ta_hypothesis_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "b0bdc0c5-2495-4e0e-9793-ed5facd68637"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#  Hypothesis testing, simple case\n",
    "\n",
    "*Author: Jose A. Hernando*, January 2020\n",
    "\n",
    "*Instituto Galego de Altas Enerxías. Universidade de Santiago de Compostela, Spain.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "nbpresent": {
     "id": "b2443ab4-16fc-4851-bb80-c90a0c6d6dee"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Last Execution  Mon Feb  5 18:04:11 2024\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "print( ' Last Execution ', time.asctime())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "nbpresent": {
     "id": "ad5486f8-4654-482a-b15c-f0d4e5c76937"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# general imports\n",
    "%matplotlib inline\n",
    "%reload_ext autoreload\n",
    "%autoreload 2\n",
    " \n",
    "# numpy and matplotlib\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "\n",
    "import httoys    as httoys\n",
    "import htcore    as htcore\n",
    "import htcatalog as htcata\n",
    "import htplot    as htplot\n",
    "\n",
    "plt.style.context('seaborn-colorblind');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Introduction\n",
    "\n",
    "\n",
    "The simple hypothesis testing involves a null hypothesis $H_0$ (i.e the SM) and al alternative hypothesis $H_1$ (i.e BSM Physics).\n",
    "\n",
    "Given data, $x$, which of both hypothesis agree better with data? \n",
    "\n",
    "Can we exclude $H_1$? At what level? \n",
    "\n",
    "Can claim an *observation* or a *discovery* of New Physics?\n",
    "\n",
    "We will try to solve these questions in this lecture."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Look at the following simple example, $H_0, H_1$ are both gaussians with sigma one, $H_0$ has mean zero and $H_1$ has mean $\\mu$. \n",
    "\n",
    "Given an observation, $x_0$, data agrees more $H_0$ or with $H_1$?\n",
    "\n",
    "*Explore* In the next Python cell, execute few events, See where the data, $x_0$, falls along the axis. Move the gaussians appart, change their widths.\n",
    "\n",
    "(Forget for the moment the printed values, except for the observed data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed data : [-0.73917088]\n",
      "H0 p-value    : 0.77009838\n",
      "H1 p-value    : 0.00000000\n",
      "CLs           : 0.00000002 \n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu0, mu1, mutrue = 0, 5, False\n",
    "httoys.gaussian(mu0, mu1, mutrue = mutrue);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**questions**:\n",
    "- That the $x$ axis in the case allow us to quatify the \"distance\" between hypotheses. To the left is more $H_0$, to the right more $H_1$.\n",
    "    \n",
    "- $H_0$ is on the left. There is a colored area behind the curve of $H_0$ and on the right of the data, $x_0$. What corresponds that area to?\n",
    "    \n",
    "- $H_1$ is on the right. There is a colored area behind the curve of $H_1$ and on the left of the data, $x_0$. Now, what corresponds that area to?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "43e100ca-3a5e-4321-b30a-75ba56b43367"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "3841b030-0070-4827-b90e-1ddb0c7e3e74"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Test statistic\n",
    "\n",
    "We need to **order** data, $x$, along the axis from $H_0$ to $H_1$, to the left is more $H_0$, to the right, more $H_1$.\n",
    "\n",
    "The **test estatistics**, $q(x)$, is a real scalar quantity that quantifies how compatible is our data, $x$, with the null, $H_0$, and the alternative, $H_1$, hypotheses. \n",
    "\n",
    "As convention, we consider that as $q(x)$ values increases, they indicate a better agreement with $H_1$ than with $H_0$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "The *optimal* test-stats is the likelihood ratio.\n",
    "\n",
    "For convenience we use (-2 log-like-ratio):\n",
    "\n",
    "$$\n",
    "q(x) = -2 \\log \\, \\frac{ \\mathcal{L}(x \\, | \\, H_0)}{ \\mathcal{L}(x \\, | \\, H_1)}\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "optimal: better efficicieny for $H_1$ for the same fraction of $H_0$ contamination (see later)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "*Note*: En many cases, we do not know how to compute $q(x)$ and then we use *multivariate methods* as **Neural Networks** (NN) or **Boosted Decision Trees** (BDTs). They provide a test-statistics!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now, we need to compute the pdf of $q$ for both hypothesis, $g(q| H_0)$ and $g(q | H_1)$.\n",
    "\n",
    "In some cases we can do it analytically, but in others is almost impossible.\n",
    "\n",
    "Nevertheless, we can do **simulations** and compute the $q$ values and obtain its distribution for *all possible events* of the $H_0$ type, $\\{ x \\}_0$, and $H_1$, $\\{ x \\}_1$. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "614260a3-f2b7-41ac-bab7-3f27221c62c3"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "### Gaussian as an example\n",
    "\n",
    "**Example:** Consider as $H_0$ a gaussian distribution with mean $\\mu_0$ and $\\sigma_0$;\n",
    "and $H_1$ again a gaussian distribution with $\\mu_1$ and $\\sigma_1$. Obtain the pdfs,  $g(q |H_0)$ and $g(q|H_1)$ for $\\mu_0 = 0, \\, \\sigma_0 = 1, \\, \\mu_1 = 4, \\, \\sigma_1 = 2$. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "nbpresent": {
     "id": "e2c6911d-d7b5-4bc5-b7b5-4aacf1f5e16c"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def two_gaussian(mu0, sigma0, mu1, sigma1, size = 10000):\n",
    "\n",
