{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bump Hunter P-value issues\n",
    "Kyle Cranmer, Dec 2, 2015"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "require(['codemirror/mode/clike/clike'], function(Clike) { console.log('ROOTaaS - C++ CodeMirror module loaded'); });"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "IPython.CodeCell.config_defaults.highlight_modes['magic_text/x-c++src'] = {'reg':[/^%%cpp/]};"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to ROOTaaS 6.05/03\n"
     ]
    }
   ],
   "source": [
    "%pylab inline --no-import-all\n",
    "import ROOT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Poisson probability $p(n|b)$ -- note this is NOT a p-value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p_n_b = 3.31e-08"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17.2237325546\n"
     ]
    }
   ],
   "source": [
    "bump_hunter_test_stat = -np.log(p_n_b)\n",
    "print bump_hunter_test_stat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.4011907104779615"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r\n",
      "\u001b[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby\u001b[0m \r\n",
      "                Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University\r\n",
      "                All rights reserved, please read http://roofit.sourceforge.net/license.txt\r\n",
      "\r\n"
     ]
    }
   ],
   "source": [
    "#currently reported local significance (NOT correct b/c this is not a p-value)\n",
    "ROOT.RooStats.PValueToSignificance(p_n_b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the p-value for this observation?\n",
    "I don't have the observed number of events in the peak or expected background handy, but looking at the plots I see 4 bins with roughly 30 events / bin in the peak gives ~120 background events and roughly 60 events signal. So hold n=180 and scan b to get the right p(n|b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.34924599381561e-08"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_estimate = 118.6\n",
    "ROOT.TMath.Poisson(180,b_estimate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.18965474521e-08\n"
     ]
    }
   ],
   "source": [
    "p_value = ROOT.Math.poisson_cdf_c(180,b_estimate)\n",
    "print p_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.287804625259286"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ROOT.RooStats.PValueToSignificance(p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_array = np.arange(120,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/cranmer/projects/roostats/root-v5-34/lib/ROOT.py:301: UserWarning: Module readline was already imported from /System/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/lib-dynload/readline.so, but /Library/Python/2.7/site-packages is being added to sys.path\n",
      "  return _orig_ihook( name, *args, **kwds )\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import poisson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3492459938157053e-08"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson.pmf(180, b_estimate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.1896547452065547e-08"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson.sf(180, b_estimate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "iIiIiIiIiEg9+3/fTARTik1wHwAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1161b6890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(n_array, poisson.sf(n_array, b_estimate))\n",
    "plt.plot(n_array, poisson.pmf(n_array, b_estimate))\n",
    "plt.semilogy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
       "        18, 19]),\n",
       " array([ 0. ,  0.1,  0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8,  0.9,  1. ,\n",
       "         1.1,  1.2,  1.3,  1.4,  1.5,  1.6,  1.7,  1.8,  1.9,  2. ,  2.1,\n",
       "         2.2,  2.3,  2.4,  2.5,  2.6,  2.7,  2.8,  2.9,  3. ,  3.1,  3.2,\n",
       "         3.3,  3.4,  3.5,  3.6,  3.7,  3.8,  3.9,  4. ,  4.1,  4.2,  4.3,\n",
       "         4.4,  4.5,  4.6,  4.7,  4.8,  4.9]))"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nobs_array = np.arange(1,20)\n",
    "b_array = np.arange(0,5, .1)\n",
    "nobs_array, b_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p_with = np.zeros(nobs_array.size*b_array.size)\n",
    "p_without = p_with*0.\n",
    "\n",
    "for i, ntoy in enumerate(nobs_array):\n",
    "    for j, btoy in enumerate(b_array):\n",
    "        p_with[i*b_array.size+j] = ROOT.RooStats.NumberCountingUtils.BinomialObsZ(ntoy,btoy,.5)\n",
    "        p_without[i*b_array.size+j] = ROOT.RooStats.NumberCountingUtils.BinomialObsZ(ntoy,btoy,.0005)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 8)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "iaBWKio9vS/7vaudWonsfN7nk6I85COi2+PPLH1lvkPMSLpfDKxOOLXL58Q+j4tumSdEHvqFJdpz\n",
       "+usi/JXoYnlEDI4PZ3/2D6J//tOLtv9Idtsnsvt6XHTlbHVywPcPReB+XEzR/fCifZ/t+J94/X+J\n",
       "gdrviq66E+4SA+APiwHfE5Y6vmX4qez+HxWDvyu10E2SJBegMvs1I2YHvSuPbXmpuEXcbSRJkqxY\n",
       "HxVXeM/g43luy0vB74nutcuq7F6SJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJMvq/wdD\n",
       "zrs1nhxWZgAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116eba490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(p_with,p_without, alpha=.1)\n",
    "plt.ylabel('Significance without systematics')\n",
    "plt.xlabel('Significance with systematics')\n",
    "plt.xlim(0,8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x116b97110>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "L51XgLdRkbw+Uot6ZxxqY4HtgLsisuXjOBT4ScnzI4GrI7KlN6aycpilUNk+nrDDLMcQnh79i5Bj\n",
       "5nugK/KjojZkBeJoNdhUoJpwF0BjqCheHrUh/WAe4cbMAR4CZtrj+cC3ojNllWyGZi8l0d+B64BT\n",
       "I7WoJ1NZeQG04AydQzgLi1PpaWeoevQv/k64Yv4i2s53oW3XRGtOD/ZEF5leQj3zENkOjUEvongP\n",
       "94jUotUzj7CzWTYDHifA9LQVOItiauJ16F9oIXAjGsfvQP8aOxbVn/sIKzVxRTuPI2w9chzHcRzH\n",
       "cRzHcRzHcRzHcRzHcRzHcRzHcRzHcRzHcRzHcRzHcRxnsPl/2d4gqTxbD8MAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116d05490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(p_with,p_without)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}