Jasper Marijn Everink:** ***Different assumptions on uncertainty might give different conclusions*

When a body is scanned by a CT scanner, the measurements obtained by the scanner are inaccurate, and when we want to reconstruct the body from those measurements, our mathematical model might not reflect reality. If we do not take these mistakes into account, then we would get a misleading picture of the body, which could result in an incorrect conclusion.

To improve the reconstructions, one must make assumptions on what type of behavior we expect from our solution. Typically, we expect some form of smoothness or jumps in the image, or perhaps a solution that is mostly empty. Such behavior can be incorporated by penalizing badly behaving feasible solutions. In a Bayesian framework, this penalization is often given in the form of a prior probability distribution, which, together with a likelihood distribution modeling the measurement device, errors and mistakes, gives us a probability distribution on the set of feasible solutions called the posterior distribution.

Efficient sampling from the posterior distribution often requires explicit descriptions of the prior knowledge in the form of a probability distribution, yet there are many possible prior assumptions for which implicit descriptions are more natural. A topic of study in this PhD project is to improve our understanding of the use of implicit priors, for example, as obtained through solutions of stochastic optimization problems.

Sampling from high-dimensional distributions can be very costly and requires a lot of samples to obtain accurate information on the distribution. Another part of the project will be to explore how recent progress on stochastic optimization methods can be used to create efficient computational sampling methods.

The general goal of the project is to construct scalable and robust sampling methods for inverse problems that can be used by researchers and practitioners alike.

This project is part of the research initiative CUQI (Computational Uncertainty Quantification for Inverse problems) funded by Villum Fonden (https://www.compute.dtu.dk/english/cuqi). The goal of CUQI is to make uncertainty quantification (UQ) for inverse problems readily available for non-experts.

**By**: Jasper Marijn Everink

**Section**: Scientific Computing

**Principal supervisor**: Martin Skovgaard Andersen

**Co-supervisor**: Yiqiu Dong

**Project title**: Computational Uncertainty Quantification for Inverse Problems with Implicit Priors

**Term**: 01/10/2021 → 30/09/2024