Lecture2.ipynb

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    {
     "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/]};"
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     "name": "stdout",
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     "text": [
      "Welcome to ROOTaaS 6.06/08\n",
      "\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": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import pandas as pd\n",
    "from IPython.display import HTML, IFrame, Image, SVG, Latex\n",
    "import ROOT\n",
    "from ROOT import RooFit, RooStats\n",
    "%matplotlib inline\n",
    "#%matplotlib nbagg\n",
    "#%matplotlib notebook\n",
    "from ipywidgets import interact, interactive, fixed\n",
    "import colormaps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<link rel=\"stylesheet\" href=\"custom.css\" type=\"text/css\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from matplotlib import rcParams\n",
    "rcParams.update({'font.size': 18})\n",
    "HTML('<link rel=\"stylesheet\" href=\"custom.css\" type=\"text/css\">')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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    "slideshow": {
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   "outputs": [],
   "source": [
    "#from notebook.services.config import ConfigManager\n",
    "#cm = ConfigManager()\n",
    "#cm.update('livereveal', {\n",
    "#          'theme': 'sans',\n",
    "#          'transition': 'zoom',\n",
    "#})"
   ]
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  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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   "source": [
    "def iter_collection(rooAbsCollection):\n",
    "    iterator = rooAbsCollection.createIterator()\n",
    "    object = iterator.Next()\n",
    "    while object:\n",
    "        yield object\n",
    "        object = iterator.Next()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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   "source": [
    "def RooDataSet2pandas(data):\n",
    "    nevents = data.numEntries()\n",
    "    columns = [x.GetName() for x in iter_collection(data.get(0))]\n",
    "    return pd.DataFrame([[x.getVal() for x in iter_collection(data.get(ievent))] for ievent in xrange(nevents)], columns=columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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   "outputs": [],
   "source": [
    "def p2z(p_value, onetail=True):\n",
    "    \"\"\" pvalue to significance \"\"\"\n",
    "    if not onetail:\n",
    "        p_value /= 2\n",
    "    return stats.norm.isf(p_value)  # inverse of the survival function\n",
    "\n",
    "def z2p(z, onetail=True):\n",
    "    \"\"\" significance to pvalue \"\"\"\n",
    "    if onetail:\n",
    "        return stats.norm.sf(z)\n",
    "    else:\n",
    "        return stats.norm.sf(z) * 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   "source": [
    "# Lecture 2\n",
    "\n",
    "<p style=\"text-align: center;\"><i class=\"icon-user icon-2x\"> [ruggero.turra@mi.infn.it](mailto:ruggero.turra@mi.infn.it)</i></p>\n",
    "<br/>\n",
    "\n",
    "## Content of the lecture\n",
    "\n",
    "   * Hypothesis testing\n",
    "   * Type or errors\n",
    "   * Likelihood ratio\n",
    "   * Neyman–Pearson lemma\n",
    "   * Exclusions\n",
    "   * Profiled likelihood ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
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   "source": [
    "## Simple and composite hypothesis\n",
    "\n",
    "* A simple hypothesis is one in which all parameters of the distribution are specified"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "## Error type\n",
    "\n",
    "   * Type I error: false positive (excessive credulity). Rate = $\\alpha = P(\\text{reject } H_0|H_0 \\text{ is true})$\n",
    "   * Type II error: false negative (excessive skepticism). Rate = $\\beta = P(\\text{don't reject } H_0|H_0 \\text{ is false})$\n",
    "   \n",
    "   * Power of the test: $1-\\beta$\n",
    "   * Remember that \"true\"/\"false\" refers to $H_1$, the alternative hypothesis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
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   },
   "outputs": [
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Jo/8A4HRf/FUf8Jj4X/6GTR//AAOi/wDiqPqtf+R/cwub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\nzm5U5KrT3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CP/AJ5PJF/3zIy/0rtK4zRvlhvov+eeo3Y/Od2H6NXPl9eVZVZz3bi//Sl9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\nMqM24ydT6VFFD9mlbZ8wbq3pWqRhzDYIBBG5/jPNRafZme4Yk5GetRXF4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UeV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\n6VomgcTs0my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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 7,
     "metadata": {
      "image/jpeg": {
       "width": "70%"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(\"img/type-i-and-type-ii-errors.jpg\", width=\"70%\")  # from https://effectsizefaq.files.wordpress.com/2010/05/type-i-and-type-ii-errors.jpg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Question:\n",
    "what is $H_0$ and $H_1$ in this sketch?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "scrolled": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "with plt.xkcd():\n",
    "    fig, ax = plt.subplots(figsize=(10, 7))\n",
    "    x = np.linspace(-5, 5, 200)\n",
    "    y0 = stats.norm.pdf(x, 0, 1)\n",
    "    y1 = stats.norm.pdf(x, 1, 1)\n",
    "    mask = x >= 2\n",
    "    ax.plot(x, y0, x, y1, '-')\n",
    "    ax.fill_between(x[mask], y0[mask], alpha=0.5)\n",
    "    ax.fill_between(x[~mask], y1[~mask], alpha=0.5)\n",
    "    ax.vlines(2, 0, 0.5, linestyle='--', lw=2)\n",
    "    #ax.set_xticklabels([])\n",
    "    #ax.set_yticklabels([])\n",
    "    ax.set_xlabel(\"$q$\")\n",
    "    ax.annotate(\"$f(q|H_1)$\", xy=(x[100], y1[100]), xytext=(0.2, 0.7), textcoords=\"figure fraction\", size=20,\n",
    "                arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\"), color='green')\n",
    "    ax.annotate(\"$f(q|H_0)$\", xy=(x[90], y0[90]), xytext=(0.3, 0.8), textcoords=\"figure fraction\", size=20,\n",
    "                arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\"), color='blue')\n",
    "    ax.annotate(r\"$\\beta$\", xy=(x[100], 0.1), xytext=(0.1, 0.5), textcoords=\"figure fraction\", size=20,\n",
    "                arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\"), color='green')\n",
    "    ax.annotate(r\"$\\alpha$\", xy=(x[142], 0.01), xytext=(0.8, 0.25), textcoords=\"figure fraction\", size=20,\n",
    "                arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\"), color='blue')\n",
    "    ax.text(2, 0.4, r'$q_\\alpha$', rotation='vertical', ha='right', size=20)\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/turra/venv/lib/python2.7/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family [u'xkcd', u'Humor Sans', u'Comic Sans MS'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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/Uy8BrW+n/5///IeysjKXBw1Ur9Cx2Wz4+vq6tC4hzgU33ngjo0aNYsaMGc7+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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd05ee17050>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that to evaluate $\\beta = P(\\text{don't reject } H_0|H_0 \\text{ is false})$ we have used an alternative hypothesis $H_1$, but remember that if $H_0$ is false doesn't mean that $H_1$ is true.\n",
    "\n",
    "The region $q > q_\\alpha$ is the rejection region where we reject $H_0$. The complementary is the acceptance region."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Hypothesis testing in practice\n",
    "\n",
    "   * Define the null hypothesis you want to try to reject\n",
    "   * Define the observables (number of events in the signal region, ...)\n",
    "   * Fix the rate of type I error $\\alpha$ of the test statistics (5%, $5\\sigma$, ...)\n",
    "   * Define the test statistic (trying to maximize the power $1-\\beta$)\n",
    "   * Find the rejection region in the observable space, which is the region where $H_0$ is rejected (p-value $<\\alpha$)\n",
    "   * Do the experiment\n",
    "   * If the outcome is outside the acceptance region reject the null-hypothesis\n",
    "   \n",
    "In complex example one don't compute the acceptance region, but just compute the observed p-value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Exercize (big): Lady tasting tea (Fisher \"The Design of Experiments\" - 1935)\n",
    "\n",
    "A lady claimed to be able to tell whether the tea or the milk was added first to a cup. Fisher proposed to give her eight cups, four of each variety, in random order. What is the critical region at 5%? If we ask for a $5\\sigma$ evidence, what's the minimum amount of cups we have to prepare? (Hint: look at the [Hypergeometric distribution](https://en.wikipedia.org/wiki/Hypergeometric_distribution), answer should be 26)\n",
