rf316_llratioplot.py

## \ingroup tutorial_roofit_main

## \notebook

## Multidimensional models: using the likelihood ratio technique to construct a signal

## enhanced one-dimensional projection of a multi-dimensional pdf

##

## \macro_image

## \macro_code

## \macro_output

##

## \date February 2018

## \authors Clemens Lange, Wouter Verkerke (C++ version)

import ROOT

# Create 3D pdf and data

# -------------------------------------------

# Create observables

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)

gx = ROOT.RooGaussian("gx", "gx", x, 0.0, 1.0)

gy = ROOT.RooGaussian("gy", "gy", y, 0.0, 1.0)

gz = ROOT.RooGaussian("gz", "gz", z, 0.0, 1.0)

sig = ROOT.RooProdPdf("sig", "sig", [gx, gy, gz])

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

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

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

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

sigyz = sig.createProjection({x})

totyz = model.createProjection({x})

# Construct the log of the signal / signal+background probability

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

data.addColumn(llratio_func)

# Extract the subset of data with large signal likelihood

dataSel = data.reduce(Cut="llratio>0.7")

# Make plot frame

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

# Plot select data on frame

dataSel.plotOn(frame2)

# Make MC projection of pdf with same LL ratio cut

# ---------------------------------------------------------------------------------------------

# Generate large number of events for MC integration of pdf projection

mcprojData = model.generate({x, y, z}, 10000)

# Calculate LL ratio for each generated event and select MC events with

# llratio)0.7

mcprojData.addColumn(llratio_func)

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

model.plotOn(frame2, ProjWData=mcprojDataSel)

c = ROOT.TCanvas("rf316_llratioplot", "rf316_llratioplot", 800, 400)

c.Divide(2)

c.cd(1)

ROOT.gPad.SetLeftMargin(0.15)

frame.GetYaxis().SetTitleOffset(1.4)

frame.Draw()

c.cd(2)

ROOT.gPad.SetLeftMargin(0.15)

frame2.GetYaxis().SetTitleOffset(1.4)

frame2.Draw()

c.SaveAs("rf316_llratioplot.png")