rs401c_FeldmanCousins.py File Reference

Detailed Description

Produces an interval on the mean signal in a number counting experiment with known background using the Feldman-Cousins technique.

Using the RooStats FeldmanCousins tool with 200 bins it takes 1 min and the interval is [0.2625, 10.6125] with a step size of 0.075. The interval in Feldman & Cousins's original paper is [.29, 10.81] Phys.Rev.D57:3873-3889,1998.

DataStore poisData (Generated From )
  Contains 1 entries
  Observables: 
    1)  x = 7  L(0 - 50)  ""
 
RooWorkspace()  contents
 
variables
---------
(mu,x)
 
p.d.f.s
-------
RooPoisson::pois[ x=x mean=mean ] = 0.0224772
 
functions
--------
RooAddition::mean[ mu + b ] = 5.5
 
named sets
----------
poissonProblem_Observables:(x)
poissonProblem_POI:(mu)
 
 
=== Using the following for poissonProblem ===
Observables:             RooArgSet:: = (x)
Parameters of Interest:  RooArgSet:: = (mu)
PDF:                     RooPoisson::pois[ x=x mean=mean ] = 0.0224772
 
FeldmanCousins: ntoys per point: adaptive
FeldmanCousins: nEvents per toy will not fluctuate, will always be 1
FeldmanCousins: Model has no nuisance parameters
FeldmanCousins: # points to test = 100
NeymanConstruction: Prog: 1/100 total MC = 240 this test stat = 1.83324
 mu=0.075 [-inf, 1.08573]  in interval = 0
 
NeymanConstruction: Prog: 2/100 total MC = 80 this test stat = 1.6497
 mu=0.225 [-inf, 0.949959]  in interval = 0
 
NeymanConstruction: Prog: 3/100 total MC = 80 this test stat = 1.4816
 mu=0.375 [-inf, 0.827185]  in interval = 0
 
NeymanConstruction: Prog: 4/100 total MC = 240 this test stat = 1.32721
 mu=0.525 [-inf, 1.32721]  in interval = 1
 
NeymanConstruction: Prog: 5/100 total MC = 80 this test stat = 1.1855
 mu=0.675 [-inf, 2.73601]  in interval = 1
 
NeymanConstruction: Prog: 6/100 total MC = 240 this test stat = 1.05546
 mu=0.825 [-inf, 1.72806]  in interval = 1
 
NeymanConstruction: Prog: 7/100 total MC = 80 this test stat = 0.936198
 mu=0.975 [-inf, 2.32979]  in interval = 1
 
NeymanConstruction: Prog: 8/100 total MC = 80 this test stat = 0.826909
 mu=1.125 [-inf, 1.424]  in interval = 1
 
NeymanConstruction: Prog: 9/100 total MC = 80 this test stat = 0.726882
 mu=1.275 [-inf, 1.2882]  in interval = 1
 
NeymanConstruction: Prog: 10/100 total MC = 80 this test stat = 0.635479
 mu=1.425 [-inf, 1.81453]  in interval = 1
 
NeymanConstruction: Prog: 11/100 total MC = 80 this test stat = 0.552124
 mu=1.575 [-inf, 1.66456]  in interval = 1
 
NeymanConstruction: Prog: 12/100 total MC = 80 this test stat = 0.476298
 mu=1.725 [-inf, 1.725]  in interval = 1
 
NeymanConstruction: Prog: 13/100 total MC = 80 this test stat = 0.40728
 mu=1.875 [-inf, 2.05965]  in interval = 1
 
NeymanConstruction: Prog: 14/100 total MC = 80 this test stat = 0.345232
 mu=2.025 [-inf, 1.9066]  in interval = 1
 
NeymanConstruction: Prog: 15/100 total MC = 80 this test stat = 0.289405
 mu=2.175 [-inf, 1.76244]  in interval = 1
 
NeymanConstruction: Prog: 16/100 total MC = 80 this test stat = 0.239437
 mu=2.325 [-inf, 1.7512]  in interval = 1
 
NeymanConstruction: Prog: 17/100 total MC = 80 this test stat = 0.195006
 mu=2.475 [-inf, 1.27174]  in interval = 1
 
NeymanConstruction: Prog: 18/100 total MC = 80 this test stat = 0.155489
 mu=2.625 [-inf, 1.99618]  in interval = 1
 
