Fitting generators to data with nuismin

Overview

nuismin expands on nuiscomp (documented here) by introducing the ability to minimise the test-statistic (i.e. the 𝜒²) by varying generator parameters (e.g. the axial mass for CCQE interactions, M_A^QE) and aspects of the data (e.g. normalisations). We recommend reading nuiscomp documentation and trying comparisons with nuiscomp before running fits with nuismin.

For the code-inclined, nuismin lives in nuisance/app/nuismin.cxx and is driven by nuisance/src/Routines/MinimizerRoutines.cxx. You can view it here.

This expands on the documentation provided by running

which is equivalent to

An example nuismin run

This example compares GENIE events to MiniBooNE data, just like in nuiscomp, and now fitting for M_A^QE. Again, the example is near identical for a different generator, you just have to Prepare appropriately and replace GENIE in the cardfile with your generator descriptor, e.g. NEUT, NUWRO, GIBUU. You also need to find the parameter in the generator you want to fit and replace the parameter in the card file appropriately, described below.

Make a plain file mbcomp_fit.card and fill it with:

• For a free parameter, use state="FREE"
• For a fixed parameter use state="FIX"

You can now run nuismin with this card file by doing

Specifying a measurement

Follows exactly the same as nuiscomp.

Options for a measurement

In nuiscomp we introduced the option of scaling an experiment using the norm keyword here. In nuismin the sample normalisation can be made a fitting parameter (with or without penalties) using the same syntax, provided type="FREE" is specified.

You can also change how the sample is treated statistically, if any corrections or masking should be applied, how it should be scaled, and so on. These can have dramatic effects on the minimisation and are documented here.

As an example of the impact of using a covariance matrix, we use a card file with

MINERvA_CC0pi_XSec_1DQ2QE_nu_norm = 4.89272 +- 0.911015 compared to a card file where we only use the diagonal errors

Specifying a generator

To change the generator you first need to have generated events with said generator and linked NUISANCE to the generator. You can find notes on this here. You also need to have prepared generator files for NUISANCE use.

Once you have NUISANCE linked and prepared files you simply change the input field to match your generator (GENIE, NEUT, NUWRO, GIBUU or NUANCE), and new file location. For example input="NUWRO:PATH_TO_PREPARED_NUWRO_FILE.root".

Changing systematics via event reweighting in nuismin

Recalling the mbcomp_fit.card from above, we set

If no state is given for a systematic it is assumed to be fixed at the nominal value.

Making fake-data via event reweighting

Fake-data can be provided to nuismin in two ways:

• Giving the -d parameter to nuismin (outlined later)
• Specifying a fakeparameter field

A card file for MiniBooNE CCQE in 1D Q2 for neutrino, setting the fake-data to be GENIE with MaCCQE set to 1 sigma above the default, would be

Running nuismin

nuismin takes a number of command line arguments, one of which is required. It requires either

• -c mycard.card where mycard.card is the provided card file (see above)
• -i 'card file contents'

The -i option follows the same structure as a card file but is instead an argument. For example

would acheive the same effect as providing nuismin with the simple mbcomp.card earlier.

The complete list of arguments and their types is:

• -c string: the cardfile to read
• -o string: the output file to create (default: append ".root" to cardfile name)
• -n int: the number of events to run on (default: all)
• -d string: fakedata input, can be either (default: empty)
• "MC": for setting the data to the nominal MC prediction
• "fakedata.root": Direct path to root file containing a MC histogram called the measurement name with "_MC" at the end (the default format for NUISANCE MC histograms)
• -f string: Fitting routines
Study methods:
• FixAtLim:
• FixAtLimBreak:
• ErrorBands:
• DataToys:
• Chi2Scan1D:
• Chi2Scan2D:

---

Fitting methods:
• Migrad: (Minuit2, Migrad)
• Simplex: (Minuit2, Simplex)
• Combined: (Minuit2, Combined)
• Brute: (Minuit2, Scan)
• Fumili: (Minuit2, Fumili)
• ConjugateFR: (GSLMultiMin, ConjugateFR)
• ConjugatePR: (GSLMultiMin, ConjugatePR)
• BFGS: (GSLMultiMin, BFGS)
• BFGS2: (GSLMultiMin, BFGS2)
• SteepDesc: (GSLMultiMin, SteepestDescent)
• GSLSimAn: (GSLSimAn)
• MCMC

---

Debugging:
• LowStat: Can be included to routines to run with low statistics (testing or debugging mode), e.g. LowStatMigrad or LowStatChi2Scan1D
• -i string: card file-like XML commands (default: empty)
• -q string: config arguments, which overwrite nuisance/parameters/config.xml (default: empty)
• e +/- error level relative that in nuisance/parameters/config.xml
• v +/- verbosity level relative that in nuisance/parameters/config.xml

Running nuismin as

NUISANCE produces various output as it sets up, using different verbosity logging levels, defined in nuisance/parameters/config.xml.

Inspecintg nuismin output