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.