    "    # the test-statistic function\n",
    "    def q(x, m1=mu1, s1=sigma1, m0=mu0, s0=sigma0):\n",
    "        return (x-m0)*(x-m0)/(s0*s0) - (x-m1)*(x-m1)/(s1*s1)\n",
    "\n",
    "    # hipothesis\n",
    "    h0 = stats.norm(mu0, sigma0)\n",
    "    h1 = stats.norm(mu1, sigma1)\n",
    "\n",
    "    # m-experiments for both hypothesis\n",
    "    x0s = h0.rvs(size = int(size))\n",
    "    x1s = h1.rvs(size = int(size))\n",
    "\n",
    "    # the q-values for the m-experiments of both hypothesis\n",
    "    q0s = q(x0s) \n",
    "    q1s = q(x1s)\n",
    "\n",
    "    return q0s, q1s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def plt_test_stats(q0s, q1s, bins = 100, range = None):\n",
    "    range = (np.min(q0s), np.max(q1s)) if range is None else range\n",
    "    plt.hist(q0s, bins, density = True, range = range, color = 'blue', \n",
    "             alpha = 0.8, label = '$q(x|H_0)$', histtype = 'step');\n",
    "    plt.hist(q1s, bins, density = True, range = range, color = 'red' , \n",
    "             alpha = 0.8, label = '$q(x|H_1)$', histtype = 'step');\n",
    "    plt.xlabel('$q(x)$'); plt.ylabel('$g(q|x)$')\n",
    "    plt.legend(); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q0s, q1s = two_gaussian(0., 1., 3., 1., size = 1e6)\n",
    "plt_test_stats(q0s, q1s);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "285ab068-3282-460b-a021-01bc47b5f6a6"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Question:** Consider that we measure $q(x) = -10$, what can you say about $H_1$? And if we measure $q(x) = 30$?\n",
    "\n",
    "\n",
    "**Question:** Discuss what happens when the distributions overlap and when they do not.\n",
    "\n",
    "**Note:** why using $-2 \\ln$ is convenient! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### A counting experiment\n",
    "\n",
    "Several experiments are called **counting experiments**, they search for a signal, expecting a given number of events $s$, over a background level, $b$. This is a first approximation for a Rare Event Search.\n",
    "\n",
    "The distribution of the data follows a poisson distribution with mean, $b$, in the case of only background and a poission distribution with mean $b+s$ in the presence of signal.\n",
    "\n",
    "**Explore** in the following cell how the distributions changes with $b$ and $s$, and how the result of the experiment changes depending on $data$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed data : 6\n",
      "H0 p-value    : 0.08391794\n",
      "H1 p-value    : 0.13014142\n",
      "CLs           : 0.13465346 \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu0, mu1, mutrue = 3, 10., True\n",
    "httoys.poisson(mu0, mu1, mutrue = mutrue);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Exercise**: Consider now a poisson distribution with $\\mu_0 = b$ for $H_0$ and $H_1$ another poisson distribution with $\\mu_1 = b + s$ for $H_1$, consider $b=3, s=2$. Obtain the pdfs of the test-stadistics, $g(q| H_0), \\; g(q | H_1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def two_poisson(b, s, size = 1000000):\n",
    "\n",
    "    def q(n):\n",
    "        return 2 *n * ( np.log(b+s) - np.log(b)) \n",
    "    \n",
    "    # hipothesis\n",
    "    h0 = stats.poisson(b)\n",
    "    h1 = stats.poisson(b + s) \n",
    "\n",
    "    # m-experiments for both hypothesis\n",
    "    x0s = h0.rvs(size = int(size))\n",
    "    x1s = h1.rvs(size = int(size))\n",
    "\n",
    "    # the q-values for the m-experiments of both hypothesis\n",
    "    q0s = q(x0s) \n",
    "    q1s = q(x1s)\n",
    "\n",
    "    return q0s, q1s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q0s, q1s = two_poisson(3, 8)\n",
    "plt_test_stats(q0s, q1s, bins = 80, range = (0, 100));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "**Exercise** Consider now NEXT experiment as a counting experiment. Compute now the number of possible $\\beta\\beta0\\nu$ events in 100 kg of Xenon if the half-lifetime is $10^{-25}$ y. Compute also the number of expected background events, if the background index is $4 \\times 10^{-4}$ counts/(keV kg y) and with 1% energy resolution at $Q_{\\beta\\beta} = 2.458$ MeV. Obtain the pdfs of the test statistics. Consider that the signal is gaussian distributed and take 3 sigmas as Region of Interest (RoI). \n",
    "\n",
    "**Explore**: Modify now the background index, the resolution, the Xe mass and the half-lifetime."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### N-poisson case\n",
    "\n",
    "Another case very common is a n-bin counting experiments. For example the first $B_s \\to \\mu^+ \\mu^-$ very rare [decay search](https://arxiv.org/pdf/1110.2411) at LHCb. In every bin there is an expectation for the background and for the signal. If the bins are independent, each one is like a single-counting experiment.\n",
    "\n",
    "**Explore**: In the following cell we are simulating one event for a n-bin counting experiment. Play with the background and the signal, and the number of bins.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b, s = [1., 2., 2., 1.], [1, 3, 3, 1]\n",
    "httoys.npoisson_rvs(b, s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Exercise**: Consider a counting experiment with four independent bins. The background for $H_0$ is poisson distributed in each bin with ${\\bf b} = (2, 1.5, 1, 0.5)$ and $H_1$ a signal, is also poisson distributed on top of the background ${\\bf b} + {\\bf s}$ with ${\\bf s} = (1, 2, 2, 1)$. Obtain the pdfs of the test-statistics $g(q|H_0), \\; g(q |H_1)$. \n",
    "\n",
    "Tip: simulate many experiments for each hypothesis and obtain the pdfs of the test-statistics, $g(q|H_0), \\, g(q|H_1)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "*Guide*:\n",
