There are several tutorials which have been run over the last few years with instructions and examples for running the combine tool.

### Citations

There is no document currently which can be cited for using the combine tool, however you can use the following publications for the procedures we use,

• Summer 2011 public ATLAS-CMS note for any Frequentist limit setting procedures with toys or Bayesian limits, constructing likelihoods, descriptions of nuisance parameter options (like log-normals (lnN) or gamma (gmN), and for definitions of test-statistics.

• CCGV paper if you use any of the asymptotic (eg with -M AsymptoticLimits or -M Significance approximations for limits/p-values.

• If you use the Barlow-Beeston approach to MC stat (bin-by-bin) uncertainties, please cite their paper Barlow-Beeston. You should also cite this note if you use the autoMCStats directive to produce a single parameter per bin.

• If you use shape uncertainties for template (TH1 or RooDataHist) based datacards, you can cite this note from J. Conway.

• If you are extracting uncertainties from LH scans - i.e using $-2\Delta Log{L}=1$ etc for the 1$\sigma$ intervals, you can cite either the ATLAS+CMS or CMS Higgs paper.

• There is also a long list of citation recommendations from the CMS Statistics Committee pages.

# FAQ

• Why does combine have trouble with bins that have zero expected contents?
• If you're computing only upper limits, and your zero-prediction bins are all empty in data, then you can just set the background to a very small value instead of zero as anyway the computation is regular for background going to zero (e.g. a counting experiment with $B\leq1$ will have essentially the same expected limit and observed limit as one with $B=0$). If you're computing anything else, e.g. p-values, or if your zero-prediction bins are not empty in data, you're out of luck, and you should find a way to get a reasonable background prediction there (and set an uncertainty on it, as per the point above)
• How can an uncertainty be added to a zero quantity?
• You can put an uncertainty even on a zero event yield if you use a gamma distribution. That's in fact the more proper way of doing it if the prediction of zero comes from the limited size of your MC or data sample used to compute it.
• Why does changing the observation in data affect my expected limit?
• The expected limit (if using either the default behaviour of -M AsymptoticLimits or using the LHC-limits style limit setting with toys) uses the post-fit expectation of the background model to generate toys. This means that first the model is fit to the observed data before toy generation. See the sections on blind limits and toy generation to avoid this behavior.
• How can I deal with an interference term which involves a negative contribution?
• You will need to set up a specific PhysicsModel to deal with this, however you can see this section to implement such a model which can incorperate a negative contribution to the physics process
• How does combine work?
• That is not a question which can be answered without someone's head exploding so please try to formulate something specific.
• What does fit status XYZ mean?
• Combine reports the fit status in some routines (for example in the FitDiagnostics method). These are typically the status of the last call from Minuit. For details on the meanings of these status codes see the Minuit2Minimizer documentation page.
• Why does my fit not converge?
• There are several reasons why some fits may not converge. Often some indication can be obtained from the RooFitResult or status which you will see information from when using the --verbose X (with $X>2$) option. Sometimes however, it can be that the likelihood for your data is very unusual. You can get a rough idea about what the likelihood looks like as a function of your parameters (POIs and nuisances) using combineTool.py -M FastScan -w myworkspace.root (use --help for options).
• We have seen often that fits in combine using RooCBShape as a parametric function will fail. This is related to an optimisation that fails. You can try to fix the problem as described in this issue: https://github.com/cms-analysis/HiggsAnalysis-CombinedLimit/issues/347 (i.e add the option --X-rtd ADDNLL_CBNLL=0).
• Why does the fit/fits take so long?
• The minimisation routines are common to many methods in combine. You can tune the fitting using the generic optimisation command line options described here. For example, setting the default minimizer strategy to 0 can greatly improve the speed since this avoids running Hesse. In calculations such as AsymptoticLimits, Hesse is not needed and hence this can be done, however, for FitDiagnostics the uncertainties and correlations are part of the output so using strategy 0 may not be particularly accurate.
• Why are the results for my counting experiment so slow or unstable?
• There is a known issue with counting experiments with large numbers of events which will cause unstable fits or even the fit to fail. You can avoid this by creating a "fake" shape datacard (see this section from the setting up the datacards page). The simplest way to do this is to run combineCards.py -S mycountingcard.txt > myshapecard.txt. You may still find that your parameter uncertainties are not correct when you have large numbers of events. This can be often fixed using the --robustHesse option. An example of this issue is detailed here.
• Why do some of my nuisance parameters have uncertainties > 1?
• When running -M FitDiagnostics you may find that the post-fit uncertainties of the nuisances are $> 1$ (or larger than their pre-fit values). If this is the case, you should first check if the same is true when adding the option --minos all which will invoke minos to scan the likelihood as a function of these parameters to determine the crossing at $-2\times\Delta\log\mathcal{L}=1$ rather than relying on the estimate from Hesse. However, this is not guaranteed to succeed, in which case you can scan the likelihood yourself using MultiDimFit (see here ) and specifying the option --poi X where X is your nuisance parameter.
• How can I avoid using the data?
• For almost all methods, you can use toy data (or an Asimov dataset) in place of the real data for your results to be blind. You should be careful however as in some methods, such as -M AsymptoticLimits or -M HybridNew --LHCmode LHC-limits or any other method using the option --toysFrequentist, the data will be used to determine the most likely nuisance parameter values (to determine the so-called a-posteriori expectation). See the section on toy data generation for details on this.
• What if my nuisance parameters have correlations which are not 0 or 1?
• Combine is designed under the assumption that each source of nuisance parameter is uncorrelated with the other sources. If you have a case where some pair (or set) of nuisances have some known correlation structure, you can compute the eigenvectors of their correlation matrix and provide these diagonalised nuisances to combine. You can also model partial correlations, between different channels or data taking periods, of a given nuisance parameter using the combineTool as described in this page.
• My nuisances are (artificially) constrained and/or the impact plot show some strange behaviour, especially after including MC statistical uncertainties. What can I do?
• Depending on the details of the analysis, several solutions can be adopted to mitigate these effects. We advise to run the validation tools at first, to identify possible redundant shape uncertainties that can be safely eliminated or replaced with lnN ones. Any remaining artificial constrain should be studies. Possible mitigating strategies can be to (a) smooth the templates or (b) adopt some rebinning in order to reduce statistical fluctuations in the templates. A description of possible strategies and effects can be found in this talk by Margaret Eminizer
• What do CLs, CLs+b and CLb in the code mean?
• The names CLs+b and CLb are rather outdated and should instead be referred to as p-values - $p_{\mu}$ and $1-p_{b}$, respectively. We use the CLs (which itself is not a p-value) criterion often in High energy physics as it is designed to avoid excluding a signal model when the sensitivity is low (and protects against excluding due to underfluctuations in the data). Typically, when excluding a signal model the p-value $p_{\mu}$ often refers to the p-value under the signal+background hypothesis, assuming a particular value of the signal stregth ($\mu$) while $p_{b}$ is the p-value under the background only hypothesis. You can find more details and definitions of the CLs criterion and $p_{\mu}$ and $p_{b}$ in section 39.4.2.4 the 2016 PDG review.