# 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)