    "\n",
    "Are we interested in the rare case when the lady never guess? What is \"more extreme\" in this case?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Example: Lady tasting tea 2.0\n",
    "\n",
    "Suppose that the lady doesn't know how many cups of a kind are present. The acceptance region and the power (using p=90% as alternative hypothesis) can be computed easily from the binomial distribution.\n",
    "\n",
    "To compute the rejection region we have to find the minimum $q_\\alpha$ such that:\n",
    "\n",
    "$$\\sum_{n\\geq q_{\\alpha}} B(n|p=50\\%, N=8) \\leq \\alpha$$\n",
    "\n",
    "with $\\alpha=5\\%$. The solution can be found iteratively or inverting the formula (see the code). The lady has to guess correctly at least 7 cups. To compute the power simply using the definition\n",
    "\n",
    "$$\\text{power} = 1 - \\beta = 1 - P(\\text{don't reject $H_0$} | \\text{$H_0$ is false}) = 1 - \\sum_{n<7} B(n|p=90\\%, N=8) = 81\\%$$\n",
    "\n",
    "Since $H_0$ is not a simple hypothesis (it doesn't tell us automatically how much is $p$) we have to assume one particular $H_1$ ($p=90\\%$) to compute the power."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "N = np.arange(1, 70)\n",
    "alpha = np.sort(np.concatenate((np.logspace(-8, -3, 20), np.arange(0.001, 0.2, 0.002))))\n",
    "\n",
    "kalpha = stats.binom.isf(alpha.reshape(len(alpha), 1), N, 0.5)\n",
    "results_must_guess = kalpha.T + 1\n",
    "power = stats.binom.sf(kalpha, N, 0.9).T\n",
    "min_N = np.ceil(np.log(alpha) / np.log(0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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j4fTYuhY/hcEeWjM1us2uo5/NoCeDLY5P62TT7vj322qPf53H5pDXmhfltYqk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\nDVRFRERERETEV/4/HqJrbCEY8F8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd05d1f5850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(15, 6))\n",
    "p = ax[1].pcolormesh(alpha, N, power, vmin=0, vmax=1, cmap='viridis')\n",
    "div = make_axes_locatable(ax[1])\n",
    "cax = div.append_axes(\"right\", size=\"5%\", pad=0.05)\n",
    "cbar = plt.colorbar(p, cax=cax)\n",
    "ax[0].set_xscale('log')\n",
    "ax[1].set_xscale('log')\n",
    "p = ax[0].pcolormesh(alpha, N, results_must_guess, vmin=0, cmap='viridis')\n",
    "div = make_axes_locatable(ax[0])\n",
    "cax = div.append_axes(\"right\", size=\"5%\", pad=0.05)\n",
    "cbar = plt.colorbar(p, cax=cax)\n",
    "\n",
    "ax[0].fill_between(alpha, min_N, color='white')\n",
    "ax[1].fill_between(alpha, min_N, color='white')\n",
    "\n",
    "ax[1].set_title('power')\n",
    "ax[0].set_title('minimum corrected guess to reject H0', fontsize=15)\n",
    "ax[1].set_xlabel('alpha')\n",
    "ax[1].set_ylabel('number of cups')\n",
    "ax[0].set_xlabel('alpha')\n",
    "ax[0].set_ylabel('number of cups')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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j4fTYuhY/hcEeWjM1us2uo5/NoCeDLY5P62TT7vj322qPf53H5pDXmhfltYqk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\nDVRFRERERETEV/4/HqJrbCEY8F8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd05d1f5850>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Neyman–Pearson lemma\n",
    "Having two simple hypotheses (no additional parameters) $H_0: \\theta = \\theta_0$ and $H_1: \\theta = \\theta_1$, the likelihood-ratio test:\n",
    "$$\n",
    "\\Lambda(x) = \\frac{L(\\theta_0|x)}{L(\\theta_1|x)}\n",
    "$$\n",
    "\n",
    "which rejects $H_0$ in favour of $H_1$ when $\\Lambda \\leq k_\\alpha$ (rejection region) with $\\alpha=P(\\Lambda(X)\\leq k_\\alpha|H_0)$ is the most powerful test with size $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Example\n",
    "Suppose you have a rock that seems to be opal (density 2.2 g/cm<sup>3</sup>), but may be also quartz (2.6 g/cm<sup>3</sup>). You have two instruments to measure the density, the first with resolution 0.2 g/cm<sup>3</sup>, the second with resolution 0.5 g/cm<sup>3</sup>. Opal is much expensive, we want to check if it is opal. $H_0:$quartz. What is the rejection region at 5%? Assume gaussian errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "ws = ROOT.RooWorkspace()\n",
    "true_density = ws.factory(\"true_density[2, 3]\")\n",
    "ws.factory(\"Gaussian::pdf1(density1[0,50], true_density, resolution1[0.5])\")\n",
    "ws.factory(\"Gaussian::pdf2(density2[0,50], true_density, resolution2[0.2])\")\n",
    "pdf = ws.factory(\"PROD::pdf(pdf1, pdf2)\")\n",
    "\n",
    "pdf_opal = ws.factory(\"EDIT:pdf_opal(pdf, true_density=density_opal[2.2])\")\n",
    "pdf_quartz = ws.factory(\"EDIT:pdf_quartz(pdf, true_density=density_quartz[2.6])\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  1) RooRealVar:: density1 = 2.69947\r\n",
      "  2) RooRealVar:: density2 = 2.11305\r\n"
     ]
    }
   ],
   "source": [
    "# do the experiment, use H1 to generate (opal)\n",
    "data = pdf_opal.generate(ROOT.RooArgSet(ws.var('density1'),\n",
    "                                        ws.var('density2')), 1)  # generate with 1 entry\n",
    "data.get(0).Print(\"V\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "opal_model = RooStats.ModelConfig(\"opal (H1)\", ws)   \n",
    "opal_model.SetPdf(pdf_opal)\n",
    "opal_model.SetParametersOfInterest('density_opal')  # not useful\n",
    "opal_model.SetObservables('density1,density2')  # no space\n",
    "opal_model.SetSnapshot(ROOT.RooArgSet(ws.var('density_opal')))\n",
    "\n",
    "quartz_model = opal_model.Clone(\"quartz (H0)\")\n",
    "quartz_model.SetParametersOfInterest('density_quartz')  # not useful\n",
    "quartz_model.SetPdf(pdf_quartz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r\n",
      "=== Using the following for quartz (H0) ===\r\n",
      "Observables:             RooArgSet:: = (density1,density2)\r\n",
      "Parameters of Interest:  RooArgSet:: = (density_quartz)\r\n",
      "PDF:                     RooProdPdf::pdf_quartz[ pdf1_pdf_quartz * pdf2_pdf_quartz ] = 0\r\n",
      "Snapshot:                \r\n",
      "  1) 0x559a7c9cbff0 RooRealVar:: density_opal = 2.2 C  L(-INF - +INF)  \"density_opal\"\r\n",
      "\r\n",
      "\r\n",
      "=== Using the following for opal (H1) ===\r\n",
      "Observables:             RooArgSet:: = (density1,density2)\r\n",
      "Parameters of Interest:  RooArgSet:: = (density_opal)\r\n",
      "PDF:                     RooProdPdf::pdf_opal[ pdf1_pdf_opal * pdf2_pdf_opal ] = 0\r\n",
      "Snapshot:                \r\n",
      "  1) 0x559a7c9e4480 RooRealVar:: density_opal = 2.2 C  L(-INF - +INF)  \"density_opal\"\r\n",
      "\r\n",
      "[#0] PROGRESS:Generation -- Test Statistic on data: 2.39039\r\n",
      "[#1] INFO:InputArguments -- Using a ToyMCSampler. Now configuring for Null.\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 1000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 1500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 2000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 2500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 3000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 3500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 4000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 4500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 5000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 5500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 6000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 6500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 7000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 7500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 8000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 8500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 9000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 9500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 10000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 10500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 11000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 11500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 12000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 12500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 13000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 13500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 14000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 14500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 15000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 15500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 16000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 16500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 17000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 17500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 18000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 18500 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 19000 / 20000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 19500 / 20000\r\n",