NeymanConstruction: Prog: 19/100 total MC = 80 this test stat = 0.121494
 mu=2.775 [-inf, 1.86244]  in interval = 1
 
NeymanConstruction: Prog: 20/100 total MC = 80 this test stat = 0.0920776
 mu=2.925 [-inf, 1.73057]  in interval = 1
 
NeymanConstruction: Prog: 21/100 total MC = 80 this test stat = 0.0670922
 mu=3.075 [-inf, 1.60585]  in interval = 1
 
NeymanConstruction: Prog: 22/100 total MC = 80 this test stat = 0.0463567
 mu=3.225 [-inf, 2.10098]  in interval = 1
 
NeymanConstruction: Prog: 23/100 total MC = 80 this test stat = 0.0296823
 mu=3.375 [-inf, 1.96524]  in interval = 1
 
NeymanConstruction: Prog: 24/100 total MC = 80 this test stat = 0.0168841
 mu=3.525 [-inf, 1.97094]  in interval = 1
 
NeymanConstruction: Prog: 25/100 total MC = 80 this test stat = 0.00778646
 mu=3.675 [-inf, 2.07549]  in interval = 1
 
NeymanConstruction: Prog: 26/100 total MC = 80 this test stat = 0.00222463
 mu=3.825 [-inf, 1.59677]  in interval = 1
 
NeymanConstruction: Prog: 27/100 total MC = 80 this test stat = 4.47494e-05
 mu=3.975 [-inf, 2.06902]  in interval = 1
 
NeymanConstruction: Prog: 28/100 total MC = 80 this test stat = 0.00110295
 mu=4.125 [-inf, 2.39501]  in interval = 1
 
NeymanConstruction: Prog: 29/100 total MC = 80 this test stat = 0.00526396
 mu=4.275 [-inf, 1.6175]  in interval = 1
 
NeymanConstruction: Prog: 30/100 total MC = 80 this test stat = 0.0123995
 mu=4.425 [-inf, 1.70627]  in interval = 1
 
NeymanConstruction: Prog: 31/100 total MC = 80 this test stat = 0.0223862
 mu=4.575 [-inf, 1.79627]  in interval = 1
 
NeymanConstruction: Prog: 32/100 total MC = 80 this test stat = 0.0351041
 mu=4.725 [-inf, 2.04845]  in interval = 1
 
NeymanConstruction: Prog: 33/100 total MC = 80 this test stat = 0.0504339
 mu=4.875 [-inf, 2.94484]  in interval = 1
 
NeymanConstruction: Prog: 34/100 total MC = 80 this test stat = 0.0682548
 mu=5.025 [-inf, 3.0571]  in interval = 1
 
NeymanConstruction: Prog: 35/100 total MC = 80 this test stat = 0.0888053
 mu=5.175 [-inf, 2.27954]  in interval = 1
 
NeymanConstruction: Prog: 36/100 total MC = 80 this test stat = 0.111493
 mu=5.325 [-inf, 2.26305]  in interval = 1
 
NeymanConstruction: Prog: 37/100 total MC = 80 this test stat = 0.136468
 mu=5.475 [-inf, 2.03894]  in interval = 1
 
NeymanConstruction: Prog: 38/100 total MC = 80 this test stat = 0.163629
 mu=5.625 [-inf, 1.55152]  in interval = 1
 
NeymanConstruction: Prog: 39/100 total MC = 80 this test stat = 0.192899
 mu=5.775 [-inf, 1.81715]  in interval = 1
 
NeymanConstruction: Prog: 40/100 total MC = 80 this test stat = 0.224207
 mu=5.925 [-inf, 1.71475]  in interval = 1
 
NeymanConstruction: Prog: 41/100 total MC = 80 this test stat = 0.257484
 mu=6.075 [-inf, 2.75427]  in interval = 1
 
NeymanConstruction: Prog: 42/100 total MC = 80 this test stat = 0.292951
 mu=6.225 [-inf, 2.03573]  in interval = 1
 
NeymanConstruction: Prog: 43/100 total MC = 80 this test stat = 0.330045
 mu=6.375 [-inf, 1.92767]  in interval = 1
 
NeymanConstruction: Prog: 44/100 total MC = 80 this test stat = 0.368932
 mu=6.525 [-inf, 2.0544]  in interval = 1
 
