Rf 3 1 6_Llratioplot¶

Multidimensional models: using the likelihood ratio techique to construct a signal enhanced one-dimensional projection of a multi-dimensional pdf

Author: Clemens Lange, Wouter Verkerke (C++ version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, January 19, 2022 at 10:20 AM.

In [ ]:
import ROOT

Create 3D pdf and data¶

Create observables

In [ ]:
x = ROOT.RooRealVar("x", "x", -5, 5)
y = ROOT.RooRealVar("y", "y", -5, 5)
z = ROOT.RooRealVar("z", "z", -5, 5)

Create signal pdf gauss(x)gauss(y)gauss(z)

In [ ]:
gx = ROOT.RooGaussian("gx", "gx", x, ROOT.RooFit.RooConst(0), ROOT.RooFit.RooConst(1))
gy = ROOT.RooGaussian("gy", "gy", y, ROOT.RooFit.RooConst(0), ROOT.RooFit.RooConst(1))
gz = ROOT.RooGaussian("gz", "gz", z, ROOT.RooFit.RooConst(0), ROOT.RooFit.RooConst(1))
sig = ROOT.RooProdPdf("sig", "sig", [gx, gy, gz])

Create background pdf poly(x)poly(y)poly(z)

In [ ]:
px = ROOT.RooPolynomial("px", "px", x, [-0.1, 0.004])
py = ROOT.RooPolynomial("py", "py", y, [0.1, -0.004])
pz = ROOT.RooPolynomial("pz", "pz", z)
bkg = ROOT.RooProdPdf("bkg", "bkg", [px, py, pz])

Create composite pdf sig+bkg

In [ ]:
fsig = ROOT.RooRealVar("fsig", "signal fraction", 0.1, 0.0, 1.0)
model = ROOT.RooAddPdf("model", "model", [sig, bkg], [fsig])

data = model.generate({x, y, z}, 20000)

Project pdf and data on x¶

Make plain projection of data and pdf on x observable

In [ ]:
frame = x.frame(Title="Projection of 3D data and pdf on X", Bins=40)
data.plotOn(frame)
model.plotOn(frame)

Define projected signal likelihood ratio¶

Calculate projection of signal and total likelihood on (y,z) observables i.e. integrate signal and composite model over x

In [ ]:
sigyz = sig.createProjection({x})
totyz = model.createProjection({x})

Construct the log of the signal / signal+background probability

In [ ]:
llratio_func = ROOT.RooFormulaVar("llratio", "log10(@0)-log10(@1)", [sigyz, totyz])

Plot data with a LL ratio cut¶

Calculate the llratio value for each event in the dataset

In [ ]:

Extract the subset of data with large signal likelihood

In [ ]:
dataSel = data.reduce(Cut="llratio>0.7")

Make plot frame

In [ ]:
frame2 = x.frame(Title="Same projection on X with LLratio(y,z)>0.7", Bins=40)

Plot select data on frame

In [ ]:
dataSel.plotOn(frame2)

Make MC projection of pdf with same LL ratio cut¶

Generate large number of events for MC integration of pdf projection

In [ ]:
mcprojData = model.generate({x, y, z}, 10000)

Calculate LL ratio for each generated event and select MC events with llratio)0.7

In [ ]:
mcprojDataSel = mcprojData.reduce(Cut="llratio>0.7")

Project model on x, projected observables (y,z) with Monte Carlo technique on set of events with the same llratio cut as was applied to data

In [ ]:
model.plotOn(frame2, ProjWData=mcprojDataSel)

c = ROOT.TCanvas("rf316_llratioplot", "rf316_llratioplot", 800, 400)
c.Divide(2)
c.cd(1)