      "[#1] INFO:InputArguments -- Using a ToyMCSampler. Now configuring for Alt.\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 500 / 1000\r\n"
     ]
    }
   ],
   "source": [
    "# define the test-statistic\n",
    "\n",
    "test = RooStats.SimpleLikelihoodRatioTestStat(pdf_quartz, pdf_opal)  # null, alt\n",
    "test.EnableDetailedOutput(True)\n",
    "\n",
    "hypoCalc = RooStats.FrequentistCalculator(data, opal_model, quartz_model)  # alt, null\n",
    "hypoCalc.SetToys(20000, 1000)  # generate much more toys for bkg-only\n",
    "\n",
    "toy_sampler = hypoCalc.GetTestStatSampler()\n",
    "toy_sampler.SetTestStatistic(test)  # our test statistics\n",
    "toy_sampler.SetNEventsPerToy(1)\n",
    "\n",
    "htr = hypoCalc.GetHypoTest()\n",
    "htr.SetPValueIsRightTail(True)  # the \"extreme\" cases are on the right tail\n",
    "htr.SetBackgroundAsAlt(False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "TROOT::Append:0: RuntimeWarning: Replacing existing TH1: opal (H1) (Potential memory leak).\n",
      "TROOT::Append:0: RuntimeWarning: Replacing existing TH1: quartz (H0) (Potential memory leak).\n"
     ]
    },
    {
     "data": {
      "image/png": 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vsQoPV7Pn1Sg0TRNqEeQHKhUO+vu9ilZ3VGden0chYxbnV4jX//vd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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot = RooStats.HypoTestPlot(htr, 100, -15, 15)\n",
    "canvas = ROOT.TCanvas()\n",
    "plot.Draw()\n",
    "canvas.Draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed qvalue:  2.39038791766\n",
      "observed p-value:  0.015\n",
      "k_alpha =  1.18552453524\n",
      "power =  0.694\n"
     ]
    }
   ],
   "source": [
    "print \"observed qvalue: \", test.Evaluate(data, ROOT.RooArgSet(ws.var('density_quartz')))\n",
    "print \"observed p-value: \", htr.NullPValue()\n",
    "alpha = 0.05\n",
    "kalpha = htr.GetNullDistribution().InverseCDF(1 - alpha)\n",
    "beta = htr.GetAltDistribution().CDF(kalpha)\n",
    "print \"k_alpha = \", kalpha\n",
    "print \"power = \", 1 - beta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Exercize\n",
    "Show that the in this case the likelihood ratio is equivalent to the weighted mean of the two measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def eval_test_stat():\n",
    "    d = ROOT.RooDataSet(\"d\", \"d\", ROOT.RooArgSet(ws.var('density1'), ws.var('density2')))\n",
    "    d.add(ROOT.RooArgSet(ws.var('density1'), ws.var('density2')))\n",
    "    return test.Evaluate(d, ROOT.RooArgSet(ws.var('true_density')))\n",
    "\n",
    "fig_opal, ax = plt.subplots(figsize=(12, 7))\n",
    "\n",
    "x = np.linspace(1.3, 3.5, 100)\n",
    "y = np.linspace(1.5, 3.5, 100)\n",
    "\n",
    "qvalues = np.zeros((len(x), len(y)))\n",
    "pdf_opal_values = np.zeros((len(x), len(y)))\n",
    "pdf_quartz_values = np.zeros((len(x), len(y)))\n",
    "for ix, xx in enumerate(x):\n",
    "    for iy, yy in enumerate(y):        \n",
    "        ws.var('density1').setVal(xx)\n",
    "        ws.var('density2').setVal(yy)\n",
    "        qvalues[iy, ix] = eval_test_stat()\n",
    "        pdf_opal_values[iy, ix] = pdf_opal.getVal()\n",
    "        pdf_quartz_values[iy, ix] = pdf_quartz.getVal()\n",
    "        \n",
    "c = plt.pcolormesh(x, y, qvalues, cmap=colormaps.viridis)\n",
    "cs = ax.contour(x, y, qvalues, [kalpha], linestyles='dashed')\n",
    "ax.clabel(cs, fontsize=14, fmt=r\"$k_\\alpha$ = %1.3f\", inline_spacing=30, use_clabeltext=True)\n",
    "ax.contour(x, y, pdf_opal_values, cmap='Blues', alpha=0.6)\n",
    "ax.contour(x, y, pdf_quartz_values, cmap='Oranges', alpha=0.6)\n",
    "ax.plot(ws.var('density_opal').getVal(), ws.var('density_opal').getVal(), 'o', label='opal (H1)')\n",
    "ax.plot(ws.var('density_quartz').getVal(), ws.var('density_quartz').getVal(), 'o', label='quartz (H0)')\n",
    "ax.text(1.5, 1.6, \"reject\", size=20)\n",
    "ax.text(1.8, 3.2, \"accept\", size=20)\n",
    "datalist = [x.getVal() for x in iter_collection(data.get(0))]\n",
    "ax.plot(datalist[0], datalist[1], 'v', label='observed', color='red')\n",
    "\n",
    "ax.set_xlabel('density1')\n",
    "ax.set_ylabel('density2')\n",
    "ax.legend()\n",
    "ax.set_aspect('equal')\n",
    "plt.colorbar(c)\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Since we have just two observables we can easily show the acceptance / rejection region in the space of the observables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DoiH+b9Ft3/4zzD7Oq23b9p8AKPS8dffFl59RVb2X2/6xiLPmnuMle98Di/bJ5lEjRrPu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5/uvYfZ19nFEVXlh6Vksljk7OIiZxYXmS1dnZFmXZU53jL7InG7zFBqD8+1X7djHsuob/GT9Rdo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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd05ced1190>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig_opal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercize\n",
    "Compute the acceptance region using the simple mean as test-statistics: show that it is less powerful. What kind of shape is the acceptance region in this case?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Plot the power as a function of the size of the test for the likelihood ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aqqvK+NgJk+IORUSkXyjR9KM12xp4eu0OLjl9CuUlw+IOR0SkXyjR9KP7l2+irLiIuadO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd054c21810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alphas = np.linspace(0, 1, 100)\n",
    "powers = []\n",
    "\n",
    "for alpha in alphas:\n",
    "    kalpha = htr.GetNullDistribution().InverseCDF(1 - alpha)\n",
    "    beta = htr.GetAltDistribution().CDF(kalpha)\n",
    "    powers.append(1 - beta)\n",
    "    \n",
    "plt.plot(alphas, powers)   \n",
    "plt.xlabel(r'$\\alpha$')\n",
    "plt.ylabel(r'power')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Exercize\n",
    "Compute $\\text{power}(\\alpha)$ for the simple mean and compare with the weighted mean.\n",
    "### Exercize\n",
    "Explain why the previous plot remembers the ROC curve (bkg-rejection vs signal-efficiency)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Exclusion and frequentist intervals\n",
    "\n",
    "By now we have done statistical test to discover something (a signal), defining the null hypothesis to be the background only case. Suppose we have counted $n_{obs}$ events in a Poissonian process with mean $\\lambda$. What are the values $[n_{up}, \\infty]$ that we can exclude? This is something called hypothesis inversion. As usual we define the null hypothesis: $H_0: \\lambda = N$ with $N > n_{obs}$. The likelihood:\n",
    "\n",
    "$$L = \\text{Pois}(n|N)$$\n",
    "\n",
    "than the p-value of our observation $n_{obs}$:\n",
    "\n",
    "$$\\text{p-value} = \\sum_{n\\geq n_{obs}} \\text{Pois}(n|N)$$\n",
    "\n",
    "if p-value $<\\alpha$ we consider $N$ to be inside the exluded region $[n_{up}, \\infty]$. The general approach is to scan for many value of $N$ until we found the one with p-value $=\\alpha$, which is $n_{up}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Example: RooFit asymmetric error bars\n",
    "\n",
    "Let's do a two-side test and compute the excluded intervals $[-\\infty, n_{down}]$ and $[n_{up}, \\infty]$ with $\\alpha=1 - 0.6827$. This means that every single interval should be tested with $\\alpha=(1-0.6827)/2.=0.15865$. We can solve it analytically or with a scan. Suppose $n_{obs} = 4$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NOBS = 4\n",
    "ALPHA = z2p(1)  # 0.158...\n",
    "\n",
    "def compute_pvalue(nobs, ntrue, left):\n",
    "    if left:\n",
    "        return stats.poisson(ntrue).cdf(nobs)\n",
    "    else:\n",
    "        return stats.poisson(ntrue).sf(nobs) + stats.poisson(ntrue).pmf(nobs)\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(13, 4))\n",
    "x = np.linspace(NOBS, NOBS + 3 * NOBS, 20)\n",
    "\n",
    "axs[1].plot(x, compute_pvalue(NOBS, x, left=True), 'r')\n",
    "axs[1].hlines(ALPHA, np.min(x), np.max(x), linestyles='--')\n",
    "\n",
    "x = np.linspace(max(NOBS - NOBS * 3, 0), NOBS, 20)\n",
    "axs[0].plot(x, compute_pvalue(NOBS, x, left=False), 'b')\n",
    "axs[0].hlines(ALPHA, np.min(x), np.max(x), linestyles='--')\n",
    "\n",
    "from scipy.optimize import brenth\n",
    "nup = brenth(lambda x: compute_pvalue(NOBS, x, True) - ALPHA, NOBS, NOBS * 3)\n",
    "ndown = brenth(lambda x: compute_pvalue(NOBS, x, False) - ALPHA, 1E-5, NOBS)\n",
    "\n",
    "axs[1].plot(nup, compute_pvalue(NOBS, nup, True), 'ro')\n",
    "axs[0].plot(ndown, compute_pvalue(NOBS, ndown, False), 'bo')\n",
    "axs[1].set_xlabel('N'); axs[0].set_xlabel('N')\n",
    "axs[1].set_ylabel('$P(n\\leq n_{obs})$')\n",
    "axs[0].set_ylabel('$P(n\\geq n_{obs})$')\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x7fd05d0c5890>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(0, NOBS * 3)\n",