NeymanConstruction: Prog: 45/100 total MC = 80 this test stat = 0.409554
 mu=6.675 [-inf, 2.14188]  in interval = 1
 
NeymanConstruction: Prog: 46/100 total MC = 80 this test stat = 0.45186
 mu=6.825 [-inf, 2.72294]  in interval = 1
 
NeymanConstruction: Prog: 47/100 total MC = 80 this test stat = 0.495797
 mu=6.975 [-inf, 2.03823]  in interval = 1
 
NeymanConstruction: Prog: 48/100 total MC = 80 this test stat = 0.541318
 mu=7.125 [-inf, 2.41011]  in interval = 1
 
NeymanConstruction: Prog: 49/100 total MC = 80 this test stat = 0.588375
 mu=7.275 [-inf, 1.83449]  in interval = 1
 
NeymanConstruction: Prog: 50/100 total MC = 80 this test stat = 0.636924
 mu=7.425 [-inf, 2.80213]  in interval = 1
 
NeymanConstruction: Prog: 51/100 total MC = 80 this test stat = 0.686922
 mu=7.575 [-inf, 1.82957]  in interval = 1
 
NeymanConstruction: Prog: 52/100 total MC = 80 this test stat = 0.738329
 mu=7.725 [-inf, 1.9093]  in interval = 1
 
    ----> Doing a re-scan first
NeymanConstruction: Prog: 53/100 total MC = 80 this test stat = 0.791008
 mu=7.875 [-inf, 1.98986]  in interval = 1
 
    ----> Doing a re-scan first
NeymanConstruction: Prog: 54/100 total MC = 80 this test stat = 0.845195
 mu=8.025 [-inf, 2.82912]  in interval = 1
 
    ----> Doing a re-scan first
    ----> Doing a re-scan first
NeymanConstruction: Prog: 55/100 total MC = 80 this test stat = 0.900613
 mu=8.175 [-inf, 2.23216]  in interval = 1
 
NeymanConstruction: Prog: 56/100 total MC = 80 this test stat = 0.957212
 mu=8.325 [-inf, 1.51348]  in interval = 1
 
NeymanConstruction: Prog: 57/100 total MC = 80 this test stat = 1.01518
 mu=8.475 [-inf, 2.32128]  in interval = 1
 
NeymanConstruction: Prog: 58/100 total MC = 80 this test stat = 1.07427
 mu=8.625 [-inf, 4.56136]  in interval = 1
 
NeymanConstruction: Prog: 59/100 total MC = 80 this test stat = 1.13452
 mu=8.775 [-inf, 1.83847]  in interval = 1
 
NeymanConstruction: Prog: 60/100 total MC = 80 this test stat = 1.19586
 mu=8.925 [-inf, 1.80373]  in interval = 1
 
NeymanConstruction: Prog: 61/100 total MC = 80 this test stat = 1.25841
 mu=9.075 [-inf, 2.45852]  in interval = 1
 
NeymanConstruction: Prog: 62/100 total MC = 80 this test stat = 1.32199
 mu=9.225 [-inf, 1.95466]  in interval = 1
 
NeymanConstruction: Prog: 63/100 total MC = 80 this test stat = 1.38662
 mu=9.375 [-inf, 2.24328]  in interval = 1
 
NeymanConstruction: Prog: 64/100 total MC = 80 this test stat = 1.45228
 mu=9.525 [-inf, 2.50319]  in interval = 1
 
NeymanConstruction: Prog: 65/100 total MC = 80 this test stat = 1.51895
 mu=9.675 [-inf, 3.02403]  in interval = 1
 
NeymanConstruction: Prog: 66/100 total MC = 240 this test stat = 1.58659
 mu=9.825 [-inf, 1.60365]  in interval = 1
 
NeymanConstruction: Prog: 67/100 total MC = 80 this test stat = 1.6552
 mu=9.975 [-inf, 3.20706]  in interval = 1
 
NeymanConstruction: Prog: 68/100 total MC = 80 this test stat = 1.72474
 mu=10.125 [-inf, 2.42844]  in interval = 1
 
