# Overview¶

`UndersmoothedUnfolding`

is a software for unfolding particle spectra in high energy physics with focus on optimal *uncertainty quantification*. Most existing unfolding software implementations only provide
methods for optimal point estimation; however, as as demonstrated in Kuusela (2016) 1,
confidence intervals formed from such point estimates can suffer from significant undercoverage,
and thus might not be suitable for statistical inference and uncertainty quantification.

`UndersmoothedUnfolding`

is a ROOT 3 implementation of the data-driven
undersmoothing technique introduced in Kuusela (2016) 1, which aims at
choosing the regularization strength so that the resulting unfolded confidence intervals have
nearly nominal coverage.

It is extended from the existing unfolding library, TUnfold 2, which is included in ROOT 3.

## What is unfolding?¶

Particle physics measurements, including those made at the Large Hadron Collider (LHC) at CERN, are smeared by the finite resolution of the particle detectors. The goal in unfolding is to use these smeared observations to make non-parametric inferences about the underlying unsmeared particle spectrum. The image below visually illustrates folding and unfolding. This problem is an ill-posed inverse problem which complicates the task of quantifying the uncertainty of the unfolded spectrum 1.

- 1(1,2,3)
Kuusela, “Uncertainty quantification in unfolding elementary particle spectra at the Large Hadron Collider”, PhD thesis, EPFL (2016).

- 2
Schmitt, “TUnfold, an algorithm for correcting migration effects in high energy physics”, Journal of Instrumentation

**7**(2012).

- 3(1,2)
Brun and F. Rademakers, “ROOT - An Object Oriented Data Analysis Framework”, Nucl. Inst. & Meth. in Phys. Res. A

**389**(1997).