{
"cells": [
{
"cell_type": "markdown",
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"source": [
"# rs401c_FeldmanCousins\n",
"Produces an interval on the mean signal in a number counting experiment with known background using the\n",
"Feldman-Cousins technique.\n",
"\n",
"Using the RooStats FeldmanCousins tool with 200 bins\n",
"it takes 1 min and the interval is [0.2625, 10.6125]\n",
"with a step size of 0.075.\n",
"The interval in Feldman & Cousins's original paper is [.29, 10.81] Phys.Rev.D57:3873-3889,1998.\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Artem Busorgin, Kyle Cranmer (C++ version) \n",
"This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:35 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "73060641",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:36:00.913406Z",
"iopub.status.busy": "2026-05-19T20:36:00.913287Z",
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"shell.execute_reply": "2026-05-19T20:36:01.876069Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "bc6f8c80",
"metadata": {},
"source": [
"to time the macro... about 30 s"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "ee05844f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:36:01.916236Z",
"iopub.status.busy": "2026-05-19T20:36:01.916086Z",
"iopub.status.idle": "2026-05-19T20:36:02.035109Z",
"shell.execute_reply": "2026-05-19T20:36:02.034648Z"
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"outputs": [],
"source": [
"t = ROOT.TStopwatch()\n",
"t.Start()"
]
},
{
"cell_type": "markdown",
"id": "744a10af",
"metadata": {},
"source": [
"make a simple model"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "7bbee776",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:36:02.036838Z",
"iopub.status.busy": "2026-05-19T20:36:02.036719Z",
"iopub.status.idle": "2026-05-19T20:36:02.287294Z",
"shell.execute_reply": "2026-05-19T20:36:02.286849Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"\", 1, 0, 50)\n",
"mu = ROOT.RooRealVar(\"mu\", \"\", 2.5, 0, 15) # with a limit on mu>=0\n",
"b = ROOT.RooConstVar(\"b\", \"\", 3.0)\n",
"mean = ROOT.RooAddition(\"mean\", \"\", [mu, b])\n",
"pois = ROOT.RooPoisson(\"pois\", \"\", x, mean)\n",
"parameters = {mu}"
]
},
{
"cell_type": "markdown",
"id": "299ae15e",
"metadata": {},
"source": [
"create a toy dataset"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "68e79956",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:36:02.290187Z",
"iopub.status.busy": "2026-05-19T20:36:02.290056Z",
"iopub.status.idle": "2026-05-19T20:36:02.656895Z",
"shell.execute_reply": "2026-05-19T20:36:02.656302Z"
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},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"DataStore poisData (Generated From )\n",
" Contains 1 entries\n",
" Observables: \n",
" 1) x = 7 L(0 - 50) \"\"\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"RooWorkspace() contents\n",
"\n",
"variables\n",
"---------\n",
"(mu,x)\n",
"\n",
"p.d.f.s\n",
"-------\n",
"RooPoisson::pois[ x=x mean=mean ] = 0.0224772\n",
"\n",
"functions\n",
"--------\n",
"RooAddition::mean[ mu + b ] = 5.5\n",
"\n",
"named sets\n",
"----------\n",
"poissonProblem_Observables:(x)\n",
"poissonProblem_POI:(mu)\n",
"\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
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"text/plain": [
""
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"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data = pois.generate({x}, 1)\n",
"data.Print(\"v\")\n",
"\n",
"dataCanvas = ROOT.TCanvas(\"dataCanvas\")\n",
"frame = x.frame()\n",
"data.plotOn(frame)\n",
"frame.Draw()\n",
"dataCanvas.Update()\n",
"\n",
"w = ROOT.RooWorkspace()\n",
"modelConfig = ROOT.RooStats.ModelConfig(\"poissonProblem\", w)\n",
"modelConfig.SetPdf(pois)\n",
"modelConfig.SetParametersOfInterest(parameters)\n",
"modelConfig.SetObservables({x})\n",
"w.Print()"
]
},
{
"cell_type": "markdown",
"id": "9680a8dd",
"metadata": {},
"source": [
"show use of Feldman-Cousins"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "e9f8b7aa",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:36:02.659774Z",
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"shell.execute_reply": "2026-05-19T20:36:02.781770Z"
}
},
"outputs": [],
"source": [
"fc = ROOT.RooStats.FeldmanCousins(data, modelConfig)\n",
"fc.SetTestSize(0.05) # set size of test\n",
"fc.UseAdaptiveSampling(True)\n",