    "    \n",
    "  * Consider a single-counting experiment, with background $b$, expected signal $s$, and observed number of events $n$\n",
    "    \n",
    "$$\n",
    "-2 \\log \\frac{\\mathcal{L}(n | b)}{\\mathcal{L}(n | b + s)} = 2 n \\,( \\, \\log(b + s) - \\log(b) \\,)\n",
    "$$\n",
    "    \n",
    "   * Consider a m-bins-counting experiment, with background ${\\bf b} = (b_1, \\dots, b_m)$, expected signal ${\\bf s} = (s_1, \\dots, s_m)$, and observed number of events in each bin, ${\\bf n} = (n_1, \\dots, n_m)$\n",
    "    \n",
    "$$\n",
    "-2 \\log \\frac{\\mathcal{L}({\\bf n} | {\\bf b})}{\\mathcal{L}({\\bf n} | {\\bf b} + {\\bf s})} = 2 \\sum_i^m n_i \\,( \\, \\log(b_i + s_i) - \\log(b_i) \\,)\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b, s, size = np.array([2., 1.5, 1., 0.5]), np.array([1., 2., 2., 1.]), 10000\n",
    "# generators of n-poisson for b and b+s\n",
    "h0, h1 = htcata.poisson_ncounter(b), htcata.poisson_ncounter(b + s)\n",
    "# test of simple hypothesis - generate events and compute test-statistic\n",
    "ht  = htcore.htsimple(h0, h1, size)\n",
    "# plot test-statistic distribution (plot x0 if provided as argument)\n",
    "htplot.plt_htsimple(ht, nbins = 100);\n",
    "#plt_test_stats(ht.q0s, ht.q1s, range = ht.qrange())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Exercise**: Consider the expected bacground events and signal events in bins of energy in the RoI of the KamLAND-Zen experiment in Fig 2-b) [PRL-117](https://arxiv.org/abs/1605.02889). And compute now the pdfs of $q$ for only background and 10 times the signal.\n",
    "\n",
    "\n",
    "*Guide:* \n",
    "\n",
    "From Fig 2-b) Period II we can extract the following number of background, signal and observed events.\n",
    "\n",
    "*b* = [4.0, 2.0, 1.6, 1.0, 0.8, 0.7, 0.6, 0.5, 0.5, 0.5, 0.6, 0.6, 0.8, 1.1]\n",
    "\n",
    "*s* = [0.2, 0.4, 0.5, 0.6, 0.5, 0.4, 0.2, 0.1, 0.1, 0.1, 0.0, 0.0, 0.0, 0.0]\n",
    "\n",
    "*x* = [4.0, 0.0, 2.0, 4.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 2.0, 2.0, 1.0, 0.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "b = [4.0, 2.0, 1.6, 1.0, 0.8, 0.7, 0.6, 0.5, 0.5, 0.5, 0.6, 0.6, 0.8, 1.1]\n",
    "s = [0.2, 0.4, 0.5, 0.6, 0.5, 0.4, 0.2, 0.1, 0.1, 0.0, 0.0, 0.0, 0.0, 0.0]\n",
    "x = [4.0, 0.0, 2.0, 4.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 2.0, 2.0, 1.0, 0.0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "2ed92466-3a5f-4aec-8cbf-017327c70bd8"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "fd167f21-280d-4c3f-ba5c-01cd6a1ee4f2"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Significance and power\n",
    "\n",
    "\n",
    "We can classify events into $H_0$ or $H_1$ hypothesis using a threshold, $k$, on the test statistics:\n",
    "\n",
    "$$\n",
    "q(x) < k\n",
    "$$\n",
    "\n",
    "An observation data, $x_0$, with a test-statistics, $q_0 = q(x_0)$, is classified as $H_0$ if $q_0  < k $ and as $H_1$ if $q_0 \\ge k$. This is known as the Neyman's approach. \n",
    "\n",
    "What is the value of $k$? It depends of the case: if not the same to separate $b/c$ jets than to search for a new SUSY particle or a Majorana neutrino!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "\n",
    "We define the **significance**, also called *size of the test*, $\\alpha$: \n",
    "\n",
    "$$\n",
    "\\alpha = \\int_{k}^{\\infty} g(q({\\bf x}) \\, | \\, H_0) \\, \\mathrm{d}x\n",
    "$$\n",
    "\n",
    "the significance, $\\alpha$, is also called *error of 1st kind* and **p-value** of $H_0$. Its the probability of claim $H_1$ when in fact it is $H_0$. The *false positives*! The *contamination*!\n",
    "\n",
    "\n",
    "The **p-value** is the probability that we get a event with equal or less *compatibility with a given hypothesis* than for the observed data. To get an event as *extreme or more extreme* than the one observed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "Finally,\n",
    "\n",
    "$$\n",
    "\\beta = \\int_{-\\infty}^{k} g( q({\\bf x}) \\, | \\, H_1) \\, \\mathrm{d}x\n",
    "$$\n",
    "\n",
    "It is the *error of 2nd kind* or the **p-value of $H_1$**. \n",
    "\n",
    "The **power** of the test (or efficiency) is $1-\\beta$, the fraction of events classified as $H_1$ when $H_1$ is true. The true positives! The *efficiency*!\n",
    "\n",
    "The **Neyman-Person lemma** stablishes that the *optimal* test statistic is the **likelihood ratio**. Optimal indicates that we obtain the maximum power (efficiency) for a fix significance (contamination) of the test. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Example** In the case of the two gaussians, the p-values, $\\alpha$, $\\beta$, are the integrals of the colored areas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed data : [0.68410232]\n",
      "H0 p-value    : 0.24695528\n",
      "H1 p-value    : 0.01028193\n",
      "CLs           : 0.01365381 \n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu0, mu, mutrue = 0, 3, False\n",
    "httoys.gaussian(mu0, mu, mutrue = mutrue);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We call the RoC curve the efficiency (or power or $1 - \\beta$), vs rejection (or 1-$\\alpha$) of the background. This is usually the plot that shows the discrimination power of the test-statistics. \n",
    "\n",
    "As mentioned before the cut $k$ to classify an event as $H_0$ or $H_1$ depends on the case. It is not the same to identify the tag of a jet than to identify the Higgs boson.\n",
    "\n",
    "**Exercise**: In the previous case, compute the RoC curve, the $H_1$ efficiency vs $H_0$ rejection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qrange = np.linspace(*ht.qrange(), 100)\n",
