Ill-posed inverse problems are ubiquitous in the physical sciences. Examples range from deblurring of astronomical images to remote sensing of the atmosphere to unfolding of elementary particle spectra. The common aspect of these problems is that it is easy to go from the physical quantity to the observations but the inverse direction of inferring the quantity of interest based on noisy data tends to produce extremely unstable solutions. It is customary to address this using regularization which reduces the variance of the estimates at the expense of increased bias. While this can lead to well-behaved point estimates, it is extremely challenging to provide rigorous frequentist uncertainties for the regularized estimates. In this talk, I will explain why that is the case and describe approaches that can be used to obtain improved frequentist uncertainty quantification in ill-posed problems. I will argue that the key is to avoid explicit regularization and instead infer functionals of the unknown quantity that implicitly regularize the problem. I will demonstrate these ideas using practical examples from particle physics and atmospheric remote sensing.
The seminar will be done remote only, using ZOOM for this event, link to join the seminar: https://cern.zoom.us/j/222861107
M. Girone, M. Elsing, L. Moneta, M. Pierini
Event co-organised with the PHYSTAT Committee