# How to analyse a closure test

There are two validphys reports which are used to analyse closure tests. The report which compares two different closure tests is generated using the vp-comparefits tool. The individual report which compares a closure test to the PDF used as the underlying law (from which pseudodata is generated) can be found in the main nnpdf repository under validphys2/examples/closure_templates/.

## Comparison to underlying PDF

This report is very similar to the full validphys fit report produced by vp-comparefits, the main differences are: only the closure fit is specified and it is compared to the PDF specified under the key fakepdf in the fit runcard; and the report contains some additional sections dedicated to the closure test statistical estimators.

These are:

• bias

The $$\chi^2$$ between the central predictions of the closure test and the underlying PDF predictions, a measure of how well the underlying predictions are reproduced by the closure test

• variance

The mean across replicas of the $$\chi^2$$ between predictions from a single replica and the central replica. Can be thought of as the variance of the replica predictions normalised by the covariance.

• $$\Delta_{\chi^2}$$

$$\chi^2$$ between central predictions and level 1 replica minus the $$\chi^2$$ between level 1 data and underlying PDF, gives some information on the direction the central predictions are being pulled with respect the the level 1 data

Detailed information on the closure test estimators can be found here.

## Comparison to another closure test

To compare to another closure test the user can use a special command line option with vp-comparefits, running

vp-comparefits --closure <other options>


will cause vp-comparefits to use a special closure comparison report which compares to closures for the statistical estimators above.

care should be taken that both of the closure tests being compared were fitting pseudodata which had the same level 1 shift applied to the same underlying law. Clearly the closure test estimators have some underlying dependence on these. To ensure this, check that both fits have a matching fakepdf key and filterseed, additionally the fits should have been ran during a time window within which the data generation algorithm was not modified.