[#0] PROGRESS:Generation -- generated toys: 500 / 1440
[#0] PROGRESS:Generation -- generated toys: 1000 / 1440
NeymanConstruction: Prog: 69/100 total MC = 2160 this test stat = 1.79519
 mu=10.275 [-inf, 1.79519]  in interval = 1
 
NeymanConstruction: Prog: 70/100 total MC = 240 this test stat = 1.86654
 mu=10.425 [-inf, 1.86654]  in interval = 1
 
NeymanConstruction: Prog: 71/100 total MC = 80 this test stat = 1.93876
 mu=10.575 [-inf, 2.67618]  in interval = 1
 
NeymanConstruction: Prog: 72/100 total MC = 80 this test stat = 2.01184
 mu=10.725 [-inf, 1.40678]  in interval = 0
 
NeymanConstruction: Prog: 73/100 total MC = 80 this test stat = 2.08575
 mu=10.875 [-inf, 1.86151]  in interval = 0
 
NeymanConstruction: Prog: 74/100 total MC = 240 this test stat = 2.16048
 mu=11.025 [-inf, 1.7642]  in interval = 0
 
NeymanConstruction: Prog: 75/100 total MC = 80 this test stat = 2.23601
 mu=11.175 [-inf, 1.59869]  in interval = 0
 
NeymanConstruction: Prog: 76/100 total MC = 240 this test stat = 2.31232
 mu=11.325 [-inf, 1.66448]  in interval = 0
 
NeymanConstruction: Prog: 77/100 total MC = 80 this test stat = 2.38941
 mu=11.475 [-inf, 1.26987]  in interval = 0
 
NeymanConstruction: Prog: 78/100 total MC = 240 this test stat = 2.46724
 mu=11.625 [-inf, 1.40071]  in interval = 0
 
NeymanConstruction: Prog: 79/100 total MC = 80 this test stat = 2.54582
 mu=11.775 [-inf, 1.86704]  in interval = 0
 
NeymanConstruction: Prog: 80/100 total MC = 80 this test stat = 2.62511
 mu=11.925 [-inf, 1.93623]  in interval = 0
 
NeymanConstruction: Prog: 81/100 total MC = 80 this test stat = 2.70511
 mu=12.075 [-inf, 1.43268]  in interval = 0
 
NeymanConstruction: Prog: 82/100 total MC = 240 this test stat = 2.7858
 mu=12.225 [-inf, 1.49357]  in interval = 0
 
NeymanConstruction: Prog: 83/100 total MC = 80 this test stat = 2.86717
 mu=12.375 [-inf, 1.55534]  in interval = 0
 
NeymanConstruction: Prog: 84/100 total MC = 80 this test stat = 2.94921
 mu=12.525 [-inf, 1.12614]  in interval = 0
 
NeymanConstruction: Prog: 85/100 total MC = 80 this test stat = 3.03185
 mu=12.675 [-inf, 2.29398]  in interval = 0
 
NeymanConstruction: Prog: 86/100 total MC = 80 this test stat = 3.11523
 mu=12.825 [-inf, 1.7457]  in interval = 0
 
NeymanConstruction: Prog: 87/100 total MC = 80 this test stat = 3.1991
 mu=12.975 [-inf, 1.8108]  in interval = 0
 
NeymanConstruction: Prog: 88/100 total MC = 80 this test stat = 3.28355
 mu=13.125 [-inf, 2.51742]  in interval = 0
 
NeymanConstruction: Prog: 89/100 total MC = 240 this test stat = 3.36896
 mu=13.275 [-inf, 1.40455]  in interval = 0
 
NeymanConstruction: Prog: 90/100 total MC = 80 this test stat = 3.45474
 mu=13.425 [-inf, 2.01076]  in interval = 0
 
NeymanConstruction: Prog: 91/100 total MC = 240 this test stat = 3.5411
 mu=13.575 [-inf, 2.07893]  in interval = 0
 
NeymanConstruction: Prog: 92/100 total MC = 80 this test stat = 3.62804
 mu=13.725 [-inf, 2.14777]  in interval = 0
 
NeymanConstruction: Prog: 93/100 total MC = 80 this test stat = 3.71554
 mu=13.875 [-inf, 1.16754]  in interval = 0
 
NeymanConstruction: Prog: 94/100 total MC = 80 this test stat = 3.80359
 mu=14.025 [-inf, 1.70395]  in interval = 0
 