    "rej = [1. - ht.p0value(qi) for qi in qrange]\n",
    "eff = [1. - ht.p1value(qi) for qi in qrange]\n",
    "plt.plot(rej, eff); plt.grid(True);\n",
    "plt.xlabel('rejection'); plt.ylabel('efficiency');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "dca918e6-eeda-49a5-bf63-7d7e4593a8b4"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "## Discovery and rejection\n",
    "\n",
    "We claim:\n",
    "\n",
    "* **discovery** or **observation** of $H_1$ if the $H_0$ p-value ($\\alpha$) is lower that $2.87 \\times 10^{-7}$, that corresponds to $Z = 5$. \n",
    "\n",
    "Z-value is the p-value in terms of 'sigmas' of a Gaussian distribution!\n",
    "\n",
    "* **evidence** of $H_1$ if the $H_0$ p-value ($\\alpha$) is lower than $0.0027$, that is $Z=3$.\n",
    "\n",
    "**This is a convention!** And statisticians like to discuss about it!\n",
    "\n",
    "Note that *discovery* means that we *false* a hypothesis, $H_0$ (à la Popper)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Example** Consider the gaussians in the next cell, move the alternative to $\\mu = 5$ and generate some events for $H_1$ true. Have you discover $H_1$? \n",
    "\n",
    "**Question** What is the fraction of the events in whose you could claim discovery?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed data : [6.86111895]\n",
      "H0 p-value    : 0.00000000\n",
      "H1 p-value    : 0.96863631\n",
      "CLs           : 0.96863631 \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu0, mu, mutrue = 0, 5., True\n",
    "httoys.gaussian(mu0, mu, mutrue = mutrue);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We set:\n",
    "\n",
    "* an **exclusion** limit on $H_1$ at a $\\beta$ (i.e. 90) confidence level, CL, if $H_1$ p-value, is $\\le 1-\\beta$.\n",
    "\n",
    "That is the probability to get an event with lower compatibility with $H_1$ than the observed event is smaller than 10% for 90 % CL."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Example**: In the case of the gaussians, move $\\mu_1 = 2.5$ and generate events if $H_1$ is false.\n",
    "    Can you exclude $H_1$ at 90% CL? In what fraction of the events you will exclude $H_1$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed data : [1.20318058]\n",
      "H0 p-value    : 0.11445322\n",
      "H1 p-value    : 0.09734666\n",
      "CLs           : 0.10992831 \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu0, mu, mutrue = 0, 2.5, False\n",
    "httoys.gaussian(mu0, mu, mutrue = mutrue);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "We define:\n",
    "\n",
    "* the **reach** or **sensitivity** of an experiment as the expected exclusion of $H_1$, $\\beta$, for the median of the $g(q | H_0)$ pdf.\n",
    "\n",
    "That is, in the case there is no signal, and we observe data in the median of the $H_0$ distribution, the reach is the limit we impose in $H_1$, its p-value.\n",
    "\n",
    "* the **discovery potential** of an experiment is the $H_0$ p-value for the median of the $g(q | H_1)$ pdf.\n",
    "\n",
    "That is, in the case that $H_1$ is true, and we observe data in the median of the $H_1$ distribution. The potential is the p-value of $H_0$ (the falseability!)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Example** Consider the gaussian again, with $\\mu = 5, \\sigma = 2.5$, in the next cells we compute the sensitivity and the discovery potencial for this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed data : [2.21525579]\n",
      "H0 p-value    : 0.01337126\n",
      "H1 p-value    : 0.13266154\n",
      "CLs           : 0.13445943 \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu0, mu, sigma1, mutrue = 0, 5., 2.5, False\n",
    "httoys.gaussian(mu0, mu, mutrue = mutrue, sigma1 = sigma1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed data : 5.0\n",
      "H0 p-value    : 0.00000029\n",
      "H1 p-value    : 0.50000000\n",
      "CLs           : 0.50000014 \n"
     ]
    },
    {
     "data": {
      "image/png": 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80R/9Ee985zv54z/+Y6LRKJ/97GfL8FNdyhK9KU2iwjNiFwpuciZnmSWpKmemzyAIfq+/4q/X3+p80hqZHambRL+YUCjEG9/4Ro4dO8bExAT5fP6SczweD11dXVx99dWr3hHqT//0T/n0pz9NJBLhhRdeYN++fctftEqW6E1pEkPOWjT+ypcIAKdDdvqIs2RxU2UmAtW6WDpGJB6hxddSkRmxC/WGehGEkdkRru25tuKvtx6Wa3l/5jOf4VOf+hSJxGtLZweDQR544AE+/vGPr+m13/a2t6Gq/NVf/RXf//738Xq9xONxPvrRj+L3+3n729/O3XffvabXKLIavSlNosIzYhcqfnJINmbnXymGY8PMpmcJrtMboc/ro7ulu6E6ZE+ePEkul0NEaGlx3lBzuRynTp1a870PHTrE8PAwzc3NtLU5cyAef/xx7rzzTj7/+c+XtYVvid4sT9VZtTJQmbWyF3WhQ7ZxkspKFTtiK7Fi5VKKHbKNYHh4mIcffhhw9rF+9NFH2brV2XHr85//PCMjq/97GB4e5u677+ab3/wmoVCIp556CoBwOHzhNcq5SbglerO8zDTkM+ub6JtC4O94bbVMc4nh2DCJTIKOQOU7Yov6W/uZSc2QyNT/LmAPPPAAmUyG97///Rw5coTbb7+dl19+mdtvv51MJsMDDzyw/E0WMTc3xx133MFnPvMZrr32Wj71qU/xJ3/yJwBs2bKFcNhZpnuxvoHVKinRi8htInJMRE6IyCcWeX6viBwUkRdF5ICI/Fyp15oakCxMey/31oHLCfTbyJvLCMfCZPKZio+hn29+h2y9m5ub45FHHuGxxx4jFAoBTkftV7/6VR555BHi8dVN6GtpaeH555/nne98J+DU6oszbu+44w7+5V/+hd/6rd/ive99b3l+EErojBURL/A54J04G4XvF5F9qvryvNP+HdhX2D7wRuBrwDUlXmuqXXLUeWxe500nAn0Qe9XZ1cpj4wbmS2aTDEWHaGlan47Yor5W51PdyOwIOzp3rNvruuEf//Efl3zunnvu4Z577in7a4ZCIb74xS+W/b6ltOjfBJxQ1VOqmgYeAy6aIaCqs/raLIoQoKVea2pAMgL+Dc6om/UU6AXNOxuGm4uMxceIZ+IVXd9mMa3+Vtr8bQ3Roq8npST6zcD8LeDDhWMXEZH3i8grwLeBe1ZybeH6ewtlnwNjY2OlxG7WSzKy/mUbeK1PoPiJwlwwGh9lJjlDyBda99dupA7ZelFKol/sc+Elc6BV9QlVvQa4HSj2UpR0beH6h1R1j6ru6emxfSmrRj7ntKjdSPTNXSDe1/oIzAWReISZ1AydgfWfuNTf2s/Y3BjZfHbdX9usTimJPgxsnff9FmDJKYuq+gPgShHpXum1pgqlJ5zyyXqOuCkSDwR6rEW/iNHZUZLZZEXXoF9Kf2s/ec0zFq/dT961vF7PamIvJdHvB3aJyA4R8QN3AReN5BeR10mhR0hEbgH8wEQp15oqV2xNN7vQogfnDcYS/UVUlXPRc3jFi8/rW/fXL3bI1uomJIFAgImJiZpM9qrKxMQEgUBgRdctO5RBVbMicj/wFOAFvqCqR0TkvsLzDwK/AvyaiGSABPCBQufsoteuKELjruSo07Jurtw2dZcV6IWpl2wphHnimThj8TGCPnf+PjYGN+IVb80m+uJY9VrtCwwEAmzZsmVF15Q0Zk1VnwSeXHDswXlf/wXwF6Vea2pIMuIkebeGN87vkG3d7k4MVSYSjzCbniXgXVmrrlw84qEn1FOzid7n87FjR30PDV3IZsaay3NrxE3RhURfm0mlEiLxCFOJqXVd+mCh3lBvzSb6RmSJ3iwtl4b0lHv1eYCmVqdkY3X6CyLxCLOZWTYE3U30M6kZktmkazGY0lmiN0tLFWqYboy4KRKxDtkFhmeHyeTWd+mDhXpDzpt/LY+8aSSW6M3S3FrjZqHm3sIOV7U3SqLcVJWz02cJNAXwiHv/fYuJ3so3tcESvVlachQ8Pmf5AzcF+5wyUmba3TiqwExqhqnE1LqtQb+UjuYO/F6/JfoaYYneLC0ZcSYsudhyBF4rHSWsfDM6O0osHVv3NW4WEhHrkK0hlujN0lIRdztii4qrZqYsqUTiESYTk2wMrNOWjpdhib52WKI3i8vOQWbW/fo8FPaq7bQOWZxEv96bjSylN9RLPBMnnl7duuxm/ViiN4u70BHr4oib+QK9VroBhmJD5DRHoMmdyVLzFTtkR+P271LtLNGbxVXLiJuiQB+kJ51NSBpULp/j7MxZWnzru9nIUmzkTe2wRG8Wlxx1Jio1tbodiePCJiQTbkfimsnEJLFUrCpa8wAhX4gWX4sl+hpgid4srtgRWwUtR+C1TxYN3CEbiUeIpqKuD60sspE3tcMSvbmUqvtr3Czk73KGeTbwmjeReISp5BRdLS6tJLqIYqKvxSV/G4klenOpTBRyqepK9B4vNHc3fKJPZVO0+quknIaT6NO5NDOpGbdDMZdhid5cqtpG3BQFehs60YejYRSleb03ab8M65CtDZbozaWKdfDmKtu7N9DrrKaZS7sdybrL5DKEo2FamqpjxE2RJfraUFKiF5HbROSYiJwQkU8s8vzdInKw8Oc5Eblp3nNnROSQiLwoIgfKGbypkGQEfO3Vt6NTcZZuqvFWTByfG3c2G/FVx4ibokBTgPbmdkv0VW7ZbYNExAt8Dngnzmbf+0Vkn6q+PO+008AvqOqUiLwbeAh487znb1XV8TLGbSopOVpd9fmiYkzJCLRsdjeWdTYaHyWairq6NPFSbORN9SulRf8m4ISqnlLVNPAYsHf+Car6nKpOFb79IbCyDQ1N9dA8pMarM9H7NziraTZgnT4SjzCTnKmKNW4W6g31Mj43Tl7zbodillBKot8MDM77Plw4tpSPAP8273sFvisiPxGRe5e6SETuFZEDInKgVjftrQupwuzTakz04nFW02zAsfSjs6Mkc0lam6tnxE1Rb6iXbD7LZGLS7VDMEkpJ9Iv1/Cw6aFZEbsVJ9H8w7/BbVfUW4N3Ax0TkbYtdq6oPqeoeVd3T01NlnYCNJFWlI26Kmhtz5E04FsaDB5/H53Yol7AO2epXSqIPA1vnfb8FGFp4kojcCDwM7FXVC/PUVXWo8BgBnsApBZlqlYw4s2Gbu92OZHGBXsjEnNU1G0Qym2QkNkLQF6yqETdFPS09CGKJvoqVkuj3A7tEZIeI+IG7gH3zTxCRbcDjwIdU9fi84yERaSt+DbwLOFyu4E0FJCPg3+jUwqtRoPFG3kTiEeKZeNWNuCnyeX10Bjst0VexZUfdqGpWRO4HngK8wBdU9YiI3Fd4/kHg00AX8HeFFkdWVfcAfcAThWNNwJdV9TsV+UlMeVTriJui+SNvQle4G8s6KXbEtvqqrz5fZCNvqtuyiR5AVZ8Enlxw7MF5X/8G8BuLXHcKuGnhcVOl8hlnKeAN17sdydKa2sAbaKg6fSQeIZaOMdA24HYoS+oN9XJ84jjZfJYmT0lpxawjmxlrXpMadxY0q4btA5ci0nBLIYzOjlbdGjcL9YZ6yWue8TmbLlONLNGb11TrGjcLBXqd0UENsGKiqjIYHcTr8eLzVmm/CTbyptpZojevSUZAvNBcfZNyLtLcC9kEZGfdjqTi4pk443PjVbMG/VK6gl14xWuJvkpZojevSUacCUlS5b8W8ztk69zo7CjxdLyqVqxcjNfjpaulyxJ9lary/9FmXVX7iJuiQGFCXQMk+kg8wnRymrbmNrdDWZaNvKleluiNI5d0Nhyp5o7YoqYQ+FobYimE4hj6DYENboeyrN5QL9PJaVLZlNuhmAUs0RvHhY7YGkj00DBLIYzGR0nlUoT8IbdDWVZfyOnEH5trnMlstcISvXHUyoibouIQyzoeeaOqDM4M0uRpqomx6TbypnpZojeOZAS8zc6GI7Ug0OtM8MpMux1JxUwnp5lKTtHSVH1r0C9mQ2ADPo/PEn0VskRvHKmIkzyrcNGsRTXAyJtIPFITI26KRMQ6ZKuUJXrjlD+So7XREVvUXP8jb4ojbjoCHW6HUjJL9NXJEr1xJh5lE7XTEQtOmcm/oe4TfSKbqImhlUW9oV5m07PE03G3QzHzWKI3tTfipqi4FEKdGomPkMqmCPmqf8RNUbFD1kbeVBdL9Ka2E31yHPI5tyMpu1w+R3gmTHNTM16P1+1wSmYjb6qTJXrjtIp9rc5EpFrS3Auac5ZWrjOTiUmiqWjVr3GzUKu/lWBT0BJ9lbFEb5wWfS11xBbV8cib0fgos+lZ/F6/26GsiI28qU4lJXoRuU1EjonICRH5xCLP3y0iBwt/nhORm0q91rhMtbCYWQ0m+uZuZzhoHdbpiyNuOoOdboeyYsVEr3U8ma3WLJvoRcQLfA54N7Ab+KCI7F5w2mngF1T1RuAB4KEVXGvclJ5yJh7VyozY+TxNzv62ddiij8QjJLNJ2vy1M+KmqDfUSzKbJJaOuR2KKSilRf8m4ISqnlLVNPAYsHf+Car6nKpOFb79IbCl1GuNy5KjzmMtJnqo292mhmeHSefSBH21VaMH65CtRqUk+s3A4Lzvw4VjS/kI8G8rvVZE7hWRAyJyYGzMhmatm+RoYXu+HrcjWZ1Ar9MZm8+4HUnZpHNphqJDBJuCeKp9b4BF9ISc3yVL9NWjlN+ixebEL1p8E5FbcRL9H6z0WlV9SFX3qOqenp4aTTq1KDnqlD881btN3WU19zr9DKn62at0LD5GLB0j4Au4HcqqtPhaaPO3WaKvIqUk+jCwdd73W4ChhSeJyI3Aw8BeVZ1YybXGRcnR2i3bQF2OvBmNjxJLxQh6a69sU2Qjb6pLKYl+P7BLRHaIiB+4C9g3/wQR2QY8DnxIVY+v5Frjolza6Yyt5UTv3+jsc1tPiX52lJnUTE2OuCnqDfUyFh8jr3m3QzHAsotcq2pWRO4HngK8wBdU9YiI3Fd4/kHg00AX8HfirH6YLZRhFr22Qj+LWanUmFP2qOVE7/FCoLu+En1hs5HW5la3Q1m13lAvmXyG6eQ0G4NVvtl8AyhpNwNVfRJ4csGxB+d9/RvAb5R6rakSF0bc1OAY+vmae2HunNtRlIWqMhgdRFVrZnnixRRH3ozOjlqirwK116Vvyic5Cl4/+Gu3RAAURt7MQK729yqNpWNMzE3Q4mtBamVvgEX0hHoQxOr0VcISfSMrrkFfwwkFqKsO2dFZZ+mDWm7NA/i9fjYGNzIyO+J2KAZL9I3rwtIHNVyfLyom+jpYCmFkdoTp5DSt/tqtzxf1tfZZoq8SlugbVXYWsnP1keh9G5wSVGLU7UjWbDQ+SiKTqKldpZbS39rPVHKKVLb2S2q1zhJ9o6qXjlgozOzth2Tttx5HZkdI5pJ10aLvb+0HnDcv4y5L9I2q1te4WSjQ7/xMNbxiYjafJRwN4/P4aPKUNCCuqvWFnN8tK9+4zxJ9o0qOgq8damxjiyUF+51RN+mp5c+tUmPxMaKpKC1NLW6HUhbtze0Em4KMzlqL3m2W6BtVvXTEFgWcMkEtl2+KSx80N9X2iJsiEaG/td9a9FXAEn0jyucgOVYf9fmiQA+IBxK1m1RGZ0eZTk3TGajxeQ3z9LX2EYlHbCkEl1mib0SpMWev1eAmtyMpH4/P2XGqxlv0qWyKtuba22xkKf2t/WTyGSYT9bevby2xRN+IEsPOY7HcUS+C/TXdog9Hw+TyOQJNtbk88WKKI2+sfOMuS/SNKDnijDtv7nI7kvIK9EMm6swPqDGxVIxIPFLzSx8s1N3SjUc81iHrMkv0jSgx7CTFOkoogNOih5os3wzPDjObnq3ZzUaW0uRpoqelx1r0LrNE32hUnURYT/X5ouIoohos3wzHhplMTNLhr/0ZsQvZyBv3WaJvNKkJZ8OReqvPAzSFnLkBNdqiT2aTdbH0wUJ9rX3E0jHmMrVXUqsXJSV6EblNRI6JyAkR+cQiz18jIs+LSEpEfn/Bc2dE5JCIvCgiB8oVuFmlYhKsxxY91GyHbDgaJpVNEfKH3A6l7KxD1n3LJnoR8QKfA94N7AY+KCK7F5w2CfwO8JdL3OZWVX29qu5ZS7CmDBLDztZ7zXW6AXug39koPJ91O5KSxcxnH3kAABzySURBVNNxhmPDBHwBPFJ/H7JtKQT3lfJb9SbghKqeUtU08Biwd/4JqhpR1f1ApgIxmnJKDDsTpTxetyOpjGA/aL6m1qYfmR0hlq7tzcAvJ+QP0dHcwXBs2O1QGlYpiX4zMDjv+3DhWKkU+K6I/ERE7l1JcKbM6rkjtqgGl0IYig0xk5yp6T1ilzPQNsBQbMjtMBpWKYl+sTF4K1ki8K2qegtO6edjIvK2RV9E5F4ROSAiB8bGxlZwe1Oy4hjzek70/k7wNr82KawGDM8OM5eZY0Ngg9uhVMxA2wATiQmS2aTboTSkUhJ9GNg67/stQMlvzao6VHiMAE/glIIWO+8hVd2jqnt6euq0fuy2ep0RO5+I80aWqJ3W41BsiEQ2URdr0C9loG0AwMo3Likl0e8HdonIDhHxA3cB+0q5uYiERKSt+DXwLuDwaoM1a5QcLmzSUUerVi4mOOCMvMnn3I5kWYlMgnA0TLO3uS7WoF/KpjbnU6SVb9yx7G+WqmZF5H7gKcALfEFVj4jIfYXnHxSRfuAA0A7kReT3cEbodANPFKZ0NwFfVtXvVOZHMctKjDgLf3n9bkdSWcHNzqJtyVFoGXA7mssamR0hlooRrJd9AZbQ4muhM9DJ+dh5t0NpSCU1IVT1SeDJBccenPf1CE5JZ6EocNNaAjRllBiG1u1uR1F5LYWxAonzVZ/oh2eHmU5O1+X4+YUG2gYs0buk/gbtmsVlZp3O2Hquzxf5OqCppSbq9EOxIWbTs3QG62cN+qUMtA0wnZy2GbIusETfKBKFllTLSkbG1igRp3wzV/2tx/PR83XfEVtU7JC1Ov36s0TfKObCzg5MweouZZRNy4CzwUou7XYkS0plUwxGBwk0Beq6I7bIOmTdY4m+UcyFndE2Hp/bkayP4ObCBLHqHc43FBsilorR4quPzcCXE2gK0BXsskTvAkv0jUDzTr26ZbH+8jpVLFFVcflmMDrIZGKSNn/9bB24nM3tmy3Ru8ASfSNIjUMu1Rj1+aKmEPg7qrpDNhwNE8/EG6IjtmigbYBoKkosFXM7lIZiib4RzIWdx2ADteihqjtkVZUz02dI5VIN0RFbdGGG7Gz1ltTqkSX6RjAXBm+g/vaIXU5wANJTVbmH7GRikkg8QsgXqsuliZfS39qPIJyPVucbcL1qnN+wRpY479Tn622P2OVcmDhVfeWbcDRMNBmlpakxOmKL/F4/fa19DEYHlz/ZlI0l+nqXSzlrszdSfb4oOOC8uVVh+WYwOsh0arquV6xcytb2rYSjYfKadzuUhmGJvt4lhpxhho1WnwdnueLm7tf6KKpIOBomkU3U5R6xy9nWsY10Ls3o7KjboTQMS/T1rpjkGrFFD9CyDebOOUNMq0Q6l+bs9FlUlUBTwO1w1t22jm0AnJs553IkjcMSfb2bO+90wjZYLfiC0BWF8lX1tB7PR89fWMhMGq3fBOgIdNDR3GGJfh1Zoq9nqpAIN25rHpxEDxCvnqQSjoaZTEzS6mucYZULbevYxrmZc6iuZLM6s1qW6OtZZsZZtbIR6/NF/g7nT/ys25FcMBgdJJaOsTG40e1QXLO1YyuxdIyZ1IzboTQES/T1rJjcQtvcjcNtoSsKdXr3W4/FiVLpbJq25sZZ+mAhq9Ovr5ISvYjcJiLHROSEiHxikeevEZHnRSQlIr+/kmtNBcXPOhOlAr1uR+Kulm3OJ5v0pNuRMJWcYnR2lBZ/S0NNlFqoN9RLs7fZEv06WfY3TUS8wOeAd+NsD/hBEdm94LRJ4HeAv1zFtaZS4uec1nwDJxSgqur0Z6bPMJWcIuSr/x2lLscjHrZ2bLVEv05KyQBvAk6o6ilVTQOPAXvnn6CqEVXdD2RWeq2pkMyss5hZMck1suZuZ9RRFdTpz06fZTIxSVewwZajWMTW9q2MxcdIZBJuh1L3Skn0m4H585XDhWOlKPlaEblXRA6IyIGxsbESb2+WNFdoKVmid2bHFsfTu0hVOTl1kkQ2wYZg482IXWhbxzYUJRytvglt9aaURL/YQN9Se7VKvlZVH1LVPaq6p6enp8TbmyXFzzqbjAQ2uR1JdQhtg9QkZNxbHnc6OU04GqalqaUhdpRazub2zXjEY+WbdVBKog8DW+d9vwUodZWotVxr1mL2tJPcPF63I6kOVVCnPztzlqmE1eeL/F4/A20DnJk+43Yoda+URL8f2CUiO0TED9wF7Cvx/mu51qxWZtZZyCy0w+1Iqkeg3/mE42Kd/sz0GSYSE3S3dLsWQ7XZsWEH52PnSWVTbodS15ZN9KqaBe4HngKOAl9T1SMicp+I3AcgIv0iEgb+V+CPRSQsIu1LXVupH8YUxE87j6073Y2jmni8ziec4t/NOlNVXp181erzC+zs3Ele85ydcb+jvJ6VVChU1SeBJxcce3De1yM4ZZmSrjUVNnvKGT8f7Hc7kurSeiUMfxcyUfC1r+tLj8+NE54JE/KFrD4/z9aOrTR5mjg1dYqruq5yO5y61eADrOuQqpPoW3fY+PmFip9wZk+t+0ufmjrF+Nx4Q69vs5gmTxPbOrZxamr9/00aiWWCepOegvSM1ecXE+hzNg2PnVz3lz45dZLp1DR9rX3r/trVbmfnTiLxCLPpWbdDqVuW6OtN7ITz2Halu3FUIxGnVT97al3XvcnlcxyfOE4qm2ro9W2WcmWn87t6cnL934AbhSX6ehN7FZo3Nt5G4KVquxKycUiOrNtLhqNhIvEI7c3tDb2+zVL6W/tp9bfy6uSrbodSt+y3rp7kM86okrZdbkdSvVpf5zzG1i+pHJ84TiQeYUOzjbZZjIjwuo2v4+TkSdtHtkIs0deT+FnIZy3RX46v1dmIJXp83V7y2MQxoqkova0NvoroZezauItENsH5aPVt5F4PLNHXk9ir4Gmy9W2W03YVJM47JZwKm0pMcWrqFH6PvyH3hy3Vzs6dCGLlmwqxRF8vVCF6zOls9Pjcjqa6te1y/r6KHdcV9Orkq4zFx6wTdhlBX5BtHds4Nn7M7VDqkiX6epEchfQ0tF/jdiTVL7gJfG3OG2OFHRs/xkRigv5Wm7y2nGu6r2E0PspUYsrtUOqOJfp6ET3qDB9sv9rtSKpf8e9p9oTTgV0hiUyCo+NHyeVztDev70zcWnRtz7UAHB0/6nIk9ccSfb2IvuKsud5kKyOWpGM35NIVLd8cmzjG6OwoHYEORBZbsdvMtyGwgf7Wfl4Zf8XtUOqOJfp6kJqExCh0XOt2JLUjtN3ZdWrm5Yq9xNGxo0TiEfpCNhu2VNd2X8vgzKDNki0zS/T1YOaw89huib5k4nH6M2LHnSGpZZbKpjgydoRULkVnsLPs969Xu3t2oyhHIrbIbTlZoq91qjB9yFmC19/hdjS1pWM35FIVKd8cmzjGSGyEjuYOmw27Aj2hHvpCfRyOHHY7lLpiv4G1LhmB5BhsuMHtSGpP606nT2P6YNlv/dLIS4zGR61sswo39N3AYHTQRt+UkSX6WjdzyClDdFzndiS1Rzyw4XpnmGU2UbbbxlIxDkcOk8ln6GqxNYdW6vre6wGsVV9GJSV6EblNRI6JyAkR+cQiz4uIfLbw/EERuWXec2dE5JCIvCgiB8oZfMPTPEwddDbUaGpxO5ratOEm0BxEy9cpeyhyiOHZYTqDnTbaZhU2BDawrWMbL42+hK7jKqP1bNlELyJe4HPAu4HdwAdFZPeC094N7Cr8uRf4+wXP36qqr1fVPWsP2VwQO+HslrTxZrcjqV3BTRDogakXy3I7VeWF4ReIxCMMtA6U5Z6N6JZNtzA+N865Gfc2c68npbTo3wScUNVTqpoGHgP2LjhnL/DP6vghsEFENpU5VrPQ5E+dGnObTZJaNRHovBnig84Q1TUKR8McnziOz+Oj1W+7Sa3W7p7dNHub+enwT90OpS6Ukug3A4Pzvg8XjpV6jgLfFZGfiMi9S72IiNwrIgdE5MDY2FgJYTW4zKwzNLDz9c7G12b1Ol/vLAY3ufbK4v6h/ZyPnaenpcfKNmvg9/q5oe8GjowdIZlNuh1OzSsl0S/227qwcHa5c96qqrfglHc+JiJvW+xFVPUhVd2jqnt6enpKCKvBTR5wavQbb1n+XHN5TS1OZ/b0QWe27CrNZeZ4ceRFYqkYA+1WtlmrN2x6A9l8lheGX3A7lJpXSqIPA1vnfb8FGCr1HFUtPkaAJ3BKQWYt8lmY2O+swmg7SZXHxj3OmPo11Op/OvxTzs2cY0NgA02epjIG15g2tW3iio4r+NH5H9mGJGtUSqLfD+wSkR0i4gfuAvYtOGcf8GuF0TdvAWZUdVhEQiLSBiAiIeBdgI2ZWqvpQ85a6j0/43Yk9aNli/Nn/Hnnk9IKZfNZnht8jpHZEbZ2bF3+AlOSt2x5C9PJaVv/Zo2WTfSqmgXuB54CjgJfU9UjInKfiNxXOO1J4BRwAvg88NHC8T7gP0TkJeDHwLdV9Ttl/hkai6qTjIJ9ENrhdjT1QwR63grpKZhZ+eqJB0cPcnLyJCFfyDphy+jq7qvpDHTy3OBzNtRyDUr6fKmqT+Ik8/nHHpz3tQIfW+S6U8BNa4zRzBc96syG3fYrTnIy5dN+tVMKG/sPZ3mEEv9+85rnP879B+FomCs7r6xwkI3FIx7euu2tfOv4tzg1dYorN9rf72rYzNhaogqj34fmbpsJWwnigd6fh8Sws+xziQ6OHuSV8Vdo8jbZAmYVcHP/zXQ0d/D9M9+3Vv0qWaKvJTNHnNZ83y84ScmU34YbnQlUo98rqVafzWd59vSznJs5x7b2bTaksgK8Hi8/f8XPMxgd5MRk5bd/rEeWLWpFPgMjz0Cw31rzlSQe6LvVWSiuhBE4+8/v55XxV/B7/GwMblyHABvTzf030xXs4rsnv0sun3M7nJpjib5WjD/v7Am76TZrzVda+7XOss8jz1x2sbPZ9CzPnHqGwegg2zqsNV9JXo+Xd135LsbmxjgwZEtmrZRljFqQmoTI/+fsINW63e1o6p8IDPwy5BJOCWcJT598mmMTx2hvbmdDcMM6BtiYruq6ip2dO3n2zLPEUjG3w6kpluirnSqc/1enFT/wbrejaRzBfuh6kzMDefbMJU8fnzjOc4PPMTE3wc7OnesfXwMSEd5z1XvI5XN86/i3rGN2BSzRV7uJH8Psadj0S+BrdzuaxtL3DvB3QvgbzqzZgrnMHN945RscnzjOlvYt+L1+F4NsLBuDG/nFHb/IsYljvDT6ktvh1AxL9NVs7jwMfxfar3JWWDTry+uHLe+HzAyEvwmq5DXP40cf59DoIfxePwNttqbNenvzljezfcN2vn3820TiEbfDqQmW6KtVJgbnvga+NifZWEefO0Jbof+dMPMyjP1Pnj39LD8M/5Cp5BS7unZZB6wLPOLhzt130tzUzFcPf5W5zJzbIVU9S/TVKJeCM192OgOv+AA0Bd2OqLF1/wxsuJ79R/+Jp478M6enTnNV11VWsnFRq7+V/3Ldf2EmNcNXDn2FTC7jdkhVzRJ9tckl4cyXIDkKW3/V2QHJuEuEl5p28I2xITzjz/PGUIj2Zusvcdu2jm3cce0dhKNhvnL4K6TXsMR0vbNEX00yMTj9z05tftud0L7L7Yganqry/ODzPHrkqxxKK1e19fEL3gib0gtX6jZu2N2zm9uvuZ3TU6f50sEvWRlnCZboq0V8EE48BKlxuOIuZ1Et46pMLsM3XvkGXzvyNY6MHaG/bQvnu97OpHcjVyePc1XyOB5bJ911N/XfxJ2772QoNsRDP3mIoZi9CS9kid5txaUNTn0BpAl2fsQZZWNcdWb6DH9/4O/51vFvcWziGDs6djDQNkBOvBwO3sA5/1YG0kO8Ye4ntOeiboe7YqlEirvvvpu5ufpoAV/Xex2//vpfJ695Hv7pw3z/zPfJ5rNuh1U1pBonHezZs0cPHKjzac75nLN13eizkInCxpud5Q28zW5H1tDG4mM8e+ZZ9p/fz4mpE6DOjMyg79IO8Y3ZCa5KHieQTzHq6+Wsfztz3hYXol6ZsfgYTWea+Oz9n+WZZ57hHe94h9shlU0ik+DJV5/kUOQQnYFObt1xK9f3Xo+nAZYNEZGfqOqexZ6z/c7WWzLiJPipg06Cbxlw1pYPXeF2ZA0rlU1xfOI4B0cP8uLIi5yLniOWirGpdRNb2rcsOYRysqmL/aE3si19ji3pMH2ZCFNNGxjyDTDe1I1WcXJ55cfOMsz1luiDviC/svtXuHnTzTx14ikeP/o43zv9PW7qu4kb+m6gu6Xb7RBdUVKLXkRuA/4G8AIPq+qfL3heCs//MjAH/HdV/Wkp1y6mrlr02TmIn4P4WYifgsSos5xB607ofgu0Xmlj5NdZLp9jZHaEweggZ6bPcHTsKKPxUYZjw6TzaXqCPWzbsG1F+77682n6M8MMZIYJ5JPkxMuUdwNTTRuZ9nYw52mpmsQ/Fh/jG7/7DYZODnH99ddz6NAht0OqCFXl2MQxfnz+x5yeOo2ibGrdxM7OnWzr2Ma2jm2LflKrVZdr0S+b6EXECxwH3omzCfh+4IOq+vK8c34Z+G2cRP9m4G9U9c2lXLuYqk70mnfq6vkMaNZ5zCUgO+vs45qNO6Nn0hNOx2pm1rnO0wTBzU4na8d14LPt5spFVcnms2TzWTL5DNl8lkQmwVxmjngmzlxmjtn0LJOJScbnxjkfPU80FWU6Oc10cppMPkNHoIOeYA/doe41fcwXVTpzk3RnJ+jMThLMJ50YRYh7Wkh4WkhKMylPgLT4yUoTWWkiI03kaCInHhQPeaRsDYCvfPIrHH/u+EXHmnxNZDNZ/H4/6fTFwxLf97738c1vfrMsr10tYqkYhyOHOTp+lPPR8+TUWeq4zd9Gd0s3XS1dtPnbCPlDhHwhQv4QwaYgPq8Pn8dHk6cJn9dX1SWgtZZu3gScKGwLiIg8BuwF5ifrvcA/F7YU/KGIbBCRTcD2Eq4