### Speaker

### Description

Matrix inversion problems are often encountered in experimental physics, and in particular in high-energy

particle physics, under the name of unfolding. The true spectrum of a physical quantity is deformed by

the presence of a detector, resulting in an observed spectrum. If we discretize both the true and observed

spectra into histograms, we can model the detector response via a matrix. Inferring a true spectrum

starting from an observed spectrum requires therefore inverting the response matrix. Many methods exist

in literature for this task, all starting from the observed spectrum and using a simulated true spectrum as

a guide to obtain a meaningful solution in cases where the response matrix is not easily invertible.

In this Manuscript, I take a different approach to the unfolding problem. Rather than inverting the

response matrix and transforming the observed distribution into the most likely parent distribution in

generator space, I sample many distributions in generator space, fold them through the original response

matrix, and pick the generator-level distribution which yields the folded distribution closest to the data

distribution. Regularization schemes can be introduced to treat the case where non-diagonal response

matrices result in high-frequency oscillations of the solution in true space, and the introduced bias is

studied.

The algorithm performs as well as traditional unfolding algorithms in cases where the inverse problem

is well-defined in terms of the discretization of the true and smeared space, and outperforms them in

cases where the inverse problem is ill-defined—when the number of truth-space bins is larger than that of

smeared-space bins. These advantages stem from the fact that the algorithm does not technically invert

any matrix and uses only the data distribution as a guide to choose the best solution.

The algorithm is also extended, in analogy to Bayesian approaches such as Metropolis Hastings, to a full description of the posterior distribution of each bin yield.