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