FC_intervals_bounded_gaussian.ipynb

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    "# Feldman-Cousins Confidence Interval Tutorial\n",
    "\n",
    "Anil Kumar | anil.kumar@desy.de | 3 July, 2024\n",
    "\n",
    "Ref.: A Unified Approach to the Classical Statistical Analysis of Small Signals, Gary J. Feldman, Robert D. Cousins, [PRD 57 (1998) 3873-3889](https://doi.org/10.1103/PhysRevD.57.3873), [arXiv:physics/9711021](https://arxiv.org/abs/physics/9711021v2)\n",
    "\n",
    "Suppose that we wish to make an inference about a parameter $\\mu$ whose true value $\\mu_t$ is unknown. Assume that we do this by making a single measurement of an observable $x$ such that the probability density function (pdf) for obtaining the value $x$ depends on the unknown parameter $\\mu$ in a known way: we call this pdf $P(x|\\mu)$. Now suppose that the single measurement of $x$ yields the value $x_0$. One substitutes this value of $x$ into $P(x|\\mu)$ to obtain $P(x_0|\\mu)$, known as the likelihood function, which we denote as $\\mathcal{L}(x_0|\\mu)$.\n",
    "\n",
    "In the frequentist approach, we obtain a confidence interval $[\\mu_1, \\mu_2]$, which is a member of a set, such that the set has the property that \n",
    "\n",
    "\\begin{equation}\n",
    "P(\\mu \\in [\\mu_1, \\mu_2] = \\alpha.\n",
    "\\end{equation}\n",
    "\n",
    "Here $\\mu_1$ and $\\mu_2$ are functions of the measured $x$, and this equation refers to the varying confidence intervals $[\\mu_1, \\mu_2]$ from an ensemble of experiments with fixed $\\mu$. For a set of confidence intervals, this equation is true for every allowed $\\mu$. Thus, in particular, the intervals contain the fixed unknown $\\mu_t$ in a fraction $\\alpha$ of experiments. \n",
    "\n",
    "### Example: Gaussian with Boundary at Origin\n",
    "\n",
    "Consider the observable $x$ which is simply the measured value of $\\mu$ in an experiment with a Gaussian resolution function with known fixed rms deviation $\\sigma = 1$\n",
    "\n",
    "\\begin{equation}\n",
    "P(x|\\mu) = \\frac{1}{\\sqrt{2\\pi}} \\exp{\\left(-(x-\\mu)^2/2\\right)}\n",
    "\\end{equation}\n",
    "\n",
    "We consider an interesting case where only non-negative values for $\\mu$ are physically allowed. For example, if $\\mu$ is a mass. Therefore, the graph does not exist for $\\mu < 0$.\n",
    "\n",
    "In this tutorial, we will study the following type of confidence intervals:\n",
    "- Central confidence interval\n",
    "- Upper confidence limit\n",
    "- Confidence interval based on Flip-flopping policy\n",
    "- Feldmann-Cousins confidence interval"
