{ "cells": [ { "cell_type": "markdown", "id": "31773c23", "metadata": {}, "source": [ "# Zbi_Zgamma\n", "Demonstrate Z_Bi = Z_Gamma\n", "\n", "\n", "\n", "\n", "**Author:** Artem Busorgin, Kyle Cranmer and Wouter Verkerke (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." ] }, { "cell_type": "code", "execution_count": 1, "id": "0af4915d", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:36:41.856399Z", "iopub.status.busy": "2026-05-19T20:36:41.856258Z", "iopub.status.idle": "2026-05-19T20:36:42.823157Z", "shell.execute_reply": "2026-05-19T20:36:42.822721Z" } }, "outputs": [], "source": [ "import ROOT" ] }, { "cell_type": "markdown", "id": "3ad83207", "metadata": {}, "source": [ "Make model for prototype on/off problem\n", "Pois(x | s+b) * Pois(y | tau b )\n", "for Z_Gamma, use uniform prior on b." ] }, { "cell_type": "code", "execution_count": 2, "id": "b1522d21", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:36:42.837413Z", "iopub.status.busy": "2026-05-19T20:36:42.837258Z", "iopub.status.idle": "2026-05-19T20:36:43.069070Z", "shell.execute_reply": "2026-05-19T20:36:43.068692Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w1 = ROOT.RooWorkspace(\"w\")\n", "w1.factory(\"Poisson::px(x[150,0,500],sum::splusb(s[0,0,100],b[100,0,300]))\")\n", "w1.factory(\"Poisson::py(y[100,0,500],prod::taub(tau[1.],b))\")\n", "w1.factory(\"Uniform::prior_b(b)\")" ] }, { "cell_type": "markdown", "id": "7993944b", "metadata": {}, "source": [ "construct the Bayesian-averaged model (eg. a projection pdf)\n", "p'(x|s) = \\int db p(x|s+b) * [ p(y|b) * prior(b) ]" ] }, { "cell_type": "code", "execution_count": 3, "id": "7f7aca15", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:36:43.092470Z", "iopub.status.busy": "2026-05-19T20:36:43.092318Z", "iopub.status.idle": "2026-05-19T20:36:43.242539Z", "shell.execute_reply": "2026-05-19T20:36:43.241909Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:NumericIntegration -- RooRealIntegral::init(GENPROJ_[py_X_prior_b_X_px]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)\n" ] } ], "source": [ "w1.factory(\"PROJ::averagedModel(PROD::foo(px|b,py,prior_b),b)\")\n", "\n", "c = ROOT.TCanvas()" ] }, { "cell_type": "markdown", "id": "9a01bcfa", "metadata": {}, "source": [ "plot it, blue is averaged model, red is b known exactly" ] }, { "cell_type": "code", "execution_count": 4, "id": "514c4683", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:36:43.244520Z", "iopub.status.busy": "2026-05-19T20:36:43.244397Z", "iopub.status.idle": "2026-05-19T20:36:43.437543Z", "shell.execute_reply": "2026-05-19T20:36:43.437054Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:NumericIntegration -- RooRealIntegral::init(GENPROJ_[py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)\n", "[#1] INFO:NumericIntegration -- RooRealIntegral::init(SPECINT[GENPROJ_[py_X_prior_b]_Norm[b]_X_px_NORM[x]]_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)\n", "[#1] INFO:NumericIntegration -- RooRealIntegral::init(GENPROJ_[py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)\n" ] } ], "source": [ "frame = w1[\"x\"].frame()\n", "w1[\"averagedModel\"].plotOn(frame)\n", "w1[\"px\"].plotOn(frame, LineColor=\"kRed\")\n", "frame.Draw()" ] }, { "cell_type": "markdown", "id": "af68e954", "metadata": {}, "source": [ "compare analytic calculation of Z_Bi\n", "with the numerical RooFit implementation of Z_Gamma\n", "for an example with x = 150, y = 100" ] }, { "cell_type": "markdown", "id": "30fe4a70", "metadata": {}, "source": [ "numeric RooFit Z_Gamma" ] }, { "cell_type": "code", "execution_count": 5, "id": "201bca57", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:36:43.439393Z", "iopub.status.busy": "2026-05-19T20:36:43.439275Z", "iopub.status.idle": "2026-05-19T20:36:43.580240Z", "shell.execute_reply": "2026-05-19T20:36:43.579778Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hybrid p-value = [#1] INFO:NumericIntegration -- RooRealIntegral::init(GENPROJ_[py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)\n", "[#1] INFO:NumericIntegration -- RooRealIntegral::init(GENPROJ_[py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)\n", "[#1] INFO:NumericIntegration -- RooRealIntegral::init(SPECINT[GENPROJ_[py_X_prior_b]_Norm[b]_X_px_cdf_NORM[x_prime]]_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)\n", "[#1] INFO:NumericIntegration -- RooRealIntegral::init(GENPROJ_[py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)\n", "[#1] INFO:NumericIntegration -- RooRealIntegral::init(SPECINT[GENPROJ_[py_X_prior_b]_Norm[b]_X_px_cdf_Int[x_prime|CDF]_Norm[x_prime]]_Int[b|CDF]) using numeric integrator RooIntegrator1D to calculate Int(b)\n", "[#1] INFO:NumericIntegration -- RooRealIntegral::init(GENPROJ_[py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " 0.9992259057034769\n", "Z_Gamma Significance = 3.165495870670026\n" ] } ], "source": [ "w1[\"y\"].setVal(100)\n", "w1[\"x\"].setVal(150)\n", "cdf = w1[\"averagedModel\"].createCdf(w1[\"x\"])\n", "cdf.getVal() # get ugly print messages out of the way\n", "\n", "print(\"Hybrid p-value = \", cdf.getVal())\n", "print(\"Z_Gamma Significance = \", ROOT.RooStats.PValueToSignificance(1 - cdf.getVal()))" ] }, { "cell_type": "markdown", "id": "104f2cd9", "metadata": {}, "source": [ "analytic Z_Bi" ] }, { "cell_type": "code", "execution_count": 6, "id": "8d231c97", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:36:43.582096Z", "iopub.status.busy": "2026-05-19T20:36:43.581980Z", "iopub.status.idle": "2026-05-19T20:36:43.741365Z", "shell.execute_reply": "2026-05-19T20:36:43.741055Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Z_Bi significance estimation: 3.108043895747114\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Info in : png file Zbi_Zgamma.png has been created\n" ] } ], "source": [ "Z_Bi = ROOT.RooStats.NumberCountingUtils.BinomialWithTauObsZ(150, 100, 1)\n", "print(\"Z_Bi significance estimation: \", Z_Bi)\n", "\n", "c.SaveAs(\"Zbi_Zgamma.png\")" ] }, { "cell_type": "markdown", "id": "3c3090f2", "metadata": {}, "source": [ "Draw all canvases " ] }, { "cell_type": "code", "execution_count": 7, "id": "9ddd228b", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:36:43.761035Z", "iopub.status.busy": "2026-05-19T20:36:43.760897Z", "iopub.status.idle": "2026-05-19T20:36:43.958123Z", "shell.execute_reply": "2026-05-19T20:36:43.957667Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "
\n", "
\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%jsroot on\n", "from ROOT import gROOT \n", "gROOT.GetListOfCanvases().Draw()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.12" } }, "nbformat": 4, "nbformat_minor": 5 }