run_number.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import ROOT\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy import stats\n",
    "%matplotlib inline\n",
    "\n",
    "filename = \"data15_graviton_selection.root\"\n",
    "f = ROOT.TFile.Open(filename)\n",
    "tree = f.Get(\"CollectionTree\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "final_result = {}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When plotting use the RooFit frequentist recipe: the confidence interval $[n_{down}, n_{up}]$ when observing $n_{obs}$ is defined as:\n",
    "\n",
    "$$n_{down} = Max\\{\\lambda | \\sum_{n\\geq n_{obs}} Pois(n|\\lambda) < 16\\%\\}$$\n",
    "$$n_{up} = Min\\{\\lambda | \\sum_{n\\leq n_{obs}} Pois(n|\\lambda) < 16\\%\\}$$\n",
    "\n",
    "and the error simply ${}^{+n_{up} - n}_{-(n - n_{down})}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 +0.0 -1.14787446445\n",
      "1 +0.827246220977 -3.12677278009\n",
      "2 +1.29181456018 -3.92967418364\n",
      "3 +1.63270468611 -4.55089051899\n",
      "4 +1.91433918622 -5.07709235848\n"
     ]
    }
   ],
   "source": [
    "def get_confiderence_poisson(n):\n",
    "    ym = np.array([0], dtype=np.float64)\n",
    "    yp = np.array([0], dtype=np.float64)\n",
    "    ROOT.RooHistError.instance().getPoissonInterval(int(n), ym, yp, 1)\n",
    "    return ym[0], yp[0]\n",
    "\n",
    "@np.vectorize\n",
    "def get_error_poisson(n):\n",
    "    down, up = get_confiderence_poisson(n)\n",
    "    return n - down, up - down\n",
    "\n",
    "# run some examples\n",
    "for nobs in [0, 1,2,3,4]:\n",
    "    print \"{} +{} -{}\".format(nobs, *get_error_poisson(nobs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import raw data (run number, mass for every event)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false,
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Run</th>\n",
       "      <th>mass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>276262</td>\n",
       "      <td>122.760375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>276262</td>\n",
       "      <td>300.553406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>276262</td>\n",
       "      <td>322.555219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>276262</td>\n",
       "      <td>124.091711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>276262</td>\n",
       "      <td>123.070672</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Run        mass\n",
       "0  276262  122.760375\n",
       "1  276262  300.553406\n",
       "2  276262  322.555219\n",
       "3  276262  124.091711\n",
       "4  276262  123.070672"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree.Draw(\"run_number\", \"\", \"GOFF\")\n",
    "\n",
    "data_run = tree.GetV1()\n",
    "data_run.SetSize(tree.GetEntries())\n",
    "data_run = np.array(data_run)\n",
    "\n",
    "tree.Draw(\"mass\", \"\", \"GOFF\")\n",
    "data_mass = tree.GetV1()\n",
    "data_mass.SetSize(tree.GetEntries())\n",
    "data_mass = np.array(data_mass) / 1E3\n",
    "\n",
    "data = pd.DataFrame({\"Run\": pd.Series(data_run, dtype=np.int64),\n",
    "                     \"mass\": pd.Series(data_mass, dtype=np.float64)})\n",
    "del data_run\n",
    "del data_mass\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### divide the sample in the three regions depending on the invariant mass (signal / left / right) and count events per run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "count_run_sr = data[(data['mass'] > 700) & (data['mass'] < 840)].groupby('Run').size().to_frame().rename(columns={0: 'N'})\n",
    "count_run_lr = data[(data['mass'] <= 700)].groupby('Run').size().to_frame().rename(columns={0: 'N'})\n",
    "count_run_rr = data[(data['mass'] >= 840)].groupby('Run').size().to_frame().rename(columns={0: 'N'})\n",
    "\n",
    "all_df = {'signal': count_run_sr, 'left': count_run_lr, 'right': count_run_rr}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### import the luminosity for all the runs in the GRL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "List of runs: [276262, 276329, 276336, 276416, 276511, 276689, 276778, 276790, 276952, 276954, 278880, 278912, 278968, 279169, 279259, 279279, 279284, 279345, 279515, 279598, 279685, 279764, 279813, 279867, 279928, 279932, 279984, 280231, 280319, 280368, 280423, 280464, 280500, 280520, 280614, 280673, 280753, 280853, 280862, 280950, 280977, 281070, 281074, 281075, 281317, 281385, 281411, 282625, 282631, 282712, 282784, 282992, 283074, 283155, 283270, 283429, 283608, 283780, 284006, 284154, 284213, 284285, 284420, 284427, 284484]\n",
      "Total luminosity: 3209.060519\n",
      "Number of runs: 65\n",
      "Mean luminosity: 49.3701618308\n"
     ]
    }
   ],
   "source": [
    "df_lumi = pd.read_csv('lumitable.csv', sep=', ', header=False, engine='python',\n",
    "                      usecols=['Run', 'Prescale Corrected']).set_index('Run').rename(columns={'Prescale Corrected': 'lumi'})\n",
    "total_lumi = df_lumi['lumi'].sum()\n",
    "print \"List of runs:\", list(df_lumi.index)\n",
    "print \"Total luminosity:\", total_lumi\n",
    "print \"Number of runs:\", len(df_lumi)\n",
    "print \"Mean luminosity:\", total_lumi / len(df_lumi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### join the two tables (countings + luminositries)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lumi</th>\n",
       "      <th>obs_signal</th>\n",
       "      <th>obs_right</th>\n",
       "      <th>obs_left</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Run</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>276262</th>\n",
       "      <td>6.253800</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276329</th>\n",
       "      <td>11.909006</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276336</th>\n",
       "      <td>0.663047</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276416</th>\n",
       "      <td>4.221030</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276511</th>\n",
       "      <td>9.003851</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>84</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             lumi  obs_signal  obs_right  obs_left\n",
       "Run                                               \n",
       "276262   6.253800           0          0        48\n",
       "276329  11.909006           3          0        90\n",
       "276336   0.663047           0          0         9\n",
       "276416   4.221030           0          0        39\n",
       "276511   9.003851           1          1        84"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df_lumi.copy()\n",
    "for k, d in all_df.iteritems():\n",
    "    df = df.join(d).rename(columns={'N': 'obs_%s' % k})\n",
    "df = df.fillna(0)  \n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Add other derived information (expected number of events, chi2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for k in all_df:\n",
    "    df['exp_%s' % k] = df['lumi'] / total_lumi * df['obs_%s' % k].sum()\n",
    "    df['chi2_%s' % k] = (df['obs_%s' % k] - df['exp_%s' % k]) ** 2 / df['exp_%s' % k]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistics starts from here\n",
    "### Data\n",
    "\n",
    "Run number, luminosity, observed in the signal region, observed in the right region, observed in the left region, ...\n",
    "\n",
    "Expected number of events have been computed simply scaling total number of obseved event by the luminosity of each run: $L_i \\times \\sigma_{vis} = L_i \\times \\sum{n_i}/L$, where $L_i$ is the luminosity for run-$i$, $n_i$ is the number of observed events in run-$i$, $L=\\sum L_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lumi</th>\n",
       "      <th>obs_signal</th>\n",
       "      <th>obs_right</th>\n",
       "      <th>obs_left</th>\n",
       "      <th>exp_signal</th>\n",
       "      <th>chi2_signal</th>\n",
       "      <th>exp_right</th>\n",
       "      <th>chi2_right</th>\n",
       "      <th>exp_left</th>\n",
       "      <th>chi2_left</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Run</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>276262</th>\n",
       "      <td>6.253800</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>48</td>\n",
       "      <td>0.220214</td>\n",
       "      <td>0.220214</td>\n",
       "      <td>0.114979</td>\n",
       "      <td>0.114979</td>\n",
       "      <td>48.751047</td>\n",
       "      <td>0.011570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276329</th>\n",
       "      <td>11.909006</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>90</td>\n",
       "      <td>0.419349</td>\n",
       "      <td>15.881165</td>\n",
       "      <td>0.218952</td>\n",
       "      <td>0.218952</td>\n",
       "      <td>92.835798</td>\n",
       "      <td>0.086623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276336</th>\n",
       "      <td>0.663047</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.023348</td>\n",
       "      <td>0.023348</td>\n",
       "      <td>0.012190</td>\n",
       "      <td>0.012190</td>\n",
       "      <td>5.168735</td>\n",
       "      <td>2.839881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276416</th>\n",
       "      <td>4.221030</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>39</td>\n",
       "      <td>0.148634</td>\n",
       "      <td>0.148634</td>\n",
       "      <td>0.077606</td>\n",
       "      <td>0.077606</td>\n",
       "      <td>32.904735</td>\n",
       "      <td>1.129085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276511</th>\n",
       "      <td>9.003851</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>84</td>\n",
       "      <td>0.317051</td>\n",
       "      <td>1.471120</td>\n",
       "      <td>0.165540</td>\n",
       "      <td>4.206383</td>\n",
       "      <td>70.188872</td>\n",
       "      <td>2.717628</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             lumi  obs_signal  obs_right  obs_left  exp_signal  chi2_signal  \\\n",
       "Run                                                                           \n",
       "276262   6.253800           0          0        48    0.220214     0.220214   \n",
       "276329  11.909006           3          0        90    0.419349    15.881165   \n",
       "276336   0.663047           0          0         9    0.023348     0.023348   \n",
       "276416   4.221030           0          0        39    0.148634     0.148634   \n",
       "276511   9.003851           1          1        84    0.317051     1.471120   \n",
       "\n",
       "        exp_right  chi2_right   exp_left  chi2_left  \n",
       "Run                                                  \n",
       "276262   0.114979    0.114979  48.751047   0.011570  \n",
       "276329   0.218952    0.218952  92.835798   0.086623  \n",
       "276336   0.012190    0.012190   5.168735   2.839881  \n",
       "276416   0.077606    0.077606  32.904735   1.129085  \n",
       "276511   0.165540    4.206383  70.188872   2.717628  "
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare observed and expected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JiIj4rbwccnNh1So3uqSJiLSUnbmOsrz3AYhk7yOSnQ1ARW1tdxYrMBpzIyK+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wM8Za1NOYhmUP+n2H+WtfbqTv4fqj0Z+Ceo/0PVd1BGpz5tpx0NHA4ss9a+kQt9UJ9mY4+/T1d1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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa8a9948c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(3, 1, figsize=(14, 10), sharex=True)\n",
    "for k, ax in zip(all_df, axs.flat):\n",
    "    #(df['obs_%s' % k]).plot(kind='bar', alpha=0.5, label='observed', ax=ax)\n",
    "    (df['exp_%s' % k]).plot(kind='bar', color='red', alpha=0.8, label='expected', ax=ax)\n",
    "    error_down, error_up = get_error_poisson(df['obs_%s' % k])\n",
    "    ax.errorbar(np.arange(len(df)), df['obs_%s' % k], fmt='.', yerr=[error_down, error_up], label='observed')\n",
    "    ax.set_title(k)\n",
    "    ax.legend(loc=0)\n",
    "    ax.legend(numpoints=1)\n",
    "    ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot visible cross section ($n_i^{obs} / L_i$) per run, compare with the average\n",
    "The error on the total luminosity is not taken into account, since it should be (?) quite correlated across runs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6lrGxMU49dRUbN7bunEUcrxlNtDG50URrn9zbM7Xcx4BXLU+0/blq+VPXH618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Ya2odB86PaGPmeh9fNWsoGds+se+2Wz56pkfYa2odDyh9Z/7PYQe5/SyWs+xj4rdv2ELn+t07O2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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa8a99c6150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(3, 1, figsize=(14, 10), sharex=True)\n",
    "for k, ax in zip(all_df, axs.flat):\n",
    "    y = df['obs_%s' % k] / df['lumi']\n",
    "    error_down, error_up = get_error_poisson(df['obs_%s' % k])\n",
    "    ax.errorbar(np.arange(len(df)), y, fmt='.', yerr=[error_down / df['lumi'], error_up / df['lumi']], label='observed', color='k')\n",
    "    (df['obs_%s' % k] / df['lumi']).plot(kind='bar', ax=ax, alpha=0.4)\n",
    "    average_xsec = df['obs_%s' % k].sum() / total_lumi\n",
    "    ax.hlines(average_xsec, -100, 100, color='red')\n",
    "    ax.set_ylabel('visible cross section')\n",
    "    ax.set_ylim(0, 9 * average_xsec)\n",
    "    ax.set_title(k)\n",
    "    ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot signed-$\\chi^2_i = (O_i - E_i)^2 / E_i \\times sign(O_i - E_i)$ for the inclusive case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LOrS6a427XxBZ36ZWSrrG3TdJkpn9m6TnS7piXCG0g/9lAcrGcxiLJLf+nFt9+ob2X2xd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa8a84220d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(14, 5), sharex=True)\n",
    "\n",
    "obs = df['obs_signal'] + df['obs_left'] + df['obs_right']\n",
    "exp = df['exp_signal'] + df['exp_left'] + df['exp_right']\n",
    "((obs - exp) ** 2 / exp * np.sign(obs-exp)).plot(kind='bar', ax=ax)\n",
    "ax.set_ylim(-10, 10)\n",
    "ax.set_ylabel('signed $\\chi^2$')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dividing per categories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JknZidzhJkjRIdoeT+m0w3eEkSZIkaSe9agSV1t/QvHnzw8m3sQ7z5s03l3dM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\n4kPpHCsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa8a7522050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(3, 1, figsize=(14, 8), sharex=True)\n",
    "for k, ax in zip(all_df, axs.flat):\n",
    "    (df['chi2_%s' % k] * np.sign(df['obs_%s' % k] - df['exp_%s' % k])).plot(kind='bar', ax=ax)\n",
    "    ax.set_title(k)\n",
    "    ax.set_ylabel('signed $\\chi^2$')\n",
    "    ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute $\\chi^2$ test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "signal Power_divergenceResult(statistic=76.64763421827962, pvalue=0.13354384160856192)\n",
      "right Power_divergenceResult(statistic=50.57804958284882, pvalue=0.88897896005486465)\n",
      "left Power_divergenceResult(statistic=65.300965766185115, pvalue=0.4312901246639424)\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "for k in all_df:\n",
    "    print k, stats.chisquare(df['obs_%s' % k], df['exp_%s' % k])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Check if chi2 is distributed as a chi2 distribution for the signal region"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate toys using independet poisson distributions, with mean = $L_i\\times\\sigma_{vis}$. The number of total event is not fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  6,  13, 169])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def generate_toy_null(li, xsection):\n",
    "    \"\"\"\n",
    "    the model to generate the toys is just a set of poissonian.\n",
    "    The number of total event is non-constant\n",
    "      li = luminosity of the run\n",
    "      xsection = visible xsection\n",
    "    \"\"\"\n",
    "    li = np.array(li)\n",
    "    return stats.poisson.rvs(li * xsection)\n",
    "\n",
    "# test with three runs with a xsec = 2\n",
    "generate_toy_null([1, 10, 100], 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of runs 65\n",
      "mean and error of the mean of test-statistics 63.9530096168 0.305931782031\n",
      "frequentist pvalue 0.2054\n",
      "chi2-pvalue 0.133543841609\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZI2Fw2mD2H9vPlq8DXFpuTARZUjBhtemrTbRo2ILkJsluhxLT4uPi+X6379vZ\ngqlxIZOCiGSJyGYR2SYi9wWp85Szfa2I9PYpf0FECkXkC7/6LURkvohsFZF5IpJU/bdiosHigsXW\ndRQm13a/llc3vOp2GKaOKXf2kYjEA88AI4HdwHIRma2qm3zqjAE6qWqGiAwEpgOZzuYXgaeBv/s1\nfT8wX1UfcxLN/c5iYtxnBZ/ZILOPXbtg5szA206dgvr1g+87KG0Qh08dZsP+DXRv2T0yARrjJ9SZ\nwgAgV1XzVbUImAWM86szFngJQFWXAkki0spZ/wT4JkC7pfs4P8dXLXwTbWyQ+f+kpEBmJixeXHYB\nOHas/P3jJM66kEyNC3WdQgrg+zTxXcDACtRJAfaV026yqpY8wLAQsA7oWmDvkb0cOH6Abhd2czuU\nqNCjR/CzhBdeqFgb1/e4non/mUi2J9vuI2VqRKikUNG7cvl/Wit8Ny9VVREJWj87O7v0tcfjwePx\nVLRpU8MW5i/Ek+4hTmz+Qrj0b9Of+Lh4luxawqVp1i1nysrJySEnJyds7YVKCruBNJ/1NLxnAuXV\nSXXKylMoIq1UdZ+ItAb2B6vomxRMdFuwYwGXt7/c7TBqFRHhlotv4W9r/mZJwQTk/2V52rRp1Wov\n1Fe6FUCGiKSLSCJwHTDbr85s4CYAEckEDvl0DQUzG7jZeX0z8FalojZRacGOBYxoP8LtMGqdib0m\n8vrG1zledNztUEwdUG5SUNViYCrwAbAReFVVN4nIZBGZ7NSZA+SJSC4wA5hSsr+IvAIsBjqLSIGI\nTHI2/R64QkS2Apc76yaG7fhmByeKT3DRBReFrmwqJeW8FAamDuStzfbdyUReyBviqepcYK5f2Qy/\n9alB9r0hSPlBvNNcTS1R0nVkg6GRccvFtzBz9Uxu7Hmj26GYWs7uklpHHTgAkyYF3rZ+feXbW5C/\ngMvTbTwhUsZdNI4pc6ZQcLiAtGZpoXcwpookmh/7JyIazfHFsj17vFMm//a3wNsHD4bzz69YW6pK\nmyfasPjWxbRv3j5sMdZmIsKBA0qLFhXf54537yCtWRq/HPLLyAVmYp6IoKpVPmW3M4U6rEEDGDu2\n+u1s/nozDeo1sIQQBq+/Dp99Fnhbo7a38GK9idx/2f027ddEjH2yTLUt2GFdR+GyYAF8+SW0bXvu\nUlQEy94cQKOERnyU95HbYZpazM4UTLUtyF/AhK6VfBixoX9/iI8/t6ywEH73O5gy5dzyRYtg3Tph\nav+pPLPEFxx2AAATCUlEQVT8Ga7oeEXNBWrqFEsKplrOnD1DTn4Oz4x+xu1QYs7cuYHLW7YMvs+N\nPW/kgY8eIP9QPulJ6RGJy9RtlhRMtazau4rkxsm0btra7VBiTufOlat/8CAs+qgxQ5vdzL2vTefW\ntEdLtw0f7h0jMqa6LCmYanl367t8t/N33Q6j1mveHNLS4Kmn4Fj9O/i8xyAOv5VNvDZkwQLYsQPa\ntHE7SlMb2JTUOmrPHujXz/uzOvrM6MOTWU8ytN3Q8ARWRzjTBqu8/3f+9R2u6XoNk3pPok0bGDUK\nGjcuW+9734PLbQ5AnVLdKak2+8hU2a5vd7Hz8E67UZsLpvafytPLnkZVefhh6NsXLrro3GXDBliz\nxu1ITayx7iNTZe9ufZfRnUZTL84+RjVtVKdR/PSDn5KTn8Ottw4PWCcvr4aDMrWCnSmYKnt367tc\n1fkqt8Ook+IkjvsH388jnzzidiimlrGkYKrkeNFxFu1cxKhOo9wOpc6a2Gsi2w5uY+mupW6HYmoR\nSwqmSj7M+5B+bfqR1CDJ7VDqrIT4BO699F5+++lv3Q7F1CKWFEyVvLPlHes6igK39b6NZbuX8UXh\nF26HYmoJSwqm0s7qWd7d9i5XdbGk4LaGCQ25O/NuO1swYWPTRmq54mLv4u/kyaq3uXLPSpIaJNGp\nRaeqN2LC5o5+d9DhqQ5s+XoLXS7ocs62oqLA/9ciUL9+DQVoYoqdKdRyTz3lvagpKencpVu3qv9R\nmLV+lt0AL4o0rd+UewbdwwMfPXBOeb168OCDZf/vzzsPLrvMpWBN1AuZFEQkS0Q2i8g2EbkvSJ2n\nnO1rRaR3qH1FJFtEdonIamfJCs/bMYHcdZf326L/smNH5ds6c/YMr6x/hYm9JoY/UFNldw68k5V7\nV/Lpl5+Wlj32WOD/92DPazAGQiQFEYkHngGygG7ADSLS1a/OGKCTqmYAtwPTK7CvAk+oam9neT+M\n78lE0IIdC0g5L4WLLrjI7VCMj4YJDXl4+MPcO//eat0+w5hQZwoDgFxVzVfVImAWMM6vzljgJQBV\nXQokiUirCuxrT3iPQf9Y9w8m9rSzhGj0g14/4FTxKV7f+LrboZgYFioppAAFPuu7nLKK1GkTYt+p\nTnfTTBGxye4x4NjpY8zeMpvre1zvdigmgDiJ4w9X/IEHPnqA02dOux2OiVGhZh9V9Dy0st/6pwMP\nOa9/AzwO3FbJNkwNe3vL21yadinJTZLdDsUEMaLDCLpc0IU/LfkT910WcAiwXH/9Kxw6FHjbsGEw\neHA1AzRRL1RS2A2k+ayn4f3GX16dVKdOQrB9VXV/SaGIPA+8EyyA7Ozs0tcejwePxxMiZBMp/1z3\nTxtgjgFPj36aAc8NYEK3CZWeNvz443Dlld7nN/jKyQFVSwrRKCcnh5ycnLC1FyoprAAyRCQd2ANc\nB9zgV2c2MBWYJSKZwCFVLRSRA8H2FZHWqrrX2f9qIOjlmL5Jwbin8GghiwsW8+/v/9vtUEwIHZp3\n4IHLHuDH7/6Y+f81H5HKncjfcw907Hhu2a9+FcYATVj5f1meNm1atdord0xBVYvx/sH/ANgIvKqq\nm0RksohMdurMAfJEJBeYAUwpb1+n6UdFZJ2IrAWGAXdX612YiPvnun8ytstYGicGeJKLiTp3Zd7F\noZOHeGntS26HYmJMyCuaVXUuMNevbIbf+tSK7uuU31S5MI2bis8W8/Syp3nt+6+5HYqpoHpx9Xju\nqufIejmL0Z1Gh2Uc6PXXYevWsuWpqfCI3cG71rDbXJiQ3tz0JqnnpTIgZYDboZhK6N26N7decis/\nfOeHzL5+9jndSAcOwCuvlN3nyJHAbU2YAJ07ly0vKIBXX7WkUJtYUjAhPfH5E/zi0l+4HYapgmnD\npzH0xaE8seQJfn7pzwFo0QIGDoTZs8vWHzECmjQpW96nj3fx98UX3qRgag9LCqZcSwqWsP/YfsZ2\nGet2KKYKEuMTmXXNLAY+P5DBbQeTmZpJx46BzxKMAbshngnh8SWP89OBPyU+Lt7tUEwVpSelM+O7\nM7j+9es5eOKg2+GYKGdJwQSV900eOfk5TOo9ye1QTDWNv2g8V190NTe+cSNFZ4rcDsdEMUsKJqg/\nLv4jt/W+jSaJATqZTcx57IrHiJM4fvzuj+2meSYoG1MwAW38aiP/3vhvNv1kU+jKJiYkxCfw2vdf\nw/M3Dw99/BAPeh6M6PFmz4bDhwNv69kTLrkkooc3VWRJoZa4/HJYtaps+cmTMGVK5dpSVX72wc/4\n1ZBfcUGjC8IToIkKTRKb8N6N7zFo5iBSzkvhh31+GLFj/fKX0L6998E+vtatg6uusqQQrSwp1BJH\nj8Ibb0DfvmW3VfYJa3O2zSH/UD4/6f+T8ARnokpyk2Ten/g+l790OWfOnmFyv8nVau/LL+H6ADfO\nLSiAWbOgR49zyx9+uHqPgzWRZUmhFmnatOy3ssoqOlPEz+b9jCeufIKE+ITwBGaiTufzO/PxLR8z\n8h8jOXL6CPdcek+V2klLgxkzAm8bP957tbOJLZYUzDn+svwvtE9qz5iMMW6HYiKsY4uOfDLpE0b+\nfSSHTx7moeEPVfrmeUlJgc8SQnnsMe/zw/116ABr1lS+PRM+NvvIlFq/fz2PfPIIT2Y9Wek/DiY2\npZ6XyqJJi5iXN49r/n0NR04Fuc9FGN17L3z9Nezade7y8cfeblDjLjtTMAAcOXWEa167hj9e8Ud7\n/nId07JxSxbdsog7597JgOcH8OZ1b0b0M1C/fuBxrqZNg+/z9tve+zUFsnMntGtXtrxRo6qdxdR1\nlhQMqsrt797OZW0v4+ZLbnY7HOOC+vXqM+OqGTy/6nmGvDiEh4c/zI/6/og4iY7OhN/8Btq0gQv8\nJsPl53vHNQoKzi0/dgw+/TQ8SeHYMe/geDC33goZGdU/TrSwpGB4dsWzbPpqE0tuW+J2KMZlP+zz\nQwalDuLW2bcya8MsnrvquUo/vS1S/ud/oF+/itXdvRsuvtjbJRXIxRdXfFLGyZPw5z/Dr39ddtvM\nmTB8uCUFU4u8vO5lpn08jU8mfULDhIZuh2OiQPeW3Vl862L+vPTPZD6fyeS+k/nF4F/QrEGziB/7\n8GF4/vmy5V99Vbl2EhOhe3dvIvG3Zg28+y4MGVLx9ho2hAceKFu+cGHl4ooFlhTqsP9d+b9M+3ga\nH930ERnn16KvOqba4uPi+dmgn3FNt2t4MOdBMp7O4L7B93FH/ztolNAoIsc87zwYNw4+/7zstiuu\nKNt1VJ4LLwx+ljBkCOzf7x3c9te4cdnnU9c1lhRiyL59cMcdgbdt21bxdlSVP33+J55a+hQf3/Jx\n1HQPmOjTtllbXhz3Ihv2b+DXC3/N7z/7PT/s/UOm9J9CWrO0sB6rZcvAZwnhduGFcNddZct37/b+\nHD/+3PJTpyIfUzSRaL4xlohoNMdX0/LyYNAgePbZwNuHDfM+QKU8e4/s5Y737mD7N9t578b3aNus\nbfgDNSGJSEzelC73YC5PL32af6z7B0PaDeHGHjdyVZerInb2UJPy8mDt2sDbEhPhO98pW37llXDP\nPd6f0cL5bFV5TnnIpCAiWcCTQDzwvKo+GqDOU8Bo4Dhwi6quLm9fEWkBvAq0A/KBa1X1UIB2LSn4\nyMuDkSO9PytLVfnnun9yz/x7+FGfH/Hrob+mfr1K3v/ChE2sJoUS3576ljc3vckr61/h812fM6rT\nKEZ3Gs2ojqNo3bS12+HVmCuvhJtugqFDK76PiHfGVKRENCmISDywBRgJ7AaWAzeo6iafOmOAqao6\nRkQGAn9W1czy9hWRx4CvVfUxEbkPaK6q9wc4fswmhZycHDweT1jbrEpSOFF0gpe/eJk/ff4n6sfX\n57mrnqNvmwA3SPITifhrUrTHHyopRHv8vgqPFjJn2xze3/4+87fPJ+W8FNK/SWfCmAlkpmaS0SIj\n5h7SVNF//x/8AD75pOLtnj0LBw/C8eNVjy2U6iaFUGMKA4BcVc13DjYLGAf43k95LPASgKouFZEk\nEWkFtC9n37HAMGf/l4AcoExSiGXV+aVeuRKWLStbXtEZGEdOHWHBjgXMzZ3Lm5vfpF+bfvw568+M\naD+iwlcqx9IfpUAs/pqT3CSZSb0nMan3JIrPFrN672r+58H/4YPtH/DQxw9ReKyQbhd2o0fLHmS0\nyKBTi050bN6Rts3ackGjC6Ly6vmK/vu//HLl2j1+vHID5m4IlRRSAN/LQnYBAytQJwVoU86+yapa\n6LwuBJIrEXOt0bs3rF9ftry42DsD4rrrym77wQ+8P0+fOc3+Y/vZe2Qve4/uZduBbaz/aj1fFH7B\nlgNbGJgykNGdRvPppE9tZpGpMfXi6tE/pT8DUweSPSEb8H5JWb9/Pev3ryf3YC6vbXiN3IO5FHxb\nwPGi46Q0TaFVk1Zc2PhCWjZqyfmNzqd5g+Y0b9icZvWb0bR+U5omNqVJYhMaJTSiUUIjGiY0pEG9\nBtSPrx9zZyHRLlRSqGjfTUVSvQRqT1VVRIIeJ/nuqyoYQnQ5umQL0w+vpLx/wgO9lMzblaZNvX3+\nZ/Usivdn8dli1nOG4rPFnCo+xakzpzhVfIojp4/wx0e+pehMES0bt6R109a0btKaDs07cGnqpdze\n53Z6JfeicWLjmnuzxpSjaf2mDEobxKC0QWW2HS86zq5vd1F4tJD9x/az/9h+Dp44SOGxQjZ/vZnD\npw5z5PQRjpw6wtHTRzlRfILjRcc5XnSck8UnOVV8ivi4eBLjE0mMTyQhLoGE+AQS4hKoF1eP+Lh4\n70+JJz4unjiJI168P+MkDhHx/kQQEQTv+o61O/j075+WnsWUbC8hzp+8kn18BTvzEYQzZ6DhLfWB\nN8L0rxsBqhp0ATKB933WHwDu86vzLHC9z/pmvN/8g+7r1GnlvG4NbA5yfLXFFltssaVyS3l/10Mt\noc4UVgAZIpIO7AGuA27wqzMbmArMEpFM4JCqForIgXL2nQ3cDDzq/Hwr0MGrM1hijDGm8spNCqpa\nLCJTgQ/wTiud6cwemuxsn6Gqc0RkjIjkAseASeXt6zT9e+A1EbkNZ0pqBN6bMcaYSorqi9eMMcbU\nrOi4L64fEckSkc0iss25jiGqiUiaiCwUkQ0isl5E7nTKW4jIfBHZKiLzRKSaD8uMHBGJF5HVIvKO\nsx5LsSeJyOsisklENorIwBiL/27nc/OFiPxLROpHc/wi8oKIFIrIFz5lQeMVkQec3+XNIuL6tb9B\n4v+D8/lZKyL/EZFmPtuiPn6fbT8XkbPOBcIlZZWKP+qSgnPR2zNAFtANuEFEurobVUhFwN2q2h3v\nAPtPnJjvB+aramfgI6L7Woy7gI14B6ogtmL/MzBHVbsCvfBOZIiJ+EUkBfh/QF9V7Ym3q/V6ojv+\nF/H+fvoKGK+IdMM7ntjN2eevIq4/pCFQ/POA7qp6MbAV78SYWIofEUkDrgB2+pRVOn6331wgpRfM\nqWoRUHLRW9RS1X2qusZ5fRTvBXop+FzY5/wcH7gFd4lIKjAGeJ7/m14cK7E3A4ao6gvgHctS1cPE\nSPyOekAjEakHNMI7MSNq41fVT4Bv/IqDxTsOeEVVi5wLWXPx/o67JlD8qjpfVc86q0uBVOd1TMTv\neAL4hV9ZpeOPxqQQ7GK4mODMtuqN94MVKxfp/Qm4FzjrUxYrsbcHvhKRF0VklYg8JyKNiZH4VXU3\n8DjwJd5kcEhV5xMj8fsIFm8bvL/DJWLh9/lWYI7zOibiF5FxwC5VXee3qdLxR2NSiNmRbxFpgveq\nlLtU9ZwnoDs3cYq69yYi3wX2OzcxDDgFOFpjd9QD+gB/VdU+eGfAndPVEs3xi0hzvN+y0/H+AjcR\nkYm+daI5/kAqEG/UvhcR+RVwWlX/VU61qIpfRBoBvwQe9C0uZ5dy44/GpLAb8L2HYBrnZrqoJCIJ\neBPCP1S15LqLQuc+UIhIa2C/W/GV41JgrIjsAF4BLheRfxAbsYP3s7FLVZc766/jTRL7YiT+kcAO\nVT2gqsXAf4BBxE78JYJ9Xvx/n1OdsqgjIrfg7Ub9gU9xLMTfEe+XirXO73EqsFJEkqlC/NGYFEov\nmBORRLyDJLNdjqlcIiLATGCjqj7ps6nkIj0o5yI9N6nqL1U1TVXb4x3gXKCq/0UMxA7e8RygQEQ6\nO0UjgQ3AO8RA/HgHBTNFpKHzORqJd8A/VuIvEezzMhu4XkQSRaQ9kAEEuN2ju8R7m/97gXGqetJn\nU9THr6pfqGqyqrZ3fo93AX2c7rzKx1+dy6EjteB9NsMWvIMiD7gdTwXivQxvf/waYLWzZAEtgA/x\nzmaYByS5HWuI9zEMmO28jpnYgYvx3pp9Ld5v2s1iLP5svJMTvsA7SJsQzfHjPaPcA5zGO/43qbx4\n8XZt5OKdFTYqCuO/FdiGN0GX/P7+NQbiP1Xy7++3PQ9oUdX47eI1Y4wxpaKx+8gYY4xLLCkYY4wp\nZUnBGGNMKUsKxhhjSllSMMYYU8qSgjHGmFKWFIwxxpSypGCMMabU/wdn/HMrj6inAwAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa8a98bf710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "NTOYS = 5000\n",
    "\n",
    "q0_toys = []\n",
    "q0_obs = stats.chisquare(df['obs_signal'], df['exp_signal'])[0]\n",
    "xsection = df['obs_signal'].sum() / df['lumi'].sum()\n",
    "\n",
    "fractions = df['lumi'] / np.sum(df['lumi'])\n",
    "\n",
    "for itoy in xrange(NTOYS):\n",
    "    toy = generate_toy_null(df['lumi'], xsection)\n",
    "    exp = np.sum(toy) * fractions\n",
    "    q0_toy = stats.chisquare(toy, exp)[0]\n",
    "    q0_toys.append(q0_toy)\n",
    "q0_toys = np.array(q0_toys)\n",
    "\n",
    "pvalue = np.count_nonzero(q0_toys >= q0_obs) / float(NTOYS)\n",
    "\n",
    "bins = np.linspace(0, len(df['lumi']) * 2, 50)\n",
    "hist = plt.hist(q0_toys, bins=bins, normed=True, histtype='step')\n",
    "\n",
    "x = np.linspace(0, len(df['lumi']) * 2, 100) \n",
    "y = stats.chi2(len(df['lumi']) - 1).pdf(x)\n",
    "plt.plot(x, y)\n",
    "plt.vlines(q0_obs, 0, np.max(hist[0]))\n",
    "\n",
    "print \"number of runs\", len(df)\n",
    "print \"mean and error of the mean of test-statistics\", np.mean(q0_toys), stats.sem(q0_toys)\n",
    "print \"frequentist pvalue\", pvalue\n",
    "print \"chi2-pvalue\", stats.chi2(len(df) - 1).sf(q0_obs)\n",
    "\n",
    "final_result['chi2 frequentist'] = pvalue\n",
    "final_result['chi2 asym'] = stats.chi2(len(df) - 1).sf(q0_obs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not really a chi2, p-value quite different from the asymtotic one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot $G_i = 2 O_i \\log(O_i / E_i)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jNEfHurkMHaO5DB2jOTrWzWXoGM1l6BjNZehY9ADVzC6XdKWkr3D3L5f048v+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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa8a7bd2f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(3, 1, figsize=(16, 8), sharex=True)\n",
    "for k, ax in zip(all_df, axs.flat):\n",
    "    obs = df['obs_%s' % k] + 1E-5\n",
    "    (2 * obs * np.log(obs / df['exp_%s' % k])).plot(kind='bar', ax=ax)\n",
    "    ax.set_title(k)\n",
    "    ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute G-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g-test value and p-value\n",
      "signal (68.623728635494203, 0.32352642917869995)\n",
      "right (47.910916937790176, 0.93347840328090415)\n",
      "left (62.980395330734588, 0.51258720156265292)\n"
     ]
    }
   ],
   "source": [
    "def gtest(obs, exp, ddof=0):\n",
    "    mask = (obs != 0)\n",
    "    g = 2 * np.sum(obs[mask] * np.log(obs[mask] / exp[mask]))\n",
    "    return g, stats.chisqprob(g, len(obs) - 1 - ddof)\n",
    "\n",
    "print \"g-test value and p-value\"\n",
    "for k in all_df:\n",
    "    print k, gtest(df['obs_%s' % k], df['exp_%s' % k])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Check if $G$ is distributed as a $\\chi^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def test_poisson_prod(obs, exp):\n",
    "    obs = np.array(obs, dtype=float)\n",
    "    obs += np.min(obs[obs>0]) / 1E10  # introduce little bias to avoid log(0), 0 ** 0\n",
    "    q0 = 2 * np.sum(obs * np.log(obs / exp))   # g-test\n",
    "    p0 = stats.chi2(len(obs) - 1).sf(q0)\n",
    "    return q0, p0\n",
    "\n",
    "def test_poisson_prod_from_lumi(ni, li):\n",
    "    L = float(np.sum(li))\n",
    "    N = float(np.sum(ni))\n",
    "    xsec = N / L\n",
    "    return test_poisson_prod(ni, li * xsec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of runs 65\n",
      "mean and error of the mean of test-statistics 59.6708334366 0.135942262432\n",
      "frequentist pvalue 0.17\n",
      "chi2-pvalue 0.323526432275\n"
     ]
    },
    {
     "data": {
      "image/png": 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yXIbFtIhh0e5FZGVneSkxpTzHboHcVCAyz/NIrJaAq5gIxz5EJAD4CvjUGJO7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\nBEEQlERQCIIgCEp+A1RNI5EuPLb7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa8a81b0750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_toy_null(li, xsection):\n",
    "    \"\"\"\n",
    "    the model to generate the toys is just a set of poissonian.\n",
    "    The number of total event is non-constant\n",
    "      li = luminosity of the run\n",
    "      xsection = visible xsection\n",
    "    \"\"\"\n",
    "    li = np.array(li)\n",
    "    return stats.poisson.rvs(li * xsection)\n",
    "\n",
    "q0_toys = []\n",
    "xsection = df['obs_signal'].sum() / df['lumi'].sum()\n",
    "q0_obs = test_poisson_prod_from_lumi(df['obs_signal'], df['lumi'])[0]\n",
    "sums = []\n",
    "\n",
    "NTOYS = 5000\n",
    "\n",
    "for itoy in xrange(NTOYS):\n",
    "    toy = generate_toy_null(df['lumi'], xsection)     # value of xsection is not important\n",
    "    q0_toy = test_poisson_prod_from_lumi(toy, df['lumi'])[0]  # compute the g-test\n",
    "    q0_toys.append(q0_toy)\n",
    "    sums.append(toy.sum())\n",
    "q0_toys = np.array(q0_toys)        \n",
    "\n",
    "pvalue = np.count_nonzero(q0_toys >= q0_obs) / float(NTOYS)\n",
    "\n",
    "bins = np.linspace(0, len(df['lumi']) * 2, 50)\n",
    "hist = plt.hist(q0_toys, bins=bins, normed=True, histtype='step')\n",
    "\n",
    "x = np.linspace(0, len(df['lumi']) * 2, 100) \n",
    "y = stats.chi2(len(df['lumi']) - 1).pdf(x)\n",
    "plt.plot(x, y, label='ndof = %d' % (len(df['lumi']) - 1))\n",
    "\n",
    "plt.plot(x, stats.chi2(np.mean(q0_toys)).pdf(x), label='ndof = %.2f' % np.mean(q0_toys))\n",
    "\n",
    "plt.vlines(q0_obs, 0, np.max(hist[0]))\n",
    "plt.legend()\n",
    "\n",
    "print \"number of runs\", len(df)\n",
    "print \"mean and error of the mean of test-statistics\", np.mean(q0_toys), stats.sem(q0_toys)\n",
    "print \"frequentist pvalue\", pvalue\n",
    "print \"chi2-pvalue\", stats.chi2(len(df) - 1).sf(q0_obs)\n",
    "\n",
    "final_result[\"G test frequentist\"] = pvalue\n",
    "final_result[\"G test asym\"] = stats.chi2(len(df) - 1).sf(q0_obs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not really a chi2. In fact, p-value quite different. Differently than the previous case the shape seems to be corrected, but shifted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
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   "source": [
    "### DON'T RUN, this is an exact test, it will run forever\n",
    "import met\n",
    "m = met.Multinom(list(df['obs_signal'].astype(int)), list(df['exp_signal'].astype(int)))\n",
    "#m.onesided_exact_test()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multinomial test\n",
    "\n",
    "The idea is to compute the probability of the observed partitioning of the events among the runs (we assume that the total number of observed events is a fixed constant), taking into account that different runs have different probability, proportional to the luminosity. Then the p-value is computed simply as the probabily to observe a configuration less probable (here less probable is the \"more extreme\" in the p-value definition) than the observed.\n",
    "\n",
    "This means to compute all the possible partitioning and their probabilities. Since this is too expensive, a finite sampling of all the configuration is done."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "signal region\n",
      "  sum p_i (toy more extreme) / sum p_i (all toys) =  1.16885546918e-07\n",
      "  # (toy more extreme) / # (all toys) =  0.129\n",
      "right region\n",
      "  sum p_i (toy more extreme) / sum p_i (all toys) =  0.00252380274266\n",
      "  # (toy more extreme) / # (all toys) =  0.6961\n"
     ]
    }
   ],
   "source": [
    "# from: http://stats.stackexchange.com/questions/133708/how-can-i-test-if-a-sample-was-created-from-a-specific-discrete-distribution\n",
    "# comments from me\n",
    "from math import factorial\n",
    "\n",
    "def p_multinomial(probs, counts):\n",
    "    \"\"\"\n",
    "    compute the probability for a configuration (partitioning), from the\n",
    "    probabilities of each run (the fraction of the luminosity) and the\n",
    "    observed number of events\n",
    "    \"\"\"\n",
    "    result = np.float128(factorial(sum(counts)))\n",
    "    for prob, count in zip(probs, counts):\n",
    "        result *= np.float128(prob ** count) / np.float128(factorial(count))\n",
    "    return result\n",
    "\n",
    "def run_multinomial(obs, exp, ntoys=10000):\n",
    "    nevents = obs.sum()                    # total number of observed events\n",
    "\n",
    "    exp_frac = exp / exp.sum()             # expected fraction of events for all the runs (fraction of lumi)\n",
    "    p_obs = p_multinomial(exp_frac, obs)   # observed probability\n",
    "    \n",
    "    p_improbables = 0                      # accumulator, summing the probabilities of more improbable toy\n",
    "    p_tot = 0                              # accumulator, summing all the probabilities\n",
    "    n_improbables = 0                      # accumulator, couting number of toys more improbable\n",
    "\n",
    "    lumi_frac = df['lumi'] / np.sum(df['lumi'])\n",
    "    \n",
    "    for i in xrange(ntoys):\n",
    "        toy = np.random.multinomial(nevents, exp_frac, size=1)[0]   # generate a random configuration\n",
    "        ptoy = p_multinomial(lumi_frac, toy)                        # compute its probability\n",
    "        if ptoy <= p_obs:                                           # more extreme <=> less probable (two side test)\n",
    "            p_improbables += ptoy\n",
    "            n_improbables += 1\n",
    "        p_tot += ptoy\n",
    "        \n",
    "    return p_improbables / p_tot, n_improbables / float(ntoys)\n",
    "\n",
    "for k in all_df:\n",
    "    if k == 'left': continue\n",
    "    print k, \"region\"\n",
    "    result = run_multinomial(df['obs_%s' % k], df['exp_%s' % k])\n",
    "    print \"  sum p_i (toy more extreme) / sum p_i (all toys) = \", result[0]\n",
    "    print \"  # (toy more extreme) / # (all toys) = \", result[1]\n",
    "    if k == 'signal':\n",
    "        final_result['multinomial frac'] = result[1]\n",
    "        final_result['multinomail p'] = result[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is impossibile to run the test for the left region, since the factorials are too large. There could be a bug in the code, or the test is not correctly defined. The p-value for the signal region is very small. Is it correct what I am doing?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Final results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "G test asym          0.32\n",
      "G test frequentist   0.17\n",
      "chi2 asym            0.13\n",
      "chi2 frequentist     0.21\n",
      "multinomail p        0.00\n",
      "multinomial frac     0.13\n"
     ]
    }
   ],
   "source": [
    "for k in sorted(final_result):\n",
    "    print \"{:<20} {:.2f}\".format(k, final_result[k])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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