   ]
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   "source": [
    "import math\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.stats import norm\n",
    "from matplotlib import pyplot as plt\n",
    "import matplotlib\n",
    "matplotlib.rcParams.update({'font.size': 18})\n"
   ]
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   "source": [
    "# Gaussian distribution with unit $\\sigma$\n",
    "\n",
    "Here, we plot the Gaussian pdf $P(x|\\mu)$ as a function of $x$ for a given value of $\\mu$ with known fixed rms deviation $\\sigma = 1$\n",
    "\n",
    "\\begin{equation}\n",
    "P(x|\\mu) = \\frac{1}{\\sqrt{2\\pi}} \\exp{\\left(-(x-\\mu)^2/2\\right).}\n",
    "\\end{equation}\n",
    "\n",
    "We select an interval $[x_1, x_2]$ such that\n",
    "\n",
    "\\begin{equation}\n",
    "P(x \\in [x_1, x_2] | \\mu) = \\alpha.\n",
    "\\end{equation}\n",
    "\n",
    "Here, we choose $\\alpha$ to be 90\\% confidence level (CL). We refer to the interval $[x_1, x_2]$ as the \"acceptance region\" or the \"acceptance inteval\" for this $\\mu$. In order to specify uniquely the acceptance region, one must choose auxiliary criteria. One has total freedom to make this choice, if the choice is not influenced by the\n",
    "data $x_0$. \n",
    "\n",
    "## Central confidence intervals\n",
    "\n",
    "The choice for \"central confidence intervals\" is\n",
    "\n",
    "\\begin{equation}\n",
    "P(x<x_1 | \\mu) = P(x > x_2 | \\mu) = (1 - \\alpha)/2,\n",
    "\\end{equation}\n",
    "\n",
    "which satisfy \n",
    "\n",
    "\\begin{equation}\n",
    "P(\\mu < \\mu_1) = P(\\mu > \\mu_2) = (1-\\alpha)/2.\n",
    "\\end{equation}"
   ]
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   "execution_count": 2,
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " x1 (90% CL) =   0.36 \n",
      " x2 (90% CL) =   3.64\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean = 2                                   # mean of Gaussian pdf\n",
    "std = 1                                    # sigma of Gaussian pdf\n",
    "alpha = 0.9                                # 90% CL\n",
    "\n",
    "#print(f' mean = {mean}\\n sigma = {std}')\n",
    "\n",
    "xmin, xmax = mean-3*std, mean+3*std        # we plot x over 3 sigma range\n",
    "x = np.linspace(xmin, xmax, 100)\n",
    "y = norm.pdf(x, mean, std)                 # Gaussian pdf for x with given mean and sigma\n",
    "\n",
    "lower_CL =  0.5*(1 - alpha)                # lower limit for central confidence intervals\n",
    "upper_CL =  alpha + 0.5*(1 - alpha)        # upper limit for central confidence intervals\n",