tm3948m7mMvHXdoy/6E1ssa+1cNoS5+n8LxTV/IL7XEoV8PjQphbUW/jj60B97SBDcH4IeAZd5j6XxnWZ89b5XqXeb6X3Wuz8+c8t/FpRMvkMmVwGLSxPkNMcuXyOnObI5rOksikS2QSpbIpsPkte83g9XkK+EC2+Fq7YcAXtze0X/gOXowNvRNoY8bWBbzvBfIL2XIzW/Byt+VlasjN05FN4WX60jiLkEfLiQZELfy49r6DwxnDx36LQ81+7+NNXA0xPp8lknNfNZpyfc36SDzQ30dfVyv99z044suwH75rSBvwM8DN+yGz0cD4xSzgxw/jsSSYm53g5PcdcdvlJV14RmjxeBBAEEefRI3LJMYFLyn5LvXVL4ZmW5jZ+/bYvreEnXVwpiX4zMDjv+zBOq325czaXeC0AInIvcC/Atm3bSgjrUi2BTl6ZOrXwzsD8X3656LnFU5EsOFUKqV7I40HFc+E/IHjIioccvkLrzAt5gTRABphx/pTQOJNSTlqBct5vNVP9l3ozWO2yAcXk7nzjJPzivZz/YOIcFy38RxMCTQFa/a14xYuI4PP68Ir3ovvG0/FVxVOKGBAhCATB0+Uc9Cg+sjRrBh85mjSLjxw+zeFxfsMQdR49KB4tpvzXfmPlor/awjEWPxbY3MGffPbn+OLfHubggQjp1KVvMi0BL+/92X4e+YM9hIJhmAyX9e+hmvhwWqDbPeD803iAVnKqzOWyxHM54rksiXyOjObJqpLRPJm8XvjeaWxcaAI6jwr54nF97fhiljrenJ9yKgK+trL+zKUk+sX+Vy6Mc6lzSrnWOaj6EPAQOKWbEuK6xId+8W/50GouNKYBfPQu+MxnPsOnPvUpEonXNlQJBoP8Hw88wMc//nEXo3OfF6flX94UWx1KSfRhYOu877cAC2ckLHWOv4RrjTHr5OTJk+RyOUSEYDBIIpEgl8tx6tTCT8KmnpTSs7Af2CUiO0TED9wF7Ftwzj7g18TxFmBGVYdLvNYYsw6Gh4d5+OGHAac8+uijj7J1q9MO+/znP8/IyIib4ZkKWjbRq2oWuB94CjgKfE1Vj4jIfSJyX+G0J4FTwAng88BHL3dt2X8KY8yyHnjgATKZDO9///s5cuQIt99+Oy+//DK33347mUyGBx54wO0QTYWUNFBYVZ/ESebzjz0472sFPlbqtcaY9Tc3N8cjjzzCPffcc+FYKBTiq1/9Kr/0S7/ED37wAxejM5VkSyAYY0wduNw4+uod/W+MMaYsLNEbY0yds0RvjDF1ripr9CIyBpx1O46CbmDc7SCWUe0xVnt8UP0xVnt8YDGWw1riu0JVexZ7oioTfTURkQNLdXBUi2qPsdrjg+qPsdrjA4uxHCoVn5VujDGmzlmiN8aYOmeJfnkPuR1ACao9xmqPD6o/xmqPDyzGcqhIfFajN8aYOmctemOMqXOW6I0xps5Zol8BEfl9EVERqaqt5EXk/xGRV0TkoIg8ISIb3I6pSERuE5FjInJCRD7hdjzzichWEXlWRI6KyBER+V23Y1qKiHhF5AUR+ZbbsSymsH3o1wu/h0dF5Gfcjmk+EflfCv/Gh0XkKyISqIKYviAiERE5PO/YRhF5WkReLTx2luO1LNGXSES24mxyfs7tWBbxNHC9qt6Isxn7H7ocD3BhY/nPAe8GdgMfFJHd7kZ1kSzwcVW9FngL8LEqi2++38VZ6rta/Q3wHVW9BriJKopVRDYDvwPsUdXrcTaTusvdqAD4R+C2Bcc+Afy7qu4C/r3w/ZpZoi/d/wv8byy3O7gLVPW7hbX/AX6Is5NXNbiwsbyqpoHi5vBVQVWHVfWnha9jOMlps7tRXUpEtgD/GXjY7VgWIyLtwNuARwBUNa2q0+5GdYkmICgiTUALVbDTnar+AJhccHgv8E+Fr/8JuL0cr2WJvgQi8j7gvKq+5HYsJbgH+De3gyhYatP4qiMi24GbgR+5G8mi/hqnkXHprt7VYScwBnyxUF56WERCbgdVpKrngb/E+TQ+jLMD3nfdjWpJfYXd+Sg89pbjppboC0TkmUL9buGfvcAngU9XcXzFcz6JU4541L1IL1Ly5vBuEpFW4F+A31PVqNvxzCci7wEiqvoTt2O5jCbgFuDvVfVmIE6ZSg7lUKhz7wV2AANASET+m7tRra+SdphqBKr6nxY7LiI34PyCvCQi4JRFfioib1LVddtkc6n4ikTkw8B7gHdo9UyOKGVjeVeJiA8nyT+qqo+7Hc8i3gq8T0R+GQgA7SLyJVWtpkQVBsKqWvw09HWqKNED/wk4rapjACLyOPCzwJdcjWpxoyKySVWHRWQTECnHTa1FvwxVPaSqvaq6XVW34/xS37KeSX45InIb8AfA+1R1zu145qnqzeHFeed+BDiqqn/ldjyLUdU/VNUthd+9u4DvVVmSp/B/YVBEri4cegfwsoshLXQOeIuItBT+zd9BFXUWL7AP+HDh6w8D3yzHTa1FXx/+FmgGni586vihqt53+UsqT1WzIlLcHN4LfKHKNod/K/Ah4JCIvFg49keFfY7Nyvw28GjhDf0U8Osux3OBqv5IRL4O/BSntPkCVbAUgoh8BXg70C0iYeB/B/4c+JqIfATnDepXy/Ja1fMp3xhjTCVY6cYYY+qcJXpjjKlzluiNMabOWaI3xpg6Z4neGGPqnCV6Y4ypc5bojTGmzlmiN2YZIvLGwlr/AREJFdY1v97tuIwplU2YMqYEIvJ/4qw1E8RZ1+XPXA7JmJJZojemBIWp/fuBJPCzqppzOSRjSmalG2NKsxFoBdpwWvbG1Axr0RtTAhHZh7ND1g5gk6re73JIxpTMVq80Zhki8mtAVlW/XNgH9zkR+UVV/Z7bsRlTCmvRG2NMnbMavTHG1DlL9MYYU+cs0RtjTJ2zRG+MMXXOEr0xxtQ5S/TGGFPnLNEbY0yd+/8BQKlwfXHMg3wAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu0, mu, sigma1, mutrue = 0, 5., 1., True\n",
    "httoys.gaussian(mu0, mu, x0 = mu, mutrue = mutrue, sigma1 = sigma1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "19d7e813-cdc2-4ec7-8c43-f8d22cf8ba4e"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Exercise:** An experiment expects $(2, 1)$ background events in two bins, and a possible signal $(8, 9)$ on top. It observes $(9, 9)$, can claim observation?\n",
    "\n",
    "**Exercise:** In the case it observes $(1, 1)$, can reject the signal at 95 % CL?\n",
    "\n",
    "**Exercise:** Consider an experiment with several independent channels that expects as background ${\\bf b} = (2, 1.5, 1, 0.5) $ and as signal ${\\bf s} = (1, 3, 3, 1)$. It finally measures $(2, 1, 1, 0)$. Compute the p-value of $H_1$. \n",
    "\n",
    "**Exercise:** Consider the above case of KamLAND-Zen, compute the p-value of $H_0$!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "a690eefb-2be1-47d9-a5b2-2b82ca73809d"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The CLs method\n",
    "\n",
    "In some cases the $H_1$ hypothesis is 'weak' compared with $H_0$ and the distributions of the test statistic $g(q \\, | H_0)$ and $g(q \\, | \\,H_1) $ overlap. \n",
    "\n",
    "**Example**: Consider $H_0$ as a poisson of $b$ expected events, $b=4$, and the signal $s=0.5$ events. \n",
    "\n",
    "**Question**: If we measure $n \\, = \\,1$, the p-value for $H_1$ is $0.061$, bellow 10%. Do we exclude the signal at 90% CL? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed data : 1\n",
      "H0 p-value    : 0.98168436\n",
      "H1 p-value    : 0.06109948\n",
      "CLs           : 0.66718373 \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b, s, x0 = 4, 0.5, 1\n",
    "httoys.poisson(b, b + s, x0); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The pdfs of the test statistics, $g(q | H_0), \\, g(q | H_1)$, for $b=4, \\, s+b=4.5$ mostly overlap! \n",
    "\n",
    "In principle we reject $H_1$ at 90% CL. But the probability to accept $H_0$ is very small, $1-\\alpha$! \n",
    "\n",
    "It will be more prudent to not reject $H_1$ and conclude that *the experiment has no enough reach*.\n",
    "\n",
    "One solution to this problem is to use the CLs method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h0, h1, size = stats.poisson(4), stats.poisson(4.5), 10000\n",
    "ht = htcore.htsimple(h0, h1, size)\n",
    "htplot.plt_htsimple(ht);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "ns = range(12)\n",
    "qs = ht.q(ns)\n",
    "betas  = [ht.p1value(qi) for qi in qs]\n",
    "clss   = [ht.cls    (qi) for qi in qs] \n",
    "clline = 0.1*np.ones(len(ns))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.hist(ht.q0s, bins = 100, density = True, range = ht.qrange(), histtype ='step', label = '$q(x|H_0)$')\n",
