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[RF] Update RooFit
rf204b_extendedLikelihood_rangedFit tutorial
The PR root-project#7719 changed the behavior of multi-range fits in RooFit, and from then one the relative yields in the multiple regions were also considered in the fit. The tutorial `rf204b_extendedLikelihood_rangedFit` was explaining the old caveat that relative yields are not considered in non-extended fits, but since that is not a problem anymore, a big chunk of explanation in the tutorial should be removed. A Python translation of the tutorial was also added. Closes root-project#8808.
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tutorials/roofit/rf204b_extendedLikelihood_rangedFit.py
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| ## \file | ||
| ## \ingroup tutorial_roofit | ||
| ## \notebook -nodraw | ||
| ## This macro demonstrates how to set up a fit in two ranges for plain | ||
| ## likelihoods and extended likelihoods. | ||
| ## | ||
| ## ### 1. Shape fits (plain likelihood) | ||
| ## | ||
| ## If you fit a non-extended pdf in two ranges, e.g. `pdf.fitTo(data,Range="Range1,Range2")`, | ||
| ## it will fit the shapes in the two selected ranges and also take into account the relative | ||
| ## predicted yields in those ranges. | ||
| ## | ||
| ## This is useful for example to represent a full-range fit, but with a | ||
| ## blinded signal region inside it. | ||
| ## | ||
| ## | ||
| ## ### 2. Shape+rate fits (extended likelihood) | ||
| ## | ||
| ## If your pdf is extended, i.e. measuring both the distribution in the observable as well | ||
| ## as the event count in the fitted region, some intervention is needed to make fits in ranges | ||
| ## work in a way that corresponds to intuition. | ||
| ## | ||
| ## If an extended fit is performed in a sub-range, the observed yield is only that of the subrange, hence | ||
| ## the expected event count will converge to a number that is smaller than what's visible in a plot. | ||
| ## In such cases, it is often preferred to interpret the extended term with respect to the full range | ||
| ## that's plotted, i.e., apply a correction to the extended likelihood term in such a way | ||
| ## that the interpretation of the expected event count remains that of the full range. This can | ||
| ## be done by applying a correcion factor (equal to the fraction of the pdf that is contained in the | ||
| ## fitted range) in the Poisson term that represents the extended likelihood term. | ||
| ## | ||
| ## If an extended likelihood fit is performed over *two* sub-ranges, this correction is | ||
| ## even more important: without it, each component likelihood would have a different interpretation | ||
| ## of the expected event count (each corresponding to the count in its own region), and a joint | ||
| ## fit of these regions with different interpretations of the same model parameter results | ||
| ## in a number that is not easily interpreted. | ||
| ## | ||
| ## If both regions correct their interpretatin such that N_expected refers to the full range, | ||
| ## it is interpreted easily, and consistent in both regions. | ||
| ## | ||
| ## This requires that the likelihood model is extended using RooAddPdf in the | ||
| ## form SumPdf = Nsig * sigPdf + Nbkg * bkgPdf. | ||
| ## | ||
| ## \macro_image | ||
| ## \macro_code | ||
| ## \macro_output | ||
| ## | ||
| ## \authors Stephan Hageboeck, Wouter Verkerke | ||
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| import ROOT | ||
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| ROOT.gROOT.SetBatch(True) | ||
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| # PART 1: Background-only fits | ||
| # ---------------------------- | ||
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| # Build plain exponential model | ||
| x = ROOT.RooRealVar("x", "x", 10, 100) | ||
| alpha = ROOT.RooRealVar("alpha", "alpha", -0.04, -0.1, -0.0) | ||
| model = ROOT.RooExponential("model", "Exponential model", x, alpha) | ||
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| # Define side band regions and full range | ||
| x.setRange("LEFT", 10, 20) | ||
| x.setRange("RIGHT", 60, 100) | ||
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| x.setRange("FULL", 10, 100) | ||
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| data = model.generate(x, 10000) | ||
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| # Construct an extended pdf, which measures the event count N **on the full range**. | ||
| # If the actual domain of x that is fitted is identical to FULL, this has no affect. | ||
| # | ||
| # If the fitted domain is a subset of `FULL`, though, the expected event count is divided by | ||
| # \f[ | ||
| # \mathrm{frac} = \frac{ | ||
| # \int_{\mathrm{Fit range}} \mathrm{model}(x) \; \mathrm{d}x }{ | ||
| # \int_{\mathrm{Full range}} \mathrm{model}(x) \; \mathrm{d}x }. | ||
| # \f] | ||
| # `N` will therefore return the count extrapolated to the full range instead of the fit range. | ||
| # | ||
| # **Note**: When using a RooAddPdf for extending the likelihood, the same effect can be achieved with | ||
