between theory and the methods used by practitioners (such as Bayesian credible regions) in a range of modern statistical problems including structured data, inverse problems and other models based on real world applications.

The workshop aims to bring together different communities working on uncertainty quantification. First there is a relatively clear distinction between applied statisticians using uncertainty quantification in various fields of sciences, computational statisticians considering algorithmic aspects, and theoretical statisticians aiming on developing and underpinning confidence statements. Furthermore, both frequentist and Bayesian methods are widely used in practice and the workshop aims to bring together experts from both fields. The workshop will be considered a success if it will lead to valuable interaction between various views, if applied researchers and computational statisticians will learn about the theoretical limits of UQ methods and theoretical statisticians about the arising challenges in real world applied problems and computationally feasible statistical techniques, which are of emerging importance due to the ever increasing amount of available information. The long term goal is to develop new, computationally feasible statistical methods for uncertainty quantification in various fields of applied sciences which have good theoretical properties at the same time.