"fc.FluctuateNumDataEntries(False) # number counting analysis: dataset always has 1 entry with N events observed\n",
"fc.SetNBins(100) # number of points to test per parameter"
]
},
{
"cell_type": "markdown",
"id": "a74dc4b4",
"metadata": {},
"source": [
"use the Feldman-Cousins tool"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "c3c9d54e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:36:02.786265Z",
"iopub.status.busy": "2026-05-19T20:36:02.786130Z",
"iopub.status.idle": "2026-05-19T20:36:04.667471Z",
"shell.execute_reply": "2026-05-19T20:36:04.666634Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"=== Using the following for poissonProblem ===\n",
"Observables: RooArgSet:: = (x)\n",
"Parameters of Interest: RooArgSet:: = (mu)\n",
"PDF: RooPoisson::pois[ x=x mean=mean ] = 0.0224772\n",
"\n",
"FeldmanCousins: ntoys per point: adaptive\n",
"FeldmanCousins: nEvents per toy will not fluctuate, will always be 1\n",
"FeldmanCousins: Model has no nuisance parameters\n",
"FeldmanCousins: # points to test = 100\n",
"NeymanConstruction: Prog: 1/100 total MC = 240 this test stat = 1.83324\n",
" mu=0.075 [-inf, 1.08573] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 2/100 total MC = 80 this test stat = 1.6497\n",
" mu=0.225 [-inf, 0.949959] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 3/100 total MC = 80 this test stat = 1.4816\n",
" mu=0.375 [-inf, 0.827185] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 4/100 total MC = 240 this test stat = 1.32721\n",
" mu=0.525 [-inf, 1.32721] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 5/100 total MC = 80 this test stat = 1.1855\n",
" mu=0.675 [-inf, 2.73601] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 6/100 total MC = 240 this test stat = 1.05546\n",
" mu=0.825 [-inf, 1.72806] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 7/100 total MC = 80 this test stat = 0.936198\n",
" mu=0.975 [-inf, 2.32979] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 8/100 total MC = 80 this test stat = 0.826909\n",
" mu=1.125 [-inf, 1.424] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 9/100 total MC = 80 this test stat = 0.726882\n",
" mu=1.275 [-inf, 1.2882] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 10/100 total MC = 80 this test stat = 0.635479\n",
" mu=1.425 [-inf, 1.81453] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 11/100 total MC = 80 this test stat = 0.552124\n",
" mu=1.575 [-inf, 1.66456] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 12/100 total MC = 80 this test stat = 0.476298\n",
" mu=1.725 [-inf, 1.725] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 13/100 total MC = 80 this test stat = 0.40728\n",
" mu=1.875 [-inf, 2.05965] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 14/100 total MC = 80 this test stat = 0.345232\n",
" mu=2.025 [-inf, 1.9066] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 15/100 total MC = 80 this test stat = 0.289405\n",
" mu=2.175 [-inf, 1.76244] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 16/100 total MC = 80 this test stat = 0.239437\n",
" mu=2.325 [-inf, 1.7512] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 17/100 total MC = 80 this test stat = 0.195006\n",
" mu=2.475 [-inf, 1.27174] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 18/100 total MC = 80 this test stat = 0.155489\n",
" mu=2.625 [-inf, 1.99618] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 19/100 total MC = 80 this test stat = 0.121494\n",
" mu=2.775 [-inf, 1.86244] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 20/100 total MC = 80 this test stat = 0.0920776\n",
" mu=2.925 [-inf, 1.73057] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 21/100 total MC = 80 this test stat = 0.0670922\n",
" mu=3.075 [-inf, 1.60585] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 22/100 total MC = 80 this test stat = 0.0463567\n",
" mu=3.225 [-inf, 2.10098] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 23/100 total MC = 80 this test stat = 0.0296823\n",
" mu=3.375 [-inf, 1.96524] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 24/100 total MC = 80 this test stat = 0.0168841\n",
" mu=3.525 [-inf, 1.97094] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 25/100 total MC = 80 this test stat = 0.00778646\n",
" mu=3.675 [-inf, 2.07549] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 26/100 total MC = 80 this test stat = 0.00222463\n",
" mu=3.825 [-inf, 1.59677] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 27/100 total MC = 80 this test stat = 4.47494e-05\n",
