Uncertainty quantification through adaptive and honest confidence sets

Alexandra Carpentier (Universität Potsdam)
Wednesday, October 26, 2016 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Empirical uncertainty quantification of estimation procedures can be simple in parametric, low dimensional situations. However, it becomes challenging and often problematic in high and in finite dimensional models. Indeed, adaptivity to the unknown model complexity becomes key in this case, and uncertainty quantification becomes akin to model estimation.
- Such model-adaptive uncertainty quantification can be formalised through the concept of adaptive and honest confidence sets. Recent results related to this concept will be presented.
- Model estimation, or model testing, is a specific types of composite-composite testing problems. General theory and tools for this kind of problems will be presented, in particular for quantifying the impact of the null hypothesis on the testing rate.