NeymanConstruction: Prog: 95/100 total MC = 240 this test stat = 3.89219
 mu=14.175 [-inf, 1.76612]  in interval = 0
 
NeymanConstruction: Prog: 96/100 total MC = 240 this test stat = 3.98132
 mu=14.325 [-inf, 1.32819]  in interval = 0
 
NeymanConstruction: Prog: 97/100 total MC = 80 this test stat = 4.07097
 mu=14.475 [-inf, 1.38331]  in interval = 0
 
NeymanConstruction: Prog: 98/100 total MC = 80 this test stat = 4.16114
 mu=14.625 [-inf, 1.43935]  in interval = 0
 
NeymanConstruction: Prog: 99/100 total MC = 240 this test stat = 4.25182
 mu=14.775 [-inf, 1.49612]  in interval = 0
 
NeymanConstruction: Prog: 100/100 total MC = 240 this test stat = 4.343
 mu=14.925 [-inf, 2.08888]  in interval = 0
 
[#1] INFO:Eval -- 68 points in interval
Real time 0:00:05, CP time 5.110
is this point in the interval?  False
interval is [0.525, 10.575]

 
import ROOT
 
# to time the macro... about 30 s
t = ROOT.TStopwatch()
t.Start()
 
# make a simple model
x = ROOT.RooRealVar("x", "", 1, 0, 50)
mu = ROOT.RooRealVar("mu", "", 2.5, 0, 15)  # with a limit on mu>=0
b = ROOT.RooConstVar("b", "", 3.0)
mean = ROOT.RooAddition("mean", "", [mu, b])
pois = ROOT.RooPoisson("pois", "", x, mean)
parameters = {mu}
 
# create a toy dataset
data = pois.generate({x}, 1)
data.Print("v")
 
dataCanvas = ROOT.TCanvas("dataCanvas")
frame = x.frame()
data.plotOn(frame)
frame.Draw()
dataCanvas.Update()
 
w = ROOT.RooWorkspace()
modelConfig = ROOT.RooStats.ModelConfig("poissonProblem", w)
modelConfig.SetPdf(pois)
modelConfig.SetParametersOfInterest(parameters)
modelConfig.SetObservables({x})
w.Print()
 
# show use of Feldman-Cousins
fc = ROOT.RooStats.FeldmanCousins(data, modelConfig)
fc.SetTestSize(0.05)  # set size of test
fc.UseAdaptiveSampling(True)
fc.FluctuateNumDataEntries(False)  # number counting analysis: dataset always has 1 entry with N events observed
fc.SetNBins(100)  # number of points to test per parameter
 
# use the Feldman-Cousins tool
interval = fc.GetInterval()
 
# make a canvas for plots
intervalCanvas = ROOT.TCanvas("intervalCanvas")
 
print("is this point in the interval? ", interval.IsInInterval(parameters))
print("interval is [{}, {}]".format(interval.LowerLimit(mu), interval.UpperLimit(mu)))
 
# using 200 bins it takes 1 min and the answer is
# interval is [0.2625, 10.6125] with a step size of .075
# The interval in Feldman & Cousins's original paper is [.29, 10.81]
# Phys.Rev.D57:3873-3889,1998.
 
# No dedicated plotting class yet, so do it by hand:
parameterScan = fc.GetPointsToScan()
hist = parameterScan.createHistogram("mu", ROOT.RooFit.Binning(30))
hist.Draw()
 
marks = []
# loop over points to test
for i in range(parameterScan.numEntries()):
    # get a parameter point from the list of points to test.
    tmpPoint = parameterScan.get(i).clone("temp")
 
    mark = ROOT.TMarker(tmpPoint.getRealValue("mu"), 1, 25)
    if interval.IsInInterval(tmpPoint):
        mark.SetMarkerColor(ROOT.kBlue)
    else:
        mark.SetMarkerColor(ROOT.kRed)
 
    mark.Draw("s")
    marks.append(mark)
 
t.Stop()
t.Print()
 
dataCanvas.SaveAs("rs401c_FeldmanCousins_data.png")
intervalCanvas.SaveAs("rs401c_FeldmanCousins_hist.png")

Date

July 2022

Authors

Artem Busorgin, Kyle Cranmer (C++ version)

Definition in file rs401c_FeldmanCousins.py.