A data-driven convergence criterion for iterative unfolding of smeared spectra

TL;DR

This paper introduces a data-driven convergence criterion for iterative unfolding methods, enabling better bias estimation and coverage properties, especially when the response matrix is imperfectly known.

Contribution

It proposes a novel convergence criterion based on the unregularized spectrum, improving the reliability of unfolding results in particle physics analyses.

Findings

The criterion allows safe bias estimation during unfolding.

It addresses cases with imperfect response matrices.

Provides methods to recover proper coverage properties.

Abstract

A data-driven convergence criterion for the D'Agostini (Richardson-Lucy) iterative unfolding is presented. It relies on the unregularized spectrum (infinite number of iterations), and allows a safe estimation of the bias and undercoverage induced by truncating the algorithm. In addition, situations where the response matrix is not perfectly known are also discussed, and show that in most cases the unregularized spectrum is not an unbiased estimator of the true distribution. Whenever a bias is introduced, either by truncation of by poor knowledge of the response, a way to retrieve appropriate coverage properties is proposed.