    "x1 = norm.ppf(lower_CL, mean, std)         # lower limit of x for central confidence intervals\n",
    "x2 = norm.ppf(upper_CL, mean, std)         # upper limit of x for central confidence intervals\n",
    "print(f' x1 (90% CL) = {x1:6.2f} \\n x2 (90% CL) = {x2:6.2f}')\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "plt.plot(x, y)                             # plot Gaussian pdf\n",
    "plt.fill_between(                          # shade acceptance region for 90% central CL \n",
    "        x= x, \n",
    "        y1= y, \n",
    "        where= ((x > x1) & (x < x2)),      # shade region between x1 and x2\n",
    "        color= \"k\",\n",
    "        alpha= 0.2,\n",
    "        label = \"90% CL\")\n",
    "\n",
    "plt.text(x1, 0.02, r'$x_1$', horizontalalignment='right')\n",
    "plt.text(x2, 0.02, r'$x_2$', horizontalalignment='left')\n",
    "plt.xlabel('Measured Mean x')\n",
    "plt.ylabel(r'Probability density function (pdf)')\n",
    "plt.xlim([xmin, xmax])\n",
    "plt.ylim(bottom=0)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14f94599",
   "metadata": {},
   "source": [
    "## Central confidence intervals\n",
    "\n",
    "Now, we plot the parameter $\\mu$ vs. the measured quantity $x$. For each value of $\\mu$, one examines $P(x|\\mu)$ along the horizontal line through $\\mu$. We select an interval $[x_1, x_2]$ which corresponds to the confidence level of $\\alpha$. The construction is complete when horizontal acceptance intervals (gray) are drawn for each value of $\\mu$.\n",
    "\n",
    "Upon performing an experiment to measure $x$ and obtaining the value $x_0$, one draws a vertical line through $x_0$ on the horizontal axis. The confidence interval is the union of all values of $\\mu$ for which the corresponding horizontal interval is intercepted by the vertical line; typically this is a simply connected interval $[\\mu_1, \\mu_2]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "72ffc6d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fig. 3\n",
    "\n",
    "std = 1\n",
    "alpha = 0.9\n",
    "\n",
    "lower_CL =  0.5*(1 - alpha)              # lower limit for central confidence intervals\n",
    "upper_CL =  alpha + 0.5*(1 - alpha)      # upper limit for central confidence intervals\n",
    "\n",
    "ymin, ymax = 0, 6                        # only positive values of mean\n",
    "mean = np.linspace(ymin, ymax, 100)\n",
    "x1 = norm.ppf(lower_CL, mean, std)       # lower limit of x for central confidence intervals\n",