    "axs[2].plot(x, stats.poisson(nup).pmf(x), 'r', linestyle='steps',)\n",
    "axs[2].plot(x, stats.poisson(ndown).pmf(x), 'b', linestyle='steps')\n",
    "axs[2].vlines(NOBS, 0, 0.3, linestyles='--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cc1/nI46rQucamWP/BOBxoAdhJCNmVjx0zBxgOkpGJAHceSds2+ZHRooXDyaGr7/+mrFj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\npCZsRiRJkiQ18T9hPQ78Ma9XOgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd05510e250>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.08566081378 7.16275317226\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\lambda = 4.00^{+3.16}_{-1.91}$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print ndown, nup\n",
    "Latex(\"$\\lambda = %.2f^{+%.2f}_{-%.2f}$\" % (NOBS, nup - NOBS, NOBS - ndown))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question:\n",
    "why we assumed that the central value for $\\lambda$ is $n_{obs}=4$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.0856608137771171, 7.1627531722609437)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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(n, ym, yp, 1)\n",
    "    return ym[0], yp[0]\n",
    "\n",
    "get_confiderence_poisson(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the function used by RooFit to draw error bands"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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REZEpTT1dmZoiFS5BqBmpwi0wYFpKbzSherrRqKcrIiIiY1GjKyIikhGll6VmQi14ECiF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\nEcnI/wcfM7If0aC7PwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd0550187d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 5))\n",
    "trues = np.linspace(1E-5, NOBS * 4, 100)\n",
    "obss = np.arange(0, NOBS * 3)\n",
    "v = np.zeros((len(trues), len(obss)))\n",
    "limits = []\n",
    "for ix, obs in enumerate(obss):\n",
    "    limits.append(get_confiderence_poisson(obs))   \n",
    "    for iy, true in enumerate(trues):\n",
    "        v[iy, ix] = stats.poisson(true).pmf(obs)\n",
    "ax.pcolormesh(obss, trues, v, vmax=np.percentile(v, 99))\n",
    "ax.plot(obss, np.array(limits).T[0], 'k', drawstyle='steps-post')\n",
    "ax.plot(obss, np.array(limits).T[1], 'k', drawstyle='steps-post')\n",
    "ax.set_xlim(0, np.max(obss))\n",
    "ax.set_xlabel('obs')\n",
    "ax.set_ylabel('$\\lambda$'); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question: explain why this is a frequentist procedure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian approach\n",
    "\n",
    "$$P(\\lambda|n_{obs}) = P(n_{obs}|\\lambda)P(\\lambda)$$\n",
    "\n",
    "We assume the prior $P(\\lambda)$ to be flat (and zero for negative values), equivalent to a constant we can ignore. Everybody agree?\n",
    "\n",
    "$$P(\\lambda|n_{obs}) = P(n_{obs}|\\lambda)$$\n",
    "\n",
    "note that $n_{obs}$ is fixed, so this is a real function $f(\\lambda)$. Let find a region [low, high] such that\n",
    "\n",
    "$$\\int_{low}^{high} P(\\lambda|n_{obs}) = 68\\%$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.84030885559 7.16275317226\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\lambda = 4.00_{-1.16}^{+3.16}$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f(true):\n",
    "    return stats.poisson(true).pmf(NOBS)\n",
    "\n",
    "import scipy\n",
    "from scipy.optimize import brenth, brentq\n",
    "def f_low(x):\n",
    "    return scipy.integrate.quad(f, 0, x)[0] - z2p(1)\n",
    "\n",
    "def f_hi(x):\n",
    "    return scipy.integrate.quad(f, x, NOBS * 10)[0] - z2p(1)\n",
    "\n",
    "lo_bayes, hi_bayes = brentq(f_low, 1E-5, NOBS), brentq(f_hi, NOBS, NOBS * 5)\n",
    "print lo_bayes, hi_bayes\n",
    "Latex(\"$\\lambda = %.2f_{-%.2f}^{+%.2f}$\" % (NOBS, NOBS - lo_bayes, hi_bayes - NOBS))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.28988237908 6.40285900785\n"
     ]
    }
   ],
   "source": [
    "def invert(f, y, a, b):\n",
    "    return brentq(lambda x: f(x) - y, a, b)\n",
    "\n",
    "lo_bayes_el = brenth(\n",
    "    lambda x: scipy.integrate.quad(f, x, invert(f, f(x), x * (1 + 1E-5), NOBS * 20))[0] - (1 - z2p(1) * 2),\n",
    "    1E-2, NOBS - 1E-2)\n",
    "hi_bayes_el = invert(f, f(lo_bayes_el), NOBS, NOBS * 5)\n",
    "print lo_bayes_el, hi_bayes_el"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.2898822866 6.40285891537\n"
     ]
    }
   ],
   "source": [
    "def width_interval(x):\n",
    "    return brenth(lambda y: scipy.integrate.quad(f, x, y)[0] - (1 - z2p(1) * 2), x, NOBS * 20) - x\n",
    "\n",
    "sol = scipy.optimize.minimize_scalar(width_interval, (1E-1, 3), bounds=(0, NOBS), method='bounded')\n",
    "lo_bayes_min, hi_bayes_min = sol.x, sol.x + width_interval(sol.x)\n",
    "print lo_bayes_min, hi_bayes_min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, NOBS * 3, 100)\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(14, 4))\n",
    "\n",
    "axs[0].plot(x, f(x))\n",
    "axs[0].fill_between(np.linspace(0, lo_bayes, 50), f(np.linspace(0, lo_bayes, 50)))\n",
    "axs[0].fill_between(np.linspace(hi_bayes, NOBS * 3, 50), f(np.linspace(hi_bayes, NOBS * 3, 50)))\n",
    "axs[0].set_title('equal probability (central)', fontsize=15)\n",
    "axs[0].text(7, 0.16, '$\\lambda = %.2f_{-%.2f}^{+%.2f}$' % (NOBS, NOBS - lo_bayes, hi_bayes - NOBS), size=15)\n",
    "axs[0].text(4, 0.04, '68%', size=15)\n",
    "axs[0].set_xlabel('$\\lambda$')\n",
    "axs[1].plot(x, f(x))\n",
    "axs[1].fill_between(np.linspace(0, lo_bayes_el, 50), f(np.linspace(0, lo_bayes_el, 50)))\n",
    "axs[1].fill_between(np.linspace(hi_bayes_el, NOBS * 3, 50), f(np.linspace(hi_bayes_el, NOBS * 3, 50)))\n",
    "axs[1].set_title('equal likelihood', fontsize=15)\n",
    "axs[1].text(7, 0.16, '$\\lambda = %.2f_{-%.2f}^{+%.2f}$' % (NOBS, NOBS - lo_bayes_el, hi_bayes_el - NOBS), size=15)\n",
    "axs[1].text(3.5, 0.04, '68%', size=15)\n",
    "axs[1].set_xlabel('$\\lambda$')\n",
    "axs[2].plot(x, f(x))\n",
    "axs[2].fill_between(np.linspace(0, lo_bayes_min, 50), f(np.linspace(0, lo_bayes_min, 50)))\n",
    "axs[2].fill_between(np.linspace(hi_bayes_min, NOBS * 3, 50), f(np.linspace(hi_bayes_min, NOBS * 3, 50)))\n",
    "axs[2].set_title('minimum interval', fontsize=15)\n",
    "axs[2].text(7, 0.16, '$\\lambda = %.2f_{-%.2f}^{+%.2f}$' % (NOBS, NOBS - lo_bayes_min, hi_bayes_min - NOBS), size=15)\n",
    "axs[2].text(3.5, 0.04, '68%', size=15)\n",
    "axs[2].set_xlabel('$\\lambda$')\n",
    "for ax in axs: ax.set_yticklabels([])\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CTI6B2J7TV6pQ3dAqecbB3UWGJ2YOwcnsKpzPr5E0FkOUnnQUEhKC2NhYAICr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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd054920e50>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Profile likelihood ratio\n",
    "\n",
    "Suppose you have composite hypothesis as \n",
    "\n",
    "$$H_0: \\theta\\in\\Theta_0 \\quad H_1: \\theta\\in\\Theta_0^C$$\n",
    "\n",
    "where $\\Theta_0 = \\{s=0, \\ldots\\}$, $\\theta\\in\\Theta_0^C = \\{s\\neq 0, \\ldots\\}$, \n",
    "\n",
    "$$\\lambda(x) = \\frac{\\sup_{\\theta\\in\\Theta_0}{L(\\theta|x)}}{\\sup_{\\theta\\in\\Theta}{L(\\theta|x)}}$$\n",
    "\n",
    "with $\\Theta_0 \\subset \\Theta$. For example it can be $H_0: s=0$, $H_1: s\\neq 0$\n",
    "\n",
    "$$\\lambda(x) = \\frac{L(s=0, \\hat{\\hat\\theta}(0)|x)}{L(\\hat{s}, \\hat\\theta|x)}$$\n",
    "\n",
    "where $\\hat{\\hat\\theta}(0)$ is the value of $\\theta$ which optimize the likelihood for $s=0$ (conditioned likelihood), while $\\hat{s}$ and $\\hat{\\theta}$ are the values that optimize the likelihood without any constrains (unconditioned likelihood).\n",
    "\n",
    "<small>It varies between 0 and 1, low values mean that the observed result is less likely to occur under the null hypothesis as compared to the alternative.\n",
    "\n",
    "The profile likelihood ratio is nearly an optimal test-statistics</small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<small>As shown it is important to have an analytically expression $f_q$ of the distribution of the test-statistics $q$ to compute the p-value: $\\text{p-value} = \\int_{q^\\text{obs}}^{\\infty} f_q(q) dq$. Otherwise toys must be run.</small>\n",
    "\n",
    "## Wilks's theorem\n",
    "\n",
    "The quantity $t=-2\\log(\\lambda)$ is aymptotically (large sample) distributed as a $\\chi^2$ distribution with $n=\\text{dim}(\\Theta)-\\text{dim}(\\Theta_0)$ degrees of freedom when $H_0$ is true."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let resurrect the simple Poisson model $\\text{Poisson}(n|s + b)$. This time, instead of using the number of observed events as test-statistics, let use the profile likelihood ratio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed =  229.0\n"
     ]
    }
   ],
   "source": [
    "S, B = 30, 200  # expected values\n",
    "\n",
    "ws_poisson = ROOT.RooWorkspace('ws_poisson')\n",
    "b = ws_poisson.factory(\"b[%f]\" % B)\n",
    "n_exp = ws_poisson.factory(\"sum::n_exp(s[%f, -500, 500], b)\" % S)\n",
    "pdf = ws_poisson.factory(\"Poisson::pdf(n_obs[0, 1000], n_exp)\")\n",
    "aset = ROOT.RooArgSet(ws_poisson.var('n_obs'))\n",
    "data = pdf.generate(aset, 1)  # generate with 1 entry\n",
    "print \"observed = \", data.get(0).first().getVal()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# create a MC linked to the ws\n",
    "sbModel = RooStats.ModelConfig(\"sbmodel\", ws_poisson)   \n",
    "sbModel.SetPdf(pdf)\n",
    "sbModel.SetObservables('n_obs')  # it understands variable-names\n",
    "sbModel.SetParametersOfInterest('s')\n",
    "# save the value of s for (s+b)-hypothesis\n",
    "sbModel.SetSnapshot(ROOT.RooArgSet(ws_poisson.var('s')))\n",
    "getattr(ws_poisson, 'import')(sbModel)  # import is a keyword in python\n",
    "\n",
    "bModel = sbModel.Clone(\"bmodel\")  # create a bkg-only model\n",
    "ws_poisson.var('s').setVal(0)             # with no signal\n",
    "bModel.SetSnapshot(ROOT.RooArgSet(ws_poisson.var('s')))\n",
    "getattr(ws_poisson, 'import')(bModel);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r\n",
      "=== Using the following for bmodel ===\r\n",
      "Observables:             RooArgSet:: = (n_obs)\r\n",
      "Parameters of Interest:  RooArgSet:: = (s)\r\n",
      "PDF:                     RooPoisson::pdf[ x=n_obs mean=n_exp ] = 3.71273e-71\r\n",
      "Snapshot:                \r\n",
      "  1) 0x559a7e502840 RooRealVar:: s = 0  L(-500 - 500)  \"s\"\r\n",
      "\r\n",
      "\r\n",
      "=== Using the following for sbmodel ===\r\n",
      "Observables:             RooArgSet:: = (n_obs)\r\n",
      "Parameters of Interest:  RooArgSet:: = (s)\r\n",
      "PDF:                     RooPoisson::pdf[ x=n_obs mean=n_exp ] = 3.71273e-71\r\n",
      "Snapshot:                \r\n",
      "  1) 0x559a7e502840 RooRealVar:: s = 30  L(-500 - 500)  \"s\"\r\n",
      "\r\n",
      "[#0] PROGRESS:Generation -- Test Statistic on data: 2.00766\r\n",
      "[#1] INFO:InputArguments -- Using a ToyMCSampler. Now configuring for Null.\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 1000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 1500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 2000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 2500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 3000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 3500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 4000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 4500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 5000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 5500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 6000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 6500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 7000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 7500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 8000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 8500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 9000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 9500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 10000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 10500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 11000 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 12500 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 14500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 15000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 15500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 16000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 16500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 17000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 17500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 18000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 18500 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 21000 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 23000 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 24500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 25000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 25500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 26000 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 27000 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 28000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 28500 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 30000 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 61000 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 71000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 71500 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 72500 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 79500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 80000 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 81000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 81500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 82000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 82500 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 87500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 88000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 88500 / 100000\r\n",
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      "[#0] PROGRESS:Generation -- generated toys: 89500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 90000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 90500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 91000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 91500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 92000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 92500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 93000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 93500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 94000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 94500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 95000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 95500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 96000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 96500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 97000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 97500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 98000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 98500 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 99000 / 100000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 99500 / 100000\r\n",
      "[#1] INFO:InputArguments -- Using a ToyMCSampler. Now configuring for Alt.\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 500 / 5000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 1000 / 5000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 1500 / 5000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 2000 / 5000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 2500 / 5000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 3000 / 5000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 3500 / 5000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 4000 / 5000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 4500 / 5000\r\n"
     ]
    }
   ],
   "source": [
    "profll = RooStats.ProfileLikelihoodTestStat(bModel.GetPdf())\n",
    "# this modify a bit our test statistics\n",
    "profll.SetOneSidedDiscovery(1)\n",
    "\n",
    "hypoCalc = RooStats.FrequentistCalculator(data, sbModel, bModel)\n",
    "hypoCalc.SetToys(100000, 5000)  # generate much more toys for bkg-only\n",
    "\n",
    "toy_sampler = hypoCalc.GetTestStatSampler()\n",
    "toy_sampler.SetTestStatistic(profll)\n",
    "toy_sampler.SetNEventsPerToy(1)\n",
    "\n",
    "htr = hypoCalc.GetHypoTest()\n",
    "htr.SetPValueIsRightTail(True)  # the \"extreme\" cases are on the right tail\n",
    "htr.SetBackgroundAsAlt(False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jpOVZ+9hJrlp631rylOzsQsFWCUqp+VREf4RgXklYdjTCnZiIfFVx9jUui8vB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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pvalue =  0.02451  significance =  1.96841767377\n"
     ]
    }
   ],
   "source": [
    "plot = RooStats.HypoTestPlot(htr, 50, 0, 10)\n",
    "canvas = ROOT.TCanvas()\n",
    "plot.Draw()\n",
    "canvas.SetLogy(); canvas.Draw()\n",
    "print \"pvalue = \", htr.NullPValue(), \" significance = \", htr.Significance()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The distribution under the $H_0$ has a peak at 0, which does not follow the $\\chi^2$ distribution. Explain why (see test statistics for one-side-discovery and SetOneSideDiscovery(True) option)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can also use the AsymtoticCalculator, which instead of using the empirical distribution of the likelihood ratio from toys, it uses the asymptotic distribution ($\\chi^2_1$ distribution for the simple likelihood ratio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pvalue = 0.0225442843004  significance = 2.00382725112\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator::Initialize....\r\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator::Initialize - Find  best unconditional NLL on observed data\r\n",
      "AsymptoticCalculator::EvaluateNLL  ........ using Minuit / Migrad with strategy  1 and tolerance 1\r\n",
      " **********\r\n",
      " **840010 **SET NOGRAD\r\n",
      " **********\r\n",
      " PARAMETER DEFINITIONS:\r\n",
      "    NO.   NAME         VALUE      STEP SIZE      LIMITS\r\n",
      "     1 s            0.00000e+00  1.00000e+02   -5.00000e+02  5.00000e+02\r\n",
      " **********\r\n",
      " **840011 **SET ERR         0.5\r\n",
      " **********\r\n",
      " **********\r\n",
      " **840012 **SET PRINT           0\r\n",
      " **********\r\n",
      " **********\r\n",
      " **840013 **SET STR           1\r\n",
      " **********\r\n",
      " **********\r\n",
      " **840014 **MIGRAD         500           1\r\n",
      " **********\r\n",
      " MIGRAD MINIMIZATION HAS CONVERGED.\r\n",
      " MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.\r\n",
      " FCN=3.63616 FROM MIGRAD    STATUS=CONVERGED      17 CALLS          18 TOTAL\r\n",
      "                     EDM=9.65172e-08    STRATEGY= 1      ERROR MATRIX ACCURATE \r\n",
      "  EXT PARAMETER                                   STEP         FIRST   \r\n",
      "  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE \r\n",
      "   1  s            2.89953e+01   1.51301e+01   4.22724e-05  -1.02478e-02\r\n",
      "                               ERR DEF= 0.5\r\n",
      "AsymptoticCalculator::EvaluateNLL -  value = 3.63616\tfit time : Real time 0:00:00, CP time 0.000\r\n",
      "[#0] PROGRESS:Eval -- Best fitted POI value = 28.9953 +/- 15.1301\r\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator: Building Asimov data Set\r\n",
      "[#1] INFO:InputArguments -- AsymptoticCalculator: Asimov data will be generated using fitted nuisance parameter values\r\n",
      "MakeAsimov: Setting poi s to a constant value = 30\r\n",
      "Generated Asimov data for observables RooArgSet:: = (n_obs)\r\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator::Initialize Find  best conditional NLL on ASIMOV data set for given alt POI ( s ) = 30\r\n",
      "AsymptoticCalculator::EvaluateNLL -  value = 3.63834 for poi fixed at = 30\r\n",
      "\r\n",
      "[#1] INFO:Eval -- AsymptoticCalculator::GetHypoTest: - perform  an hypothesis test for  POI ( s ) = 0\r\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator::GetHypoTest -  Find  best conditional NLL on OBSERVED data set ..... \r\n",
      "AsymptoticCalculator::EvaluateNLL -  value = 5.64383 for poi fixed at = 0\r\n",
      "[#0] PROGRESS:Eval -- \t OBSERVED DATA :  qmu   = 4.01532 condNLL = 5.64383 uncond 3.63616\r\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator::GetHypoTest -- Find  best conditional NLL on ASIMOV data set .... \r\n",
      "AsymptoticCalculator::EvaluateNLL -  value = 5.78359 for poi fixed at = 0\r\n",
      "[#0] PROGRESS:Eval -- \t ASIMOV data qmu_A = 4.29049 condNLL = 5.78359 uncond 3.63834\r\n",
      "[#0] PROGRESS:Eval -- poi = 0 qmu = 4.01532 qmu_A = 4.29049 sigma = 0  CLsplusb = 0.0225443 CLb = 0.526917 CLs = 23.3726\r\n"
     ]
    }
   ],
   "source": [
    "hypoCalc = RooStats.AsymptoticCalculator(data, sbModel, bModel)\n",
    "hypoCalc.SetOneSidedDiscovery(True)\n",
    "htr_asym = hypoCalc.GetHypoTest()\n",
    "print \"pvalue =\", htr_asym.NullPValue(), \" significance =\", htr_asym.Significance()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## On/off problem\n",
    "\n",
    "Let's introduce a classical problem in high-energy / astro / ... physics. Suppose you have a source that can contain signal and background events. You have an other source that contains only background events and the background in the two source is correlated.\n",
    "\n",
    "This is the case when you have a control region, with only background, and a signal region with signal plus background. Usually the correlation of the background between the two region comes from a simulation. In astrophysics this can be the case when with telescope one wants to see if there is source in a particular region of the sky, using as control region the average of regions where there are no known source.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In term of random variables:\n",
    "\n",
    "$$ N_{SR} = S + B \\qquad N_{CR} = \\alpha B$$\n",
    "\n",
    "with $S$ and $B$ distributed as Poisson distribution. What we observe are the number of events in the signal region $n_{SR}$ and in the control region $n_{CR}$. $\\alpha$ is assumed to be a known constant. We can write the likelihood as:\n",
    "\n",
    "$$L(s, b|N_{SR}, N_{CR}) = \\text{Pois}(N_{SR}|s + b) \\text{Pois}(N_{CR}|\\alpha b)$$\n",
    "\n",
    "remember that $\\alpha$ is a known constant. The test statistics is based on the profiled likelihood ratio:\n",
    "\n",
    "$$-2\\log\\lambda = -2\\log\\frac{\\sup_{b \\in [0, \\infty], s\\in\\{0\\}}{L(s, b)}}{\\sup_{b\\in [0, \\infty], s\\in [0, \\infty]}{L(s, b)}} = -2\\log\\frac{L(0, \\hat{\\hat{b}}(s=0))}{L(\\hat{s}, \\hat{b})}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r\n",
      "RooWorkspace(ws_onoff) ws_onoff contents\r\n",
      "\r\n",
      "variables\r\n",
      "---------\r\n",
      "(alpha,b,n_cr,n_sr,s)\r\n",
      "\r\n",
      "p.d.f.s\r\n",
      "-------\r\n",
      "RooPoisson::N_CR[ x=n_cr mean=alpha_x_b ] = 0\r\n",
      "RooPoisson::N_SR[ x=n_sr mean=s_plus_b ] = 0\r\n",
      "RooProdPdf::model[ N_SR * N_CR ] = 0\r\n",
      "\r\n",
      "functions\r\n",
      "--------\r\n",
      "RooProduct::alpha_x_b[ alpha * b ] = 500\r\n",
      "RooAddition::s_plus_b[ s + b ] = 50\r\n",
      "\r\n",
      "parameter snapshots\r\n",
      "-------------------\r\n",
      "sbModel__snapshot = (s=15)\r\n",
      "bModel__snapshot = (s=0)\r\n",
      "\r\n",
      "named sets\r\n",
      "----------\r\n",
      "bModel__snapshot:(s)\r\n",
      "sbModel_Observables:(n_sr,n_cr)\r\n",
      "sbModel_POI:(s)\r\n",
      "sbModel__snapshot:(s)\r\n",
      "\r\n",
      "generic objects\r\n",
      "---------------\r\n",
      "RooStats::ModelConfig::sbModel\r\n",
      "\r\n"
     ]
    }
   ],
   "source": [
    "ws_onoff = ROOT.RooWorkspace('ws_onoff')\n",
    "model_sr = ws_onoff.factory(\"Poisson:N_SR(n_sr[0, 5000], sum:s_plus_b(s[15, 0, 100], b[50, 0, 100]))\")\n",
    "model_cr = ws_onoff.factory(\"Poisson:N_CR(n_cr[0, 5000], prod:alpha_x_b(alpha[10, 0, 10], b))\")\n",
    "model = ws_onoff.factory(\"PROD:model(N_SR, N_CR)\")\n",
    "ws_onoff.var(\"alpha\").setConstant(True)\n",
    "\n",
    "sbModel = RooStats.ModelConfig('sbModel', ws_onoff)\n",
    "sbModel.SetObservables('n_sr,n_cr')\n",
    "sbModel.SetParametersOfInterest('s')\n",
    "sbModel.SetPdf('model')\n",
    "sbModel.SetSnapshot(ROOT.RooArgSet(ws_onoff.var('s')))\n",
    "getattr(ws_onoff, 'import')(sbModel)\n",
    "\n",
    "bModel = sbModel.Clone(\"bModel\")\n",
    "ws_onoff.var('s').setVal(0)\n",
    "bModel.SetSnapshot(bModel.GetParametersOfInterest())\n",
    "\n",
    "ws_onoff.Print()\n",
    "ws_onoff.writeToFile('onoff.root')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
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       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.graphVizTree(\"on_off_graph.dot\")\n",
    "!dot -Tsvg on_off_graph.dot > on_off_graph.svg; rm on_off_graph.dot\n",
    "SVG(\"on_off_graph.svg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed  N_SR = 57, N_CR = 447\n",
      "best fit     s        b\n",
      "SR        12.3     44.7\n",
      "CR                447.0\n",
      "[#1] INFO:Minization -- RooMinuit::optimizeConst: activating const optimization\n",
      "[#1] INFO:Minization --  The following expressions will be evaluated in cache-and-track mode: (N_SR,N_CR)\n",
      " **********\n",
      " **   13 **MIGRAD        1000           1\n",
      " **********\n",
      " FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.\n",
      " START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03\n",
      " FCN=10.3401 FROM MIGRAD    STATUS=INITIATE        6 CALLS           7 TOTAL\n",
      "                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX       \n",
      "  EXT PARAMETER               CURRENT GUESS       STEP         FIRST   \n",
      "  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE \n",
      "   1  b            5.00000e+01   1.00000e+01   2.01358e-01   5.91538e+01\n",
      "   2  s            1.50000e+01   7.50000e+00   2.16811e-01   4.39475e+00\n",
      "                               ERR DEF= 0.5\n",
      " MIGRAD MINIMIZATION HAS CONVERGED.\n",
      " MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.\n",
      " COVARIANCE MATRIX CALCULATED SUCCESSFULLY\n",
      " FCN=6.91235 FROM MIGRAD    STATUS=CONVERGED      29 CALLS          30 TOTAL\n",
      "                     EDM=2.9946e-05    STRATEGY= 1      ERROR MATRIX ACCURATE \n",
      "  EXT PARAMETER                                   STEP         FIRST   \n",
      "  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE \n",
      "   1  b            4.47048e+01   2.11369e+00   7.71612e-05   8.63108e-02\n",
      "   2  s            1.23328e+01   7.76549e+00   4.89014e-04   2.16678e-02\n",
      "                               ERR DEF= 0.5\n",
      " EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5\n",
      "  4.470e+00 -4.464e+00 \n",
      " -4.464e+00  6.146e+01 \n",
      " PARAMETER  CORRELATION COEFFICIENTS  \n",
      "       NO.  GLOBAL      1      2\n",
      "        1  0.26933   1.000 -0.269\n",
      "        2  0.26933  -0.269  1.000\n",
      " **********\n",
      " **   18 **HESSE        1000\n",
      " **********\n",
      " COVARIANCE MATRIX CALCULATED SUCCESSFULLY\n",
      " FCN=6.91235 FROM HESSE     STATUS=OK             10 CALLS          40 TOTAL\n",
      "                     EDM=2.99456e-05    STRATEGY= 1      ERROR MATRIX ACCURATE \n",
      "  EXT PARAMETER                                INTERNAL      INTERNAL  \n",
      "  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   \n",
      "   1  b            4.47048e+01   2.11370e+00   1.54322e-05  -1.06103e-01\n",
      "   2  s            1.23328e+01   7.76552e+00   9.78028e-05  -8.53133e-01\n",
      "                               ERR DEF= 0.5\n",
      " EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5\n",
      "  4.470e+00 -4.465e+00 \n",
      " -4.465e+00  6.146e+01 \n",
      " PARAMETER  CORRELATION COEFFICIENTS  \n",
      "       NO.  GLOBAL      1      2\n",
      "        1  0.26934   1.000 -0.269\n",
      "        2  0.26934  -0.269  1.000\n",
      "[#1] INFO:Minization -- RooMinuit::optimizeConst: deactivating const optimization\n"
     ]
    }
   ],
   "source": [
    "sbModel.LoadSnapshot()\n",
    "data = model.generate(bModel.GetObservables(), 1)\n",
    "print \"observed  N_SR = %.f, N_CR = %.f\" % tuple([x.getVal() for x in iter_collection(data.get(0))])\n",
    "model.fitTo(data)\n",
    "print \"best fit     s        b\"\n",
    "print \"SR    {:>8.1f} {:>8.1f}\".format(ws_onoff.var('s').getVal(), ws_onoff.var('b').getVal())\n",
    "print \"CR             {:>8.1f}\".format(ws_onoff.function('alpha_x_b').getVal())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r\n",
      "=== Using the following for bModel ===\r\n",
      "Observables:             RooArgSet:: = (n_sr,n_cr)\r\n",
      "Parameters of Interest:  RooArgSet:: = (s)\r\n",
      "Nuisance Parameters:     RooArgSet:: = (b)\r\n",
      "PDF:                     RooProdPdf::model[ N_SR * N_CR ] = 0\r\n",
      "Snapshot:                \r\n",
      "  1) 0x559a7e69b3d0 RooRealVar:: s = 0  L(0 - 100)  \"s\"\r\n",
      "\r\n",
      "\r\n",
      "=== Using the following for sbModel ===\r\n",
      "Observables:             RooArgSet:: = (n_sr,n_cr)\r\n",
      "Parameters of Interest:  RooArgSet:: = (s)\r\n",
      "Nuisance Parameters:     RooArgSet:: = (b)\r\n",
      "PDF:                     RooProdPdf::model[ N_SR * N_CR ] = 0\r\n",
      "Snapshot:                \r\n",
      "  1) 0x559a7e69b3d0 RooRealVar:: s = 15  L(0 - 100)  \"s\"\r\n",
      "\r\n",
      "[#0] PROGRESS:Generation -- Test Statistic on data: 1.40286\r\n",
      "[#1] INFO:InputArguments -- Profiling conditional MLEs for Null.\r\n",
      "[#1] INFO:InputArguments -- Using a ToyMCSampler. Now configuring for Null.\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 500 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 1000 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 1500 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 2000 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 2500 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 3000 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 3500 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 4000 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 4500 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 5000 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 5500 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 6000 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 6500 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 7000 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 7500 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 8000 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 8500 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 9000 / 10000\r\n",
      "[#0] PROGRESS:Generation -- generated toys: 9500 / 10000\r\n",
      "[#1] INFO:InputArguments -- Profiling conditional MLEs for Alt.\r\n",
      "[#1] INFO:InputArguments -- Using a ToyMCSampler. Now configuring for Alt.\r\n"
     ]
    }
   ],
   "source": [
    "profll = RooStats.ProfileLikelihoodTestStat(bModel.GetPdf())\n",
    "# this modify a bit our test statistics\n",
    "profll.SetOneSidedDiscovery(True)\n",
    "\n",
    "hypoCalc = RooStats.FrequentistCalculator(data, sbModel, bModel)\n",
    "hypoCalc.SetToys(10000, 500)\n",
    "\n",
    "toy_sampler = hypoCalc.GetTestStatSampler()\n",
    "toy_sampler.SetTestStatistic(profll)\n",
    "toy_sampler.SetNEventsPerToy(1)\n",
    "\n",
    "htr = hypoCalc.GetHypoTest()\n",
    "htr.SetPValueIsRightTail(True)  # the \"extreme\" cases are on the right tail\n",
    "htr.SetBackgroundAsAlt(False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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3ZyHSVvXpEgAAB5TaKLRt+3w+785iiaqqz3UUAADH3NwoJIcE+r5v23Z5tGAYhq7rMmWV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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pvalue =  0.0443  significance =  1.70282939574\n"
     ]
    }
   ],
   "source": [
    "plot = RooStats.HypoTestPlot(htr, 50, 0, 20)\n",
    "canvas = ROOT.TCanvas()\n",
    "plot.Draw()\n",
    "canvas.SetLogy()\n",
    "canvas.Draw()\n",
    "print \"pvalue = \", htr.NullPValue(), \" significance = \", htr.Significance()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Koutp6OR3N89zSZuWBWagKQHmt6CKwon6Yz9t2+Z5HroWDt6BOVllgcs5mDsd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\nBAUAYJSgAACMEhQAgFGCAgAw6v8DTrP/lsxPNfYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[#1] INFO:Minization -- RooProfileLL::evaluate(nll_model_modelData_Profile[s]) Creating instance of MINUIT\r\n",
      "[#1] INFO:Minization -- RooProfileLL::evaluate(nll_model_modelData_Profile[s]) determining minimum likelihood for current configurations w.r.t all observable\r\n",
      "[#1] INFO:Minization -- RooProfileLL::evaluate(nll_model_modelData_Profile[s]) minimum found at (s=12.3028)\r\n",
      ".........................................................................................................................................................................................................."
     ]
    }
   ],
   "source": [
    "# create profiled log-likelihood\n",
    "prof = model.createNLL(data).createProfile(ROOT.RooArgSet(ws_onoff.var('s')))\n",
    "# multiply by 2\n",
    "minus2LL = ROOT.RooFormulaVar(\"minus2LL\", \"2 * @0\", ROOT.RooArgList(prof))\n",
    "frame = ws_onoff.var('s').frame(0, 30)\n",
    "minus2LL.plotOn(frame)\n",
    "frame.SetYTitle(\"-2 log#Lambda(s)\")\n",
    "canvas = ROOT.TCanvas()\n",
    "frame.Draw()\n",
    "canvas.Draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pvalue = 0.0469645813294  significance = 1.67502583602\n",
      "expected p-value =  0.0425802635922  significance = 1.72149782132\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator::Initialize....\r\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator::Initialize - Find  best unconditional NLL on observed data\r\n",
      "AsymptoticCalculator::EvaluateNLL  ........ using Minuit / Migrad with strategy  1 and tolerance 1\r\n",
      " **********\r\n",
      " ** 1828 **SET NOGRAD\r\n",
      " **********\r\n",
      " PARAMETER DEFINITIONS:\r\n",
      "    NO.   NAME         VALUE      STEP SIZE      LIMITS\r\n",
      "     1 b            4.47048e+01  2.11370e+00    0.00000e+00  1.00000e+02\r\n",
      "     2 s            1.23328e+01  6.16639e+00    0.00000e+00  1.00000e+02\r\n",
      " **********\r\n",
      " ** 1829 **SET ERR         0.5\r\n",
      " **********\r\n",
      " **********\r\n",
      " ** 1830 **SET PRINT           0\r\n",
      " **********\r\n",
      " **********\r\n",
      " ** 1831 **SET STR           1\r\n",
      " **********\r\n",
      " **********\r\n",
      " ** 1832 **MIGRAD        1000           1\r\n",
      " **********\r\n",
      " MIGRAD MINIMIZATION HAS CONVERGED.\r\n",
      " MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.\r\n",
      " FCN=6.91233 FROM MIGRAD    STATUS=CONVERGED      24 CALLS          25 TOTAL\r\n",
