Rf 3 0 7_Fullpereventerrors¶

Multidimensional models: usage of full pdf with per-event errors

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 Monday, January 17, 2022 at 09:59 AM.

In [ ]:
import ROOT

B-physics pdf with per-event Gaussian resolution¶

Observables

In [ ]:
dt = ROOT.RooRealVar("dt", "dt", -10, 10)
dterr = ROOT.RooRealVar("dterr", "per-event error on dt", 0.01, 10)

Build a gaussian resolution model scaled by the per-error = gauss(dt,bias,sigma*dterr)

In [ ]:
bias = ROOT.RooRealVar("bias", "bias", 0, -10, 10)
sigma = ROOT.RooRealVar("sigma", "per-event error scale factor", 1, 0.1, 10)
gm = ROOT.RooGaussModel("gm1", "gauss model scaled bt per-event error", dt, bias, sigma, dterr)

Construct decay(dt) (x) gauss1(dt|dterr)

In [ ]:
tau = ROOT.RooRealVar("tau", "tau", 1.548)
decay_gm = ROOT.RooDecay("decay_gm", "decay", dt, tau, gm, type="DoubleSided")

Construct empirical pdf for per-event error¶

Use landau pdf to get empirical distribution with long tail

In [ ]:
pdfDtErr = ROOT.RooLandau("pdfDtErr", "pdfDtErr", dterr, ROOT.RooFit.RooConst(1), ROOT.RooFit.RooConst(0.25))

Construct a histogram pdf to describe the shape of the dtErr distribution

In [ ]:
pdfErr = ROOT.RooHistPdf("pdfErr", "pdfErr", {dterr}, expHistDterr)

Construct conditional product decay_dm(dt|dterr)*pdf(dterr)¶

Construct production of conditional decay_dm(dt|dterr) with empirical pdfErr(dterr)

In [ ]:
model = ROOT.RooProdPdf("model", "model", {pdfErr}, Conditional=({decay_gm}, {dt}))

(Alternatively you could also use the landau shape pdfDtErr) ROOT.RooProdPdf model("model", "model",pdfDtErr, ROOT.RooFit.Conditional(decay_gm,dt))

Sample, fit and plot product model¶

Specify external dataset with dterr values to use model_dm as conditional pdf

In [ ]:
data = model.generate({dt, dterr}, 10000)

Fit conditional decay_dm(dt|dterr)¶

Specify dterr as conditional observable

In [ ]:
model.fitTo(data)

Plot conditional decay_dm(dt|dterr)¶

Make two-dimensional plot of conditional pdf in (dt,dterr)

In [ ]:
hh_model = model.createHistogram("hh_model", dt, Binning=50, YVar=dict(var=dterr, Binning=50))
hh_model.SetLineColor(ROOT.kBlue)

Make projection of data an dt

In [ ]:
frame = dt.frame(Title="Projection of model(dt|dterr) on dt")
data.plotOn(frame)
model.plotOn(frame)

Draw all frames on canvas

In [ ]:
c = ROOT.TCanvas("rf307_fullpereventerrors", "rf307_fullpereventerrors", 800, 400)
c.Divide(2)
c.cd(1)
hh_model.GetZaxis().SetTitleOffset(2.5)
hh_model.Draw("surf")
c.cd(2)