" mu=3.975 [-inf, 2.06902] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 28/100 total MC = 80 this test stat = 0.00110295\n",
" mu=4.125 [-inf, 2.39501] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 29/100 total MC = 80 this test stat = 0.00526396\n",
" mu=4.275 [-inf, 1.6175] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 30/100 total MC = 80 this test stat = 0.0123995\n",
" mu=4.425 [-inf, 1.70627] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 31/100 total MC = 80 this test stat = 0.0223862\n",
" mu=4.575 [-inf, 1.79627] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 32/100 total MC = 80 this test stat = 0.0351041\n",
" mu=4.725 [-inf, 2.04845] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 33/100 total MC = 80 this test stat = 0.0504339\n",
" mu=4.875 [-inf, 2.94484] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 34/100 total MC = 80 this test stat = 0.0682548\n",
" mu=5.025 [-inf, 3.0571] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 35/100 total MC = 80 this test stat = 0.0888053\n",
" mu=5.175 [-inf, 2.27954] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 36/100 total MC = 80 this test stat = 0.111493\n",
" mu=5.325 [-inf, 2.26305] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 37/100 total MC = 80 this test stat = 0.136468\n",
" mu=5.475 [-inf, 2.03894] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 38/100 total MC = 80 this test stat = 0.163629\n",
" mu=5.625 [-inf, 1.55152] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 39/100 total MC = 80 this test stat = 0.192899\n",
" mu=5.775 [-inf, 1.81715] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 40/100 total MC = 80 this test stat = 0.224207\n",
" mu=5.925 [-inf, 1.71475] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 41/100 total MC = 80 this test stat = 0.257484\n",
" mu=6.075 [-inf, 2.75427] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 42/100 total MC = 80 this test stat = 0.292951\n",
" mu=6.225 [-inf, 2.03573] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 43/100 total MC = 80 this test stat = 0.330045\n",
" mu=6.375 [-inf, 1.92767] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 44/100 total MC = 80 this test stat = 0.368932\n",
" mu=6.525 [-inf, 2.0544] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 45/100 total MC = 80 this test stat = 0.409554\n",
" mu=6.675 [-inf, 2.14188] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 46/100 total MC = 80 this test stat = 0.45186\n",
" mu=6.825 [-inf, 2.72294] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 47/100 total MC = 80 this test stat = 0.495797\n",
" mu=6.975 [-inf, 2.03823] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 48/100 total MC = 80 this test stat = 0.541318\n",
" mu=7.125 [-inf, 2.41011] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 49/100 total MC = 80 this test stat = 0.588375\n",
" mu=7.275 [-inf, 1.83449] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 50/100 total MC = 80 this test stat = 0.636924\n",
" mu=7.425 [-inf, 2.80213] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 51/100 total MC = 80 this test stat = 0.686922\n",
" mu=7.575 [-inf, 1.82957] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 52/100 total MC = 80 this test stat = 0.738329\n",
" mu=7.725 [-inf, 1.9093] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 53/100 total MC = 80 this test stat = 0.791008\n",
" mu=7.875 [-inf, 1.98986] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 54/100 total MC = 80 this test stat = 0.845195\n",
" mu=8.025 [-inf, 2.82912] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 55/100 total MC = 80 this test stat = 0.900613\n",
" mu=8.175 [-inf, 2.23216] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 56/100 total MC = 80 this test stat = 0.957212\n",
" mu=8.325 [-inf, 1.51348] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 57/100 total MC = 80 this test stat = 1.01518\n",
" mu=8.475 [-inf, 2.32128] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 58/100 total MC = 80 this test stat = 1.07427\n",
" mu=8.625 [-inf, 4.56136] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 59/100 total MC = 80 this test stat = 1.13452\n",
" mu=8.775 [-inf, 1.83847] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 60/100 total MC = 80 this test stat = 1.19586\n",
" mu=8.925 [-inf, 1.80373] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 61/100 total MC = 80 this test stat = 1.25841\n",
" mu=9.075 [-inf, 2.45852] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 62/100 total MC = 80 this test stat = 1.32199\n",
" mu=9.225 [-inf, 1.95466] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 63/100 total MC = 80 this test stat = 1.38662\n",
" mu=9.375 [-inf, 2.24328] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 64/100 total MC = 80 this test stat = 1.45228\n",
" mu=9.525 [-inf, 2.50319] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 65/100 total MC = 80 this test stat = 1.51895\n",
" mu=9.675 [-inf, 3.02403] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 66/100 total MC = 240 this test stat = 1.58659\n",
" mu=9.825 [-inf, 1.60365] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 67/100 total MC = 80 this test stat = 1.6552\n",
" mu=9.975 [-inf, 3.20706] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 68/100 total MC = 80 this test stat = 1.72474\n",
" mu=10.125 [-inf, 2.42844] in interval = 1\n",
"\n",
"[#0] PROGRESS:Generation -- generated toys: 500 / 1440\n",
"[#0] PROGRESS:Generation -- generated toys: 1000 / 1440\n",
"NeymanConstruction: Prog: 69/100 total MC = 2160 this test stat = 1.79519\n",
" mu=10.275 [-inf, 1.79519] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 70/100 total MC = 240 this test stat = 1.86654\n",
" mu=10.425 [-inf, 1.86654] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 71/100 total MC = 80 this test stat = 1.93876\n",
" mu=10.575 [-inf, 2.67618] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 72/100 total MC = 80 this test stat = 2.01184\n",
" mu=10.725 [-inf, 1.40678] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 73/100 total MC = 80 this test stat = 2.08575\n",
" mu=10.875 [-inf, 1.86151] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 74/100 total MC = 240 this test stat = 2.16048\n",
" mu=11.025 [-inf, 1.7642] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 75/100 total MC = 80 this test stat = 2.23601\n",
" mu=11.175 [-inf, 1.59869] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 76/100 total MC = 240 this test stat = 2.31232\n",
" mu=11.325 [-inf, 1.66448] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 77/100 total MC = 80 this test stat = 2.38941\n",
" mu=11.475 [-inf, 1.26987] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 78/100 total MC = 240 this test stat = 2.46724\n",
" mu=11.625 [-inf, 1.40071] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 79/100 total MC = 80 this test stat = 2.54582\n",
" mu=11.775 [-inf, 1.86704] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 80/100 total MC = 80 this test stat = 2.62511\n",
" mu=11.925 [-inf, 1.93623] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 81/100 total MC = 80 this test stat = 2.70511\n",
" mu=12.075 [-inf, 1.43268] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 82/100 total MC = 240 this test stat = 2.7858\n",
" mu=12.225 [-inf, 1.49357] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 83/100 total MC = 80 this test stat = 2.86717\n",
" mu=12.375 [-inf, 1.55534] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 84/100 total MC = 80 this test stat = 2.94921\n",
" mu=12.525 [-inf, 1.12614] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 85/100 total MC = 80 this test stat = 3.03185\n",
" mu=12.675 [-inf, 2.29398] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 86/100 total MC = 80 this test stat = 3.11523\n",
" mu=12.825 [-inf, 1.7457] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 87/100 total MC = 80 this test stat = 3.1991\n",
" mu=12.975 [-inf, 1.8108] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 88/100 total MC = 80 this test stat = 3.28355\n",
" mu=13.125 [-inf, 2.51742] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 89/100 total MC = 240 this test stat = 3.36896\n",
" mu=13.275 [-inf, 1.40455] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 90/100 total MC = 80 this test stat = 3.45474\n",
" mu=13.425 [-inf, 2.01076] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 91/100 total MC = 240 this test stat = 3.5411\n",
" mu=13.575 [-inf, 2.07893] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 92/100 total MC = 80 this test stat = 3.62804\n",
" mu=13.725 [-inf, 2.14777] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 93/100 total MC = 80 this test stat = 3.71554\n",
" mu=13.875 [-inf, 1.16754] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 94/100 total MC = 80 this test stat = 3.80359\n",
" mu=14.025 [-inf, 1.70395] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 95/100 total MC = 240 this test stat = 3.89219\n",
" mu=14.175 [-inf, 1.76612] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 96/100 total MC = 240 this test stat = 3.98132\n",
" mu=14.325 [-inf, 1.32819] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 97/100 total MC = 80 this test stat = 4.07097\n",
" mu=14.475 [-inf, 1.38331] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 98/100 total MC = 80 this test stat = 4.16114\n",
" mu=14.625 [-inf, 1.43935] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 99/100 total MC = 240 this test stat = 4.25182\n",
" mu=14.775 [-inf, 1.49612] in interval = 0\n",
"\n",
"NeymanConstruction: Prog: 100/100 total MC = 240 this test stat = 4.343\n",
" mu=14.925 [-inf, 2.08888] in interval = 0\n",
"\n",
"[#1] INFO:Eval -- 68 points in interval\n"
]
}
],
"source": [
"interval = fc.GetInterval()"
]
},
{
"cell_type": "markdown",
"id": "3334c750",
"metadata": {},
"source": [
"make a canvas for plots"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "84e22f12",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:36:04.668912Z",
"iopub.status.busy": "2026-05-19T20:36:04.668782Z",
"iopub.status.idle": "2026-05-19T20:36:04.782235Z",
"shell.execute_reply": "2026-05-19T20:36:04.781404Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"is this point in the interval? False\n",
"interval is [0.525, 10.575]\n"
]
}
],
"source": [
"intervalCanvas = ROOT.TCanvas(\"intervalCanvas\")\n",
"\n",
"print(\"is this point in the interval? \", interval.IsInInterval(parameters))\n",
"print(\"interval is [{}, {}]\".format(interval.LowerLimit(mu), interval.UpperLimit(mu)))"
]
},
{
"cell_type": "markdown",
"id": "1fdeb6b4",
"metadata": {},
"source": [
"using 200 bins it takes 1 min and the answer is\n",
"interval is [0.2625, 10.6125] with a step size of .075\n",
"The interval in Feldman & Cousins's original paper is [.29, 10.81]\n",
"Phys.Rev.D57:3873-3889,1998."
]
},
{
"cell_type": "markdown",
"id": "0f79002d",
"metadata": {},
"source": [
"No dedicated plotting class yet, so do it by hand:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "675dfd3a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:36:04.783687Z",
"iopub.status.busy": "2026-05-19T20:36:04.783543Z",
"iopub.status.idle": "2026-05-19T20:36:04.949385Z",
"shell.execute_reply": "2026-05-19T20:36:04.940413Z"
}
},
"outputs": [],
"source": [
"parameterScan = fc.GetPointsToScan()\n",
"hist = parameterScan.createHistogram(\"mu\", ROOT.RooFit.Binning(30))\n",
"hist.Draw()\n",
"\n",
"marks = []"
]
},
{
"cell_type": "markdown",
"id": "6d749827",
"metadata": {},
"source": [
"loop over points to test"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "ac70ccda",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:36:04.950850Z",
"iopub.status.busy": "2026-05-19T20:36:04.950721Z",
"iopub.status.idle": "2026-05-19T20:36:05.161480Z",
"shell.execute_reply": "2026-05-19T20:36:05.160557Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Real time 0:00:03, CP time 2.290\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rs401c_FeldmanCousins_data.png has been created\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rs401c_FeldmanCousins_hist.png has been created\n"
]
}
],
"source": [
"for i in range(parameterScan.numEntries()):\n",
" # get a parameter point from the list of points to test.\n",
" tmpPoint = parameterScan.get(i).clone(\"temp\")\n",
"\n",
" mark = ROOT.TMarker(tmpPoint.getRealValue(\"mu\"), 1, 25)\n",
" if interval.IsInInterval(tmpPoint):\n",
" mark.SetMarkerColor(\"kBlue\")\n",
" else:\n",
" mark.SetMarkerColor(\"kRed\")\n",
"\n",
" mark.Draw(\"s\")\n",
" marks.append(mark)\n",
"\n",
"t.Stop()\n",
"t.Print()\n",
"\n",
"dataCanvas.SaveAs(\"rs401c_FeldmanCousins_data.png\")\n",
"intervalCanvas.SaveAs(\"rs401c_FeldmanCousins_hist.png\")"
]
},
{
"cell_type": "markdown",
"id": "8ae233a0",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "41b2d86b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:36:05.163054Z",
"iopub.status.busy": "2026-05-19T20:36:05.162926Z",
"iopub.status.idle": "2026-05-19T20:36:05.297539Z",
"shell.execute_reply": "2026-05-19T20:36:05.296758Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
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"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
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