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"source": [
"# rs701_BayesianCalculator\n",
"Bayesian calculator: basic example\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Artem Busorgin, Gregory Schott (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 08:36 PM."
]
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"source": [
"import ROOT\n",
"\n",
"useBkg = True\n",
"confLevel = 0.90\n",
"\n",
"w = ROOT.RooWorkspace(\"w\")\n",
"w.factory(\"SUM::pdf(s[0.001,15]*Uniform(x[0,1]),b[1,0,2]*Uniform(x))\")\n",
"w.factory(\"Gaussian::prior_b(b,1,1)\")\n",
"model = w.factory(\"PROD::model(pdf,prior_b)\") # pdf*priorNuisance\n",
"nuisanceParameters = ROOT.RooArgSet(w[\"b\"])\n",
"\n",
"POI = w[\"s\"]\n",
"priorPOI = w.factory(\"Uniform::priorPOI(s)\")\n",
"priorPOI2 = w.factory(\"GenericPdf::priorPOI2('1/sqrt(@0)',s)\")\n",
"\n",
"w.factory(\"n[3]\") # observed number of events"
]
},
{
"cell_type": "markdown",
"id": "805c828c",
"metadata": {},
"source": [
"create a data set with n observed events"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "50a9f5f9",
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"outputs": [],
"source": [
"data = ROOT.RooDataSet(\"data\", \"\", {w[\"x\"], w[\"n\"]}, WeightVar=\"n\")\n",
"data.add({w[\"x\"]}, w[\"n\"].getVal())"
]
},
{
"cell_type": "markdown",
"id": "1fd59d71",
"metadata": {},
"source": [
"to suppress messages when pdf goes to zero"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "1296b168",
"metadata": {
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Bayesian Result using a Flat prior \n",
"0.9% CL central interval: [ 0.5060595505871569 - 6.893261312862889 ] or 0.95% CL limits\n",
"\n",
"\n",
"Bayesian Result using a 1/sqrt(s) prior \n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.9% CL central interval: [ 0.07462937796837057 - 5.8542450825237555 ] or 0.95% CL limits\n",
"\n"
]
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\n",
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"source": [
"ROOT.RooMsgService.instance().setGlobalKillBelow(ROOT.RooFit.FATAL)\n",
"\n",
"nuisPar = 0\n",
"if useBkg:\n",
" nuisPar = nuisanceParameters\n",
"else:\n",
" w[\"b\"].setVal(0)\n",
"\n",
"size = 1.0 - confLevel\n",
"print(\"\\nBayesian Result using a Flat prior \")\n",
"bcalc = ROOT.RooStats.BayesianCalculator(data, model, {POI}, priorPOI, nuisPar)\n",
"bcalc.SetTestSize(size)\n",
"interval = bcalc.GetInterval()\n",
"cl = bcalc.ConfidenceLevel()\n",
"print(\n",
" \"{}% CL central interval: [ {} - {} ] or {}% CL limits\\n\".format(\n",
" cl, interval.LowerLimit(), interval.UpperLimit(), cl + (1.0 - cl) / 2\n",
" )\n",
")\n",
"plot = bcalc.GetPosteriorPlot()\n",
"c1 = ROOT.TCanvas(\"c1\", \"Bayesian Calculator Result\")\n",
"c1.Divide(1, 2)\n",
"c1.cd(1)\n",
"plot.Draw()\n",
"c1.Update()\n",
"\n",
"print(\"\\nBayesian Result using a 1/sqrt(s) prior \")\n",
"bcalc2 = ROOT.RooStats.BayesianCalculator(data, model, {POI}, priorPOI2, nuisPar)\n",
"bcalc2.SetTestSize(size)\n",
"interval2 = bcalc2.GetInterval()\n",
"cl = bcalc2.ConfidenceLevel()\n",
"print(\n",
" \"{}% CL central interval: [ {} - {} ] or {}% CL limits\\n\".format(\n",
" cl, interval2.LowerLimit(), interval2.UpperLimit(), cl + (1.0 - cl) / 2\n",
" )\n",
")\n",
"plot2 = bcalc2.GetPosteriorPlot()\n",
"c1.cd(2)\n",
"plot2.Draw()\n",
"ROOT.gPad.SetLogy()\n",
"c1.Update()"
]
},
{
"cell_type": "markdown",
"id": "c8922783",
"metadata": {},
"source": [
"observe one event while expecting one background event -> the 95% CL upper limit on s is 4.10\n",
"observe one event while expecting zero background event -> the 95% CL upper limit on s is 4.74"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "1c0d53bf",
"metadata": {
"collapsed": false,
"execution": {
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"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rs701_BayesianCalculator.png has been created\n"
]
}
],
"source": [
"c1.SaveAs(\"rs701_BayesianCalculator.png\")"
]
},
{
"cell_type": "markdown",
"id": "7f523f07",
"metadata": {},
"source": [
"TODO: The BayesianCalculator has to be destructed first. Otherwise, we can get\n",
"segmentation faults depending on the destruction order, which is random in\n",
"Python. Probably the issue is that some object has a non-owning pointer to\n",
"another object, which it uses in its destructor. This should be fixed either\n",
"in the design of RooStats in C++, or with phythonizations."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "f7505ec3",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:36:05.747420Z"
}
},
"outputs": [],
"source": [
"del bcalc, bcalc2"
]
},
{
"cell_type": "markdown",
"id": "322b8258",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "854f91e2",
"metadata": {
"collapsed": false,
"execution": {
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"\n",
"\n"
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
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"display_name": "Python 3",
"language": "python",
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