    "x2 = norm.ppf(upper_CL, mean, std)       # upper limit of x for central confidence intervals\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "plt.plot(x1, mean, color = 'k')\n",
    "plt.plot(x2, mean, color = 'k')\n",
    "plt.fill_between(                        # shade acceptance region for 90% central CL between x1 and x2\n",
    "        x= x1, \n",
    "        y1= mean, \n",
    "        color= \"k\",\n",
    "        alpha= 0.2,\n",
    "        label = \"90% CL\")\n",
    "\n",
    "plt.fill_between(                       # shade acceptance region for 90% central CL between x1 and x2\n",
    "        x= x2, \n",
    "        y1= mean, \n",
    "        color= \"w\",\n",
    "        alpha= 1,\n",
    ")\n",
    "\n",
    "plt.text(-1, 1, r'$x_1$', horizontalalignment='right')\n",
    "plt.text(3, 1, r'$x_2$', horizontalalignment='left')\n",
    "\n",
    "plt.xlabel('Measured Mean x')\n",
    "plt.ylabel(r'Mean $\\mu$')\n",
    "plt.xlim([-2, 4])\n",
    "plt.ylim([ymin, ymax])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c245065c",
   "metadata": {},
   "source": [
    "## Upper confidence limit\n",
    "\n",
    "\n",
    "For the \"upper confidence limit\", the choice is \n",
    "\n",
    "\\begin{equation}\n",
    "P(x < x_1 | \\mu) = 1 - \\alpha\n",
    "\\end{equation}\n",
    "\n",
    "which satisfy \n",
    "\n",
    "\\begin{equation}\n",
    "P(\\mu > \\mu_2) = 1-\\alpha.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fe6eccd2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " x1 (90% CL) =   0.72\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean = 2\n",
    "std = 1\n",
    "alpha = 0.9\n",
    "\n",
    "#print(f' mean = {mean}\\n sigma = {std}')\n",
    "\n",
    "xmin, xmax = mean-3*std, mean+3*std\n",
    "x = np.linspace(xmin, xmax, 100)\n",
    "y = norm.pdf(x, mean, std)\n",
    "\n",
    "lower_CL =  (1 - alpha)                          # lower limit for central confidence intervals\n",
    "x1 = norm.ppf(lower_CL, mean, std)               # lower limit of x for central confidence intervals\n",
    "print(f' x1 (90% CL) = {x1:6.2f}')\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "plt.plot(x, y)\n",
    "plt.fill_between(\n",
    "        x= x, \n",
    "        y1= y, \n",
    "        where= (x > x1),                         # shade acceptance region for 90% central CL for x > x1\n",
    "        color= \"k\",\n",
    "        alpha= 0.2,\n",
    "        label = \"90% CL\")\n",
    "\n",
    "plt.xlabel('Measured Mean x')\n",
    "plt.ylabel(r'Probability density function (pdf)')\n",
    "plt.text(x1, 0.02, r'$x_1$', horizontalalignment='right')\n",