      "                     EDM=2.55118e-07    STRATEGY= 1      ERROR MATRIX ACCURATE \r\n",
      "  EXT PARAMETER                                   STEP         FIRST   \r\n",
      "  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE \r\n",
      "   1  b            4.46991e+01   2.11354e+00   7.69949e-05  -8.63126e-03\r\n",
      "   2  s            1.23028e+01   7.76596e+00   4.31671e-04   1.09713e-03\r\n",
      "                               ERR DEF= 0.5\r\n",
      "AsymptoticCalculator::EvaluateNLL -  value = 6.91233\tfit time : Real time 0:00:00, CP time 0.000\r\n",
      "[#0] PROGRESS:Eval -- Best fitted POI value = 12.3028 +/- 7.76596\r\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator: Building Asimov data Set\r\n",
      "[#1] INFO:InputArguments -- AsymptoticCalculator: Asimov data will be generated using fitted nuisance parameter values\r\n",
      "MakeAsimov: Setting poi s to a constant value = 15\r\n",
      "MakeAsimov: doing a conditional fit for finding best nuisance values \r\n",
      " **********\r\n",
      " **    1 **SET PRINT           0\r\n",
      " **********\r\n",
      " **********\r\n",
      " **    2 **SET NOGRAD\r\n",
      " **********\r\n",
      " PARAMETER DEFINITIONS:\r\n",
      "    NO.   NAME         VALUE      STEP SIZE      LIMITS\r\n",
      "     1 b            4.46991e+01  2.11354e+00    0.00000e+00  1.00000e+02\r\n",
      " **********\r\n",
      " **    3 **SET ERR         0.5\r\n",
      " **********\r\n",
      " **********\r\n",
      " **    4 **SET PRINT           0\r\n",
      " **********\r\n",
      " **********\r\n",
      " **    5 **SET STR           1\r\n",
      " **********\r\n",
      " **********\r\n",
      " **    6 **MIGRAD         500           1\r\n",
      " **********\r\n",
      " MIGRAD MINIMIZATION HAS CONVERGED.\r\n",
      " MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.\r\n",
      " FCN=6.97007 FROM MIGRAD    STATUS=CONVERGED      12 CALLS          13 TOTAL\r\n",
      "                     EDM=1.04732e-07    STRATEGY= 1      ERROR MATRIX ACCURATE \r\n",
      "  EXT PARAMETER                                   STEP         FIRST   \r\n",
      "  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE \r\n",
      "   1  b            4.45114e+01   2.03345e+00   7.75168e-05  -7.90720e-03\r\n",
      "                               ERR DEF= 0.5\r\n",
      "fit time Real time 0:00:00, CP time 0.000\r\n",
      "Generated Asimov data for observables RooArgSet:: = (n_sr,n_cr)\r\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator::Initialize Find  best conditional NLL on ASIMOV data set for given alt POI ( s ) = 15\r\n",
      "AsymptoticCalculator::EvaluateNLL  ........ using Minuit / Migrad with strategy  1 and tolerance 1\r\n",
      " **********\r\n",
      " **    7 **SET PRINT           0\r\n",
      " **********\r\n",
      " **********\r\n",
      " **    8 **SET NOGRAD\r\n",
      " **********\r\n",
      " PARAMETER DEFINITIONS:\r\n",
      "    NO.   NAME         VALUE      STEP SIZE      LIMITS\r\n",
      "     1 b            4.45114e+01  2.03345e+00    0.00000e+00  1.00000e+02\r\n",
      " **********\r\n",
      " **    9 **SET ERR         0.5\r\n",
      " **********\r\n",
      " **********\r\n",
      " **   10 **SET PRINT           0\r\n",
      " **********\r\n",
      " **********\r\n",
      " **   11 **SET STR           1\r\n",
      " **********\r\n",
      " **********\r\n",
      " **   12 **MIGRAD         500           1\r\n",
      " **********\r\n",
      " MIGRAD MINIMIZATION HAS CONVERGED.\r\n",
      " MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.\r\n",
      " FCN=6.93171 FROM MIGRAD    STATUS=CONVERGED      24 CALLS          25 TOTAL\r\n",
      "                     EDM=1.78713e-15    STRATEGY= 1      ERROR MATRIX ACCURATE \r\n",
      "  EXT PARAMETER                                   STEP         FIRST   \r\n",
      "  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE \r\n",
      "   1  b            4.45114e+01   2.03447e+00   7.70842e-05   1.03239e-06\r\n",
      "                               ERR DEF= 0.5\r\n",
      "AsymptoticCalculator::EvaluateNLL -  value = 6.93171 for poi fixed at = 15\tfit time : Real time 0:00:00, CP time 0.000\r\n",
      "[#1] INFO:InputArguments -- AsymptotiCalculator: Minimum of POI is 0 corresponds to null  snapshot   - default configuration is  one-sided discovery formulae  \r\n",
      "\r\n",
      "[#1] INFO:Eval -- AsymptoticCalculator::GetHypoTest: - perform  an hypothesis test for  POI ( s ) = 0\r\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator::GetHypoTest -  Find  best conditional NLL on OBSERVED data set ..... \r\n",
      "AsymptoticCalculator::EvaluateNLL  ........ using Minuit / Migrad with strategy  1 and tolerance 1\r\n",
      " **********\r\n",
      " **   13 **SET PRINT           0\r\n",
      " **********\r\n",
      " **********\r\n",
      " **   14 **SET NOGRAD\r\n",
      " **********\r\n",
      " PARAMETER DEFINITIONS:\r\n",
      "    NO.   NAME         VALUE      STEP SIZE      LIMITS\r\n",
      "     1 b            4.46991e+01  2.11354e+00    0.00000e+00  1.00000e+02\r\n",
      " **********\r\n",
      " **   15 **SET ERR         0.5\r\n",
      " **********\r\n",
      " **********\r\n",
      " **   16 **SET PRINT           0\r\n",
      " **********\r\n",
      " **********\r\n",
      " **   17 **SET STR           1\r\n",
      " **********\r\n",
      " **********\r\n",
      " **   18 **MIGRAD         500           1\r\n",
      " **********\r\n",
      " MIGRAD MINIMIZATION HAS CONVERGED.\r\n",
      " MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.\r\n",
      " FCN=8.31519 FROM MIGRAD    STATUS=CONVERGED      15 CALLS          16 TOTAL\r\n",
      "                     EDM=6.06418e-08    STRATEGY= 1      ERROR MATRIX ACCURATE \r\n",
      "  EXT PARAMETER                                   STEP         FIRST   \r\n",
      "  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE \r\n",
      "   1  b            4.58177e+01   2.04031e+00   8.39422e-05  -6.01192e-03\r\n",
      "                               ERR DEF= 0.5\r\n",
      "AsymptoticCalculator::EvaluateNLL -  value = 8.31519 for poi fixed at = 0\tfit time : Real time 0:00:00, CP time 0.000\r\n",
      "[#0] PROGRESS:Eval -- \t OBSERVED DATA :  qmu   = 2.80571 condNLL = 8.31519 uncond 6.91233\r\n",
      "[#0] PROGRESS:Eval -- AsymptoticCalculator::GetHypoTest -- Find  best conditional NLL on ASIMOV data set .... \r\n",
      "AsymptoticCalculator::EvaluateNLL  ........ using Minuit / Migrad with strategy  1 and tolerance 1\r\n",
      " **********\r\n",
      " **   19 **SET PRINT           0\r\n",
      " **********\r\n",
      " **********\r\n",
      " **   20 **SET NOGRAD\r\n",
      " **********\r\n",
      " PARAMETER DEFINITIONS:\r\n",
      "    NO.   NAME         VALUE      STEP SIZE      LIMITS\r\n",
      "     1 b            4.58177e+01  2.04031e+00    0.00000e+00  1.00000e+02\r\n",
      " **********\r\n",
      " **   21 **SET ERR         0.5\r\n",
      " **********\r\n",
      " **********\r\n",
      " **   22 **SET PRINT           0\r\n",
      " **********\r\n",
      " **********\r\n",
      " **   23 **SET STR           1\r\n",
      " **********\r\n",
      " **********\r\n",
      " **   24 **MIGRAD         500           1\r\n",
      " **********\r\n",
      " MIGRAD MINIMIZATION HAS CONVERGED.\r\n",
      " MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.\r\n",
      " FCN=8.98771 FROM MIGRAD    STATUS=CONVERGED      12 CALLS          13 TOTAL\r\n",
      "                     EDM=9.64579e-10    STRATEGY= 1      ERROR MATRIX ACCURATE \r\n",
      "  EXT PARAMETER                                   STEP         FIRST   \r\n",
      "  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE \r\n",
      "   1  b            4.58750e+01   2.04160e+00   8.70742e-05  -7.57817e-04\r\n",
      "                               ERR DEF= 0.5\r\n",
      "AsymptoticCalculator::EvaluateNLL -  value = 8.98771 for poi fixed at = 0\tfit time : Real time 0:00:00, CP time 0.000\r\n",
      "[#0] PROGRESS:Eval -- \t ASIMOV data qmu_A = 4.11199 condNLL = 8.98771 uncond 6.93171\r\n",
      "[#0] PROGRESS:Eval -- poi = 0 qmu = 2.80571 qmu_A = 4.11199 sigma = 0  CLsplusb = 0.0469646 CLb = 0.637873 CLs = 13.582\r\n"
     ]
    }
   ],
   "source": [
    "hypoCalc = RooStats.AsymptoticCalculator(data, sbModel, bModel)\n",
    "hypoCalc.SetOneSidedDiscovery(True)\n",
    "htr = hypoCalc.GetHypoTest()\n",
    "print \"pvalue =\", htr.NullPValue(), \" significance =\", htr.Significance()\n",
    "\n",
    "pvalue_exp = RooStats.AsymptoticCalculator.GetExpectedPValues(htr.NullPValue(), htr.AlternatePValue(), False, True)\n",
    "significance_exp = ROOT.Math.normal_quantile_c(pvalue_exp, 1)\n",
    "print \"expected p-value = \", pvalue_exp, \" significance =\", significance_exp                "
   ]
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