Uncertainty quantification plays a central role in many areas of applied sciences, from statistics to optimization. In the broad context of statistics it is of key importance to understand how much one can trust a statistical procedure by quantifying its error as accurately as possible. This is essential for making meaningful conclusions when using any statistical procedure – the lack of a reliable description of the procedure's uncertainty will invariably lead to misleading and haphazard results with limited practical applicability.

In recent years uncertainty quantification was investigated in many modern, complex statistical problems through both the lenses of theory and practice. In particular, in non-parametric settings it is well known that estimators and tests whose performance adapts to unknown features of the model (e.g., smoothness of a regression function) can be devised. However, in general it is not possible to make the corresponding adaptive confidence statements without making further (often stringent) assumptions. These results are in a sense pessimistic, as they often characterize worst-case (minimax) behavior, and thus have not prevented practitioners from using uncertainty quantification methods, sometimes in inadequate ways. Progress has been made in recent years shedding light on uncertainty quantification in complex scenarios, both in frequentist and Bayesian frameworks. Nevertheless there are still a lot of unanswered questions concerning many real world applications involving for instance network models, machine learning algorithms and financial models.

This workshop aims to introduce this broad field of research to young researchers, including Ph.D. students, postdocs and junior early stage researchers, with a balanced focus on both theory and practice.

Workshop: YES VIII "Uncertainty Quantification"