| # [RooAddPdf::fixCoefRange()](https://root.cern.ch/doc/master/classRooAddPdf.html#ab631caf4b59e4c4221f8967aecbf2a65), | ||
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| N = ROOT.RooRealVar("N", "Extended term", 0, 20000) | ||
| extmodel = ROOT.RooExtendPdf("extmodel", "Extended model", model, N, "FULL") | ||
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| # It can be instructive to fit the above model to either the LEFT or RIGHT | ||
| # range. `N` should approximately converge to the expected number of events in | ||
| # the full range. One may try to leave out `"FULL"` in the constructor, or the | ||
| # interpretation of `N` changes. | ||
| extmodel.fitTo(data, Range="LEFT", PrintLevel=-1) | ||
| N.Print() | ||
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| # If we now do a simultaneous fit to the extended model, instead of the | ||
| # original model, the LEFT and RIGHT range will each correct their local `N` | ||
| # such that it refers to the `FULL` range. | ||
| # | ||
| # This joint fit of the extmodel will include (w.r.t. the plain model fit) a product of extended terms | ||
| # \f[ | ||
| # L_\mathrm{ext} = L | ||
| # \cdot \mathrm{Poisson} \left( N_\mathrm{obs}^\mathrm{LEFT} | N_\mathrm{exp} / \mathrm{frac LEFT} \right) | ||
| # \cdot \mathrm{Poisson} \left( N_\mathrm{obs}^\mathrm{RIGHT} | N_\mathrm{exp} / \mathrm{frac RIGHT} \right) | ||
| # \f] | ||
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| c = ROOT.TCanvas("c", "c", 2100, 700) | ||
| c.Divide(3) | ||
| c.cd(1) | ||
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| r = model.fitTo(data, Range="LEFT,RIGHT", PrintLevel=-1, Save=True) | ||
| r.Print() | ||
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| frame = x.frame() | ||
| data.plotOn(frame) | ||
| model.plotOn(frame, VisualizeError=r) | ||
| model.plotOn(frame) | ||
| model.paramOn(frame, Label="Non-extended fit") | ||
| frame.Draw() | ||
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| c.cd(2) | ||
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| r2 = extmodel.fitTo(data, Range="LEFT,RIGHT", PrintLevel=-1, Save=True) | ||
| r2.Print() | ||
| frame2 = x.frame() | ||
| data.plotOn(frame2) | ||
| extmodel.plotOn(frame2) | ||
| extmodel.plotOn(frame2, VisualizeError=r2) | ||
| extmodel.paramOn(frame2, Label="Extended fit", Layout=(0.4, 0.95)) | ||
| frame2.Draw() | ||
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| # PART 2: Extending with RooAddPdf | ||
| # -------------------------------- | ||
| # | ||
| # Now we repeat the above exercise, but instead of explicitly adding an extended term to a single shape pdf (RooExponential), | ||
| # we assume that we already have an extended likelihood model in the form of a RooAddPdf constructed in the form `Nsig * sigPdf + Nbkg * bkgPdf`. | ||
| # | ||
| # We add a Gaussian to the previously defined exponential background. | ||
| # The signal shape parameters are chosen constant, since the signal region is entirely in the blinded region, i.e., the fit has no sensitivity. | ||
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| c.cd(3) | ||
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| Nsig = ROOT.RooRealVar("Nsig", "Number of signal events", 1000, 0, 2000) | ||
| Nbkg = ROOT.RooRealVar("Nbkg", "Number of background events", 10000, 0, 20000) | ||
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| mean = ROOT.RooRealVar("mean", "Mean of signal model", 40.0) | ||
| width = ROOT.RooRealVar("width", "Width of signal model", 5.0) | ||
| sig = ROOT.RooGaussian("sig", "Signal model", x, mean, width) | ||
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| modelsum = ROOT.RooAddPdf("modelsum", "NSig*signal + NBkg*background", [sig, model], [Nsig, Nbkg]) | ||
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| # This model will automatically insert the correction factor for the | ||
| # reinterpretation of Nsig and Nnbkg in the full ranges. | ||
| # | ||
| # When this happens, it reports this with lines like the following: | ||
| # ``` | ||
| # [#1] INFO:Fitting -- RooAbsOptTestStatistic::ctor(nll_modelsum_modelsumData_LEFT) fixing interpretation of coefficients of any RooAddPdf to full domain of observables | ||
| # [#1] INFO:Fitting -- RooAbsOptTestStatistic::ctor(nll_modelsum_modelsumData_RIGHT) fixing interpretation of coefficients of any RooAddPdf to full domain of observables | ||
| # ``` | ||
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| r3 = modelsum.fitTo(data, Range="LEFT,RIGHT", PrintLevel=-1, Save=True) | ||
| r3.Print() | ||
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| frame3 = x.frame() | ||
| data.plotOn(frame3) | ||
| modelsum.plotOn(frame3) | ||
| modelsum.plotOn(frame3, VisualizeError=r3) | ||
| modelsum.paramOn(frame3, Label="S+B fit with RooAddPdf", Layout=(0.3, 0.95)) | ||
| frame3.Draw() | ||
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| c.Draw() | ||
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| c.SaveAs("rf204b_extendedLikelihood_rangedFit.png") |
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