    "plt.xlim([xmin, xmax])\n",
    "plt.ylim(bottom=0)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75c83ab7",
   "metadata": {},
   "source": [
    "## Upper confidence limit\n",
    "\n",
    "For each value of $\\mu$, one examines $P(x|\\mu)$ along the horizontal line through $\\mu$ and select an interval $x_1$ which corresponds to the confidence level of $\\alpha$. Here, $x_2$ can be thought of equal to infinity. \n",
    "\n",
    "The vertical line through the measured value $x_0$ provide upper confidence limit $\\mu_2$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8ca9b06d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dO3aQlZVF8+bNoyY0QMEhIhJVvvrqKwKBADk5OQSDQS655JKoCg2Iol5VIiJl3aeffkqrVq3Izc0lKyuLZs2aRV1ogIJDRCQq/Pe//yUQCBAXF0d2djZNmzbFzPwuq0AKDhERn33wwQcEAgHi4+PJzs6mcePGURsaoOAQEfHVokWLaNOmDVWrViUYDHLhhRdGdWiAgkNExDdvvfUW7dq14/jjjyc7O5tGjRpFfWiAgkNExBevvfYaHTp04KSTTiIYDHLeeef5XVKRKThERErYyy+/TKdOnTj11FPJzs6mYcOGfpcUFgWHiEgJev755+natSsNGjQgGAxy5pln+l1S2BQcIiIl5P/+7//o0aMHZ511FsFgkN/97nd+l3RUFBwiIiXgscceIyUlhXPPPZesrCxOO+00v0s6agoOEZFi9re//Y3+/ftz4YUXkpWVRb169fwu6ZgoOEREitG9997LkCFDuOiii8jIyKBu3bp+l3TMFBwiIsXkzjvvZPjw4Vx66aVkZGRQp04dv0uKCAWHiEgx+Mtf/sLo0aNp2bIl6enp1K5d2++SIkbBISISYTfeeCMTJkygVatWzJw5M6ZCA3Q/DhGRiHHOkZmZyaxZs0hKSmLq1KnUrFnT77IiTsEhIhIBzjlmzJhBdnY27dq1Y/LkydSoUcPvsoqFgkNE5Bg550hNTeWWW26hY8eOTJw4kWrVqvldVrFRcIiIHAPnHOPGjeO2226jS5cujBs3jqpVq/pdVrFScIiIHKXc3Fyuv/567r77bnr06MGYMWOoUqWK32UVOwWHiMhR2LdvHyNGjOD++++nd+/eXHfddVSuXNnvskqEgkNEJEw5OTkMGTKEv//97/Tr14+RI0dy3HHH+V1WiVFwiIiEYe/evfTv359//OMfDBo0iOHDhxMfH+93WSVKwSEiUkR79uwhJSWFZ555hmHDhjF48OAyFxqg4BARKZJdu3bRs2dPXnzxRUaOHMmAAQPKZGiAgkNE5Ih27txJ165dWbhwIaNHj6ZPnz5UqlTJ77J8o+AQETmM7du307lzZ958803GjRtHr169qFixot9l+UrBISJSiK1bt9KxY0cWLVrEhAkT6NGjR5kPDVBwiIgUaPPmzVx55ZV89NFHTJ48ma5du1KhQgW/y4oKCg4RkXx++eUX2rVrx6effsqUKVPo3Lkz5cvr63I/vRMiInls2LCBNm3asHTpUtLS0ujQoYNCIx+9GyIiIevWrSMpKYlvv/2W6dOn065dO4VGAfSOiIgAa9asISkpiZUrV5Kenk5SUpJCoxB6V0SkzPvhhx8IBAKsXbuWWbNmkZiYSFxcnN9lRS0Fh4iUaStWrCAxMZGNGzcye/ZsrrjiCoXGESg4RKTM+vbbbwkEAvz6669kZmbyhz/8gXLlyvldVtRTcIhImbRs2TICgQA7duwgMzOT5s2bKzSKSMEhImXOF198QXJyMjk5OQSDQS655BKFRhii9p0ys+PM7H9m5szsDr/rEZHY8Omnn5KYmEhubi7BYJBmzZopNMIUze9WBnCi30WISOz4+OOPD/SYCgaDXHzxxZiZ32WVOlEZHGZ2ETAOmOVzKSISI95//30CgQAJCQlkZ2fTpEkThcZRirrgMLM44B7gFeBpn8sRkRjw7rvv0qZNG6pXr04wGOTCCy9UaByDaGwcHw80BHr4XYiIlH5vvvkmnTp1onbt2mRlZdGwYUO/Syr1ouqIw8waAHOADOfciiK+ZoSZLTazxRs2bCjW+kSkdFm4cCEdOnTg5JNPJjs7W6ERIVEVHMB84H/An4v6AufcAudcU+dc01q1ahVfZSJSqrz00kt07tyZevXqkZ2dzdlnn+13STEjak5VmVl/oC1whXNur9/1iEjp9eyzz9KrVy/OOOMMMjMzadCggd8lxZSoCA4zq4R3lPES8JOZnRmaVTf0XD00baNzbrMPJYpIKfHkk0/St29fzjnnHDIyMjjttNP8LinmRMupqgSgFtARWJ7n8VZofv/Qz8P8KE5ESodHHnmElJQUzjvvPDIzMxUaxSQqjjiA7cDVBUyvBdyF1zX3PuCzkixKREqPBx54gKFDh9KkSRNmzZpF3bp1j/wiOSpRERyhNo3/yz/dzE4P/fM759wh80VEABYsWMDIkSO55JJLSE9Pp06dOn6XFNOi5VSViMhRueOOOxg5ciTNmzdnzpw5Co0SEBVHHIUJXcuhyztFpEB/+tOfmDRpEi1btmT69OmoS37J0BGHiJRKc+fOZdKkSbRu3ZqZM2cqNEpQVB9xiIjk55xjzpw5zJkzh+TkZKZMmULNmjX9LqtMUXCISKnhnGPatGnceOONtGvXjsmTJ1OjRg2/yypzFBwiUio455g0aRJ//vOf6dSpExMmTKBatWp+l1UmKThEJOrl5uYyduxY7rjjDrp27crYsWOpWrWq32WVWQoOEYlqubm5jBo1igULFtCzZ09Gjx5NlSpV/C6rTFNwiEjU2rdvH8OGDePBBx8kJSWFUaNGUblyZb/LKvMUHCISlXJychg8eDCPPPII/fv3Z8SIERx33HF+lyUoOEQkCu3du5d+/frx5JNPMnjwYIYNG0Z8fLzfZUmIgkNEosru3btJSUnh2WefZfjw4QwaNEihEWUUHCISNXbt2kXPnj158cUXufbaa+nfv79CIwopOEQkKuzYsYOuXbvyr3/9izFjxpCSkkKlSpX8LksKoOAQEd9t27aNq666irfffptx48bRq1cvKlas6HdZUggFh4j46tdff6VDhw689957TJw4kR49elChQgW/y5LDUHCIiG82b95M+/bt+fjjj0lNTaVLly4KjVIgrOAws1uAT4D/Al8751y++XWBX5xzOyNXoojEop9//pm2bdvy+eefM3XqVDp16kT58vpbtjQI97c0AdgfFjvN7DO8EPkk9EgBEoFLIlahiMScDRs2kJyczLJly5g2bRpXXnmlQqMUCfc3dTxwUb7HtXg3hNofKDsiVp2IxJyffvqJ5ORkvvvuO2bMmEGbNm0UGqVMWL8t59xm4I3QAwAzqwp0AGYDJwJjIleeiMSS1atXEwgE+OGHH5g5cyZJSUkKjVLomG8d65zb6px7Au/01Ha88BAROciqVato1aoVq1evZtasWSQnJys0SqmI3XPcObcNeAgYH6l1ikhs+N///kerVq1Yv349GRkZJCYmEhcX53dZcpQiHfcbgDoRXqeIlGLLly8nEAiwdetWMjMzadGiBeXKRexvVvFBuN1xN/Bbd9z/Av91zn0bmmdAR2BxpIsUkdLp66+/JhAIsGvXLjIzM2nevLlCIwaEe8TxH+D3QHLoZ2dmW4GvgVqhxyAzq+Cc2xu5MkWktPniiy9ISkpi3759BINBmjZtqtCIEeH2quoCYGY1gMZAk9BzY6BeaH3/B+SY2TfA58CnzrmbIlWwiES/JUuWkJycTFxcHNnZ2Vx00UV4JyUkFhxVG0eoW+5boQcAZlYRuIDfgqQJ3qmr3oCCQ6SMWLx4MW3btqVSpUpkZmbSuHFjhUaMiVjjuHNuD7+1fRxgZmdEahsiEt3ee+892rdvT9WqVcnKyuKCCy5QaMSgYj/h6Jz7rri3ISL+e+edd2jbti01atQgOztboRHD1FIlIsfs9ddfp3379px44olkZ2dz/vnnKzRimIJDRI7Jq6++SqdOnahTpw7Z2dk0bNjQ75KkmCk4ROSo/fOf/6Rz587Ur1+fYDDI2Wef7XdJUgIUHCJyVJ5++mm6devGGWecQTAY5Mwzz/S7JCkhCg4RCdsTTzxBr169aNiwIcFgkAYNGvhdkpSgsLvjmtllwGjgLOAEIH8LmHPOqQuuSIz6+9//zqBBg2jUqBGzZ8+mXr16fpckJSzcsaoGAg8Ae4FvgFXFUZSIRKf777+fYcOG0aRJE2bNmkXdunX9Lkl8EO4Rx3RgGZDsnFtTDPWISJS6++67GTVqFM2aNSM9PZ2TTz7Z75LEJ+G2cZwGzFdoiJQtt912G6NGjeKyyy5j9uzZCo0yLtzg+BGoVByFiEh0uvnmmxk7diyXX3456enp1K5d2++SxGfhBsfdQD8z0627RMqAYDBIamoqiYmJzJgxg1q1avldkkSBcNs4PgZ6AB+a2Z3A/4B9+Rdyzv07ArWJiE+cc8yePZuMjAzatGlDamoqNWvW9LssiRLhBsfref59L+DyzbfQtLCPSMzsHCAduAg4BaiA12vrJeBm59zacNcpIuFzzpGWlsZNN91E+/btmTx5MtWrV/e7LIki4QbHkGKpwnMq3v3Kn8FrS8kBGgEjgBQza+ycW1+M2xcp85xzTJgwgXnz5tGpUycmTJhAtWrV/C5Loky4dwD8W3EV4px7nYOPaAAws38D/wAGA38sru2LlHW5ubmMGTOGu+66i65duzJu3DiqVKnid1kShSJ2I6ditDL0rBOsIsUkNzeXkSNHcu+993L11Vdz/fXXKzSkUEcVHGbWFLgU78s8f88s55zLPNqCzCweqALEA+fx221nXzradYpI4fbt28c111zDQw89RJ8+fbj22mupXLmy32VJFAt3yJEE4GmgLb81hO8fq8rlmXbUwQEMA27P8/MKoL9z7p1jWKeIFCAnJ4eBAwfy2GOPMWDAAEaMGEFCQoLfZUmUC/eIIx0vNIJ47RFvAoOA9UAakAAMPMaangW+xjvqaAJ0BgrtPG5mI/Aa0Klfv/4xblqk7NizZw99+/blqaeeYsiQIQwdOpT4+Hi/y5JSwJzL36P2MAubLQc+ds6lmNkJwAa8caveMLPywEfAK865tIgVaHZhaL2znXNzD7ds06ZN3eLFiyO1aZGYtXv3bnr16sXzzz/P8OHDGTRokEKjDGvatOlS59x5RV0+3CvH6wFvh/69/8K/igDOuRzgMSAlzHUelnPuM+AT4LpIrlekrNq5cyfdunXj+eefZ9SoUQwePFihIWEJ91TV1jyv2Qrk4l2st98WoDhGP0sAji+G9YqUKTt27KBLly68/vrr3HDDDfTu3ZtKlTT8nIQn3COO74CzAZxz+4AvgZ4AZmZAd+CHoynEzAoMHDNLBC4A3j+a9YqIZ9u2bXTo0IE33niDcePGkZKSotCQoxLuEcdrwDVmNi4UHH8F7jCz7/B6UzUAph1lLfPNrA7wBt61G/HAxXinvrYCE49yvSJl3pYtW+jQoQMffPABEydOpHv37lSoUMHvsqSUCjc4bgQeJtQF1zl3V+i6i/54bR73cPRXdz+G10NrAF4vKocXIH/FG6tKdxsUOQqbNm2iXbt2fPLJJ6SmptK5c2eFhhyTcIcc2YZ3B8C80/4M/PlYC3HO/QNvaBERiZCff/6ZNm3a8OWXX5KWlkbHjh0pX740DBgh0eyoP0FmVgk4EdjgnNsTuZJEJBLWr19PcnIy33zzDdOmTaN9+/YKDYmIcBvHMbOLzOwNvHaHVUDL0PTaZva6mSVHuEYRCdPatWtp3bo1y5cvZ+bMmQoNiaiwgsPMGgPvAGcAD+WdFxryPAGvnUJEfPLjjz/SqlUrVq5cyaxZs2jTpo1CQyIq3COODGANcD4wld/GqdrvdaBZBOoSkaOwcuVKWrVqxZo1a5g9ezaBQIC4ON3pWSIr3OC4HLgn1Ehe0Fglqzj4gkARKSHff/89V1xxBRs3biQjI4NWrVopNKRYhHv8Go93dXhhdKswER8sX76cxMREtm/fTkZGBi1atKBcubCbMEWKJNzg+A7vorzCBICvjr4cEQnX0qVLCQQC7Nmzh8zMTC699FKFhhSrcD9djwID8vWccgBmNhFoj3eBoIiUgM8//5xWrVqRk5NDVlYWzZs3V2hIsQv3iOMWoA3wKt49MxzwFzOrhTe44b+AuyJaoYgU6JNPPjnQYyozM5MmTZrgDRknUrzC+tMkdKFfG2ASsBPYhTfo4UYgFejknMuNdJEicrCPPvqIQCBAxYoVCQaDCg0pUWF37g7dd+MvoYeIlLD//Oc/XHnllVStWpXMzEwaNWqk0JASpZOhIqXIv//9b9q2bUuNGjWYO3cuF154oUJDStwRjzhCw4uEwznnko6yHhEpxOuvv85VV13FySefTGZmJg0bNvS7JCmjinKqqjWwFyjqQIZFv4m5iBTJK6+8Qrdu3Tj11FPJzMzkrLPO8rskKcOKEhw5eEOLvAY8APxTDeAiJeeFF16gZ8+eNGjQgMzMTH73u9/5XZKUcUVp46gLpAFnAs8Aq83sJjM7p1grExGeeuopunfvzllnnUUwGFRoSFQ4YnA45zY45/7knGsEXAY8B4wAvjKz98xsmJlVLe5CRcqaxx57jN69e3PuueeSmZnJ6aef7ndJIkD413F86Jy7FqgDDAS2493adY2Z9S+G+kTKpIceeoj+/fvTqFEjMjMzqV+/vt8liRxwVIP0O+d2AY+Y2QogF0gGdAwtEgH33Xcfw4cP56KLLmLWrFmccooGnJboEnZwmNkpeEcbg4Gz8O7PMRev4VxEjsHdd9/NqFGjuPTSS0lPT+ekk07yuySRQxQpOMysAtAFGAK0BfYBzwPjgVfVy0rk2N16662MGzeOFi1aMGPGDGrXru13SSIFKsoFgLcBfYGawGfARODvzrlfirk2kTLjj3/8I1OmTKFVq1ZMnTqVWrVq+V2SSKGKcsQxGm9Aw8eA/4ZeM/gwwxw455zGsRIpoqysLGbOnEkgECAtLY2aNWv6XZLIYRW1jSMB76ijbxGWdWgARJEjcs6Rnp5OVlYWbdq0YcqUKdSoUcPvskSOqCjBkVjsVYiUMc45pk6dyh//+EeuvPJKJk2aRPXq1f0uS6RIjhgczrm3S6IQkbLCOceECROYN28eV111FePHj6datWp+lyVSZEd1HYeIHJ3c3FxGjx7N/Pnz6datG2PHjqVKlSp+lyUSFgWHSAnZt28fI0eO5L777qN3795cd911VK5c2e+yRMKm4BApATk5OVxzzTU8/PDD9OvXj5EjR3Lcccf5XZbIUVFwiBSzvXv3MmDAAJ544gkGDhzI8OHDSUhI8LsskaOm4BApRnv27KFPnz48/fTTDB06lCFDhhAfH+93WSLHRMEhUkx2797N1VdfzQsvvMCIESMYOHCgQkNigoJDpBjs3LmT7t2788orr3D99dfTt29fKlWq5HdZIhGh4BCJsO3bt9O5c2fefPNNxo4dS69evRQaElMUHCIRtHXrVjp16sS7777LhAkT6NGjBxUrVvS7LJGIUnCIRMiWLVvo0KEDH3zwAZMnT6Zr165UqFDB77JEIk7BIRIBmzZtol27dnzyySdMmTKFzp07U768/ntJbNInW+QYbdy4kTZt2vDVV1+RlpZGx44dFRoS0/TpFjkG69atIzk5meXLlzN9+nTatWun0JCYp0+4yFFau3YtgUCAFStWMHPmTJKTkxUaUiboUy5yFH788UcCgQBr1qxh9uzZJCYmEhcX53dZIiWinN8F7GdmZ5tZhpm9b2YbzGyrmS0xs+lmpiFEJWqsWLGCK664grVr1yo0pEyKpiOOa4DrgeeBR4C9eHcfzAJ6mVlz59xOH+sT4bvvviMQCLB582YyMjJo2bIl5cpFzd9fIiUimoLj/4C5zrkteabdbWbLgenAUOAOXyoTAZYtW0YgEGDHjh1kZWXRvHlzhYaUSVHzqXfOLc4XGvs9EXq+oCTrEcnrq6++olWrVuzevZtgMKjQkDItmo44CnNq6Hmdr1VImfXZZ5+RnJyMc46srCyaNm2KmfldlohvovpPJjOLA9KBHODRQpYZYWaLzWzxhg0bSrQ+iX3//e9/SUxMpFy5cmRnZys0RIjy4ADmAc2BdOfcsoIWcM4tcM41dc41rVWrVokWJ7Htgw8+IBAIEB8fTzAYpEmTJgoNEaI4OMwsExgNLHDOzfW7HilbFi1aRJs2bahatSrBYJDf//73Cg2RkKgMDjObDcwAHgCu9bcaKWveeust2rVrx/HHH092djaNGjVSaIjkEXXBYWazgFnAQ8Aw55zzuSQpQ1577TU6dOjASSedRDAY5LzzzvO7JJGoE1XBYWbpwGzgYWCIcy7X34qkLHnppZfo1KkTp556KtnZ2TRs2NDvkkSiUtR0xzWz64E5wCrgNaBvvtMD65xz//KjNol9zz33HFdffTVnnHEGGRkZ/O53v/O7JJGoFTXBAVwSeq4P/K2A+W8DCg6JuCeffJK+fftyzjnnMGfOHE4//XS/SxKJalFzqso5N9g5Z4d5tPa7Rok9jz76KCkpKZx33nlkZWUpNESKIGqCQ6Sk/e1vf6N///40btyYzMxM6tWr53dJIqWCgkPKpHvuuYchQ4Zw8cUXM2fOHOrWret3SSKlhoJDypw777yTESNGcOmll5KRkUGdOnX8LkmkVFFwSJkyb948Ro8ezR/+8AfS09OpXbu23yWJlDoKDikzbrrpJsaPH88VV1zBzJkzFRoiRymauuOKFJvMzEzS09MJBAKkpaVRs2ZNv0sSKbUUHBLTnHPMnDmTYDBIu3btmDx5MjVq1PC7LJFSTcEhMcs5R2pqKrfccgsdOnRg0qRJVKtWze+yREo9BYfEJOcc48aN47bbbqNz586MGzdOoSESIQoOiTm5ublcd911/PWvf6VHjx6MGTOGKlWq+F2WSMxQcEhM2bdvH8OHD+eBBx4gJSWFUaNGUblyZb/LEokpCg6JGTk5OQwePJhHHnmEfv36MXLkSI477ji/yxKJOQoOiQl79+6lf//+/OMf/2DQoEEMHz6c+Ph4v8sSiUkKDin19uzZQ0pKCs888wzDhg1j8ODBCg2RYqTgkFJt165d9OzZkxdffJFrr72W/v37KzREipmCQ0qtnTt30rVrVxYuXMjo0aPp06cPlSpV8rsskZin4JBSafv27XTu3Jk333yTcePG0atXLypWrOh3WSJlgoJDSp2tW7fSsWNHFi1axIQJE+jRo4dCQ6QEKTikVNm8eTNXXnklH330EZMnT6Zr165UqFDB77JEyhQFh5Qav/zyC23btuWzzz5jypQpdO7cmfLl9REWKWn6XyelwoYNG2jTpg1Lly4lLS2NDh06KDREfKL/eRL11q1bR1JSEt9++y0zZsygbdu2Cg0RH+l/n0S1NWvWkJSUxMqVK0lPTycpKUmhIeIz/Q+UqPXDDz8QCARYu3Yts2bNIjExkbi4OL/LEinzFBwSlVasWEFiYiIbN25kzpw5XH755QoNkSih4JCo8+233xIIBPj111/JysqiRYsWlCtXzu+yRCREwSFRZdmyZQQCAXbu3ElmZibNmzdXaIhEGQWHRI0vvviC5ORkcnJyCAaDNG3aVKEhEoUUHBIVPv30U5KTkzEzgsEgF198MWbmd1kiUgD9OSe++/jjj0lMTKR8+fJkZ2crNESinIJDfPX++++TlJREQkICwWCQxo0bKzREopyCQ3zz7rvv0qZNG6pVq0YwGOTCCy9UaIiUAgoO8cWbb75Ju3btOPHEE8nOzqZRo0YKDZFSQsEhJW7hwoV06NCBk08+mWAwyLnnnut3SSISBgWHlKiXXnqJzp07U69ePbKzsznnnHP8LklEwqTgkBLz7LPP0rVrVxo0aEB2djZnnnmm3yWJyFFQcMSgnTt3cuqpp1K/fn1279590Lxhw4YRFxfH448/XqI1Pfnkk1x99dWcc845BINBGjRoUKLbF5HIUXDEoISEBObMmcMPP/zAXXfddWB6Wloa9913H7fffjspKSklVs8jjzxCSkoK559/PhkZGZx22mkltm0RiTwFR4waPHgw559/PnPnzmXbtm3MmzePG2+8kTlz5nