How to use

UndersmoothTau is the core functionality of UndersmoothedUnfolding, and is implemented so that it can be used with any initial pilot estimate of \(\tau\) from, say, cross-validation, L-curve, etc. For typical usage, users simply need to add a call to UndersmoothTau to their usual TUnfold workflow.

Given an initial estimate of \(\tau\), UndersmoothTau gradually reduces the amount of regularization until the 68% target coverage is met within a tolerance \(\epsilon\).

UndersmoothTau depends on another core functionality, ComputeCoverage. Under certain assumptions, the coverage probability of the unfolded confidence intervals can be written down in closed form, thus providing UndersmoothTau a principled way of choosing the amount of undersmoothing. The expression for the coverage depends on the unknown true spectrum, which UndersmoothTau substitutes with a nontrivial plug-in estimate when calling ComputeCoverage. For more mathematical and technical detail, please refer to Kuusela (2016) 1.

Example usage

UndersmoothTau is implemented so that it can be used with any initial estimate of \(\tau\). Below is an example usage of UndersmoothTau with the inital estimate from the TUnfold::ScanLcurve method.

TUnfold unfold = new TUnfold();          // construct a TUnfold object
unfold.ScanLcurve();                     // unfold using ScanLcurve method
TauFromLcurve = unfold.GetTau();         // retrieve tau chosen by ScanLcurve

// starting from tau chosen by ScanLcurve, reduce tau until the minimum estimated coverage
// meets the target coverage, which is the nominal 68% minus the tolerance epsilon (0.01 in this example).
TauFromUndersmoothing = unfold.UndersmoothTau(TauFromLcurve, 0.01, 1000);
unfold.DoUnfold(TauFromUndersmoothing);   // unfold again with undersmoothed tau

Expected input/output

Please refer to function references page for details about supported input and expected output.

1

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