    "ax.hist(ht.q1s, bins = 100, density = True, range = ht.qrange(), histtype ='step', label = '$q(x|H_1)$')\n",
    "axb = ax.twinx()\n",
    "axb.plot(qs, betas , marker='s', color = 'green', label = '$p-value$');\n",
    "#axb.plot(qs, clss  , marker='o', color = 'red', label = '$CLs$');\n",
    "axb.plot(qs, clline, color = 'black');\n",
    "axb.set_ylabel('CL');\n",
    "axb.legend(); ax.legend(loc = 4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "The [CLs method](https://arxiv.org/abs/hep-ex/9902006) was developed to prevent these cases.\n",
    "\n",
    "\n",
    "Instead of using the $H_1$ p-value, $\\beta$, to reject $H_1$, it uses the value:\n",
    "\n",
    "$$\n",
    "CL_s \\equiv \\frac{CL_{s+b}}{CL_b} = \\frac{\\beta}{1-\\alpha}\n",
    "$$\n",
    "\n",
    "That is, a ratio of fractions. Given an observation, the fraction of possible equal or worse events if we consider the $H_1$ hypothesis, with respect the fraction of possible equal or better events if we do the same with $H_0$.\n",
    "\n",
    "Notice that $CLs$ is conservative, $CLs \\ge \\beta$. And that $1-\\alpha \\ge \\beta$, the probability to accept $H_0$ is always greater than to reject $H_1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In the previous example, the $H_1$ p-value was 0.06, but CLs value is 0.66! Therefore, we do not exclude $H_1$. \n",
    "\n",
    "The CLs has prevent us to do an exclusion when the experiment has not enough sensitivity!\n",
    "\n",
    "In the case that $H_1$ is well separated compared with $H_0$ a cut on $CL_s$ is equivalent to a cut on $\\beta$.\n",
    "\n",
    "The CLs method has been criticized as conservative, but has been and is frequenly used in HEP."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "**Example** In the previous examples we have impossed $H_1$ p-value and $CL_s$, if we observe $n=1$, we will not reject $H_1$ using the CLs method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.hist(ht.q0s, bins = 100, density = True, range = ht.qrange(), histtype ='step', label = '$q(x|H_0)$')\n",
    "ax.hist(ht.q1s, bins = 100, density = True, range = ht.qrange(), histtype ='step', label = '$q(x|H_1)$')\n",
    "axb = ax.twinx()\n",
    "axb.plot(qs, betas , marker='s', color = 'green', label = '$p-value$');\n",
    "axb.plot(qs, clss  , marker='o', color = 'red', label = '$CLs$');\n",
    "axb.plot(qs, clline, color = 'black');\n",
    "axb.set_ylabel('CL');\n",
    "axb.legend(); ax.legend(loc = 4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
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   "source": [
    "## Nuissance parameters \n",
    "\n",
    "Sometime the pdf depends also not only on $\\mu$ but on other parameters, $\\nu$ of no \"physical interest\". There are called **nuissance parameters**.\n",
    "\n",
    "The pdf $g(x \\, | \\, \\mu, \\nu)$, were $\\mu$ is the parameter of interest, and $\\nu$ the nuisance parameter. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In some cases, we can marginalize the nuissance parameters. One possibility is use [the Cousins-Highland method](http://www.sciencedirect.com/science/article/pii/0168900292907945) also known as a bayesian-frequentist hybrid method.\n",
    "\n",
    "If we know the pdf of the nuisance parameter: $\\pi(\\nu)$, we can marginalize its effect:\n",
    "\n",
    "$$\n",
    "g(x \\, | \\, \\mu) = \\int g( x \\, | \\, \\mu, \\nu) \\, \\pi(\\nu) \\, \\mathrm{d}\\nu\n",
    "$$\n",
    "\n",
    "Its common to take $\\pi(\\nu)$ as a gaussian with mean $\\hat{\\nu}$ and sigma $\\sigma_\\nu$.\n",
    "\n",
    "Notice that this method is a hybrid: frequentist-bayesian."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Exercise:** Consider the case of an experiment that expects $b=2 \\pm 0.2$ background events, and search for a signal $s=5$. What is the effect of the uncertainty on $b$ in the expected 95% CL limit?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "7a51d248-ab99-4db8-8cad-f38f21a9fd3d"
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    "slideshow": {
     "slide_type": "slide"
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   },
   "source": [
    "## Intro to composite hypothesis\n",
    "\n",
    "Often the $H_1$ hypothesis is not complete, it depends on several parameters.  \n",
    "\n",
    "A typical example if searching for a new signal with a unkown cross-section or half-lifetime. We resume the unknown into a parameter, $\\mu$, that quantifies the strength of the signal.\n",
    "\n",
    "$H_1$ depends now on $\\mu$. When $\\mu=0$, we recuperate the case $H_0$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "We have a continuous set of hypothesis. This is know as **composite hypothesis testing**. How we proceed? \n",
    "\n",
    "We can scan along $\\mu$ and repeat the hypothesis test. But this can be *computationally expensive.*\n",
    "\n",
    "In some case there are simpler solutions, but first we need to go back to the concept of **Confidence Intervals**.\n",
    "\n",
    "As we shall see composite hypothesis testing and confidence intervals are in fact connected!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "fd994b19-bfe4-47e4-9b0b-b0608e652de4"
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    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Exercise** An experiment searches for a new signal expected $s=1$ according with SM, in a background $b=0.5$, but the strength of the signal can be 10 times more. If there is no signal, what is the 90% CL exclusion sensitivity in terms of $\\mu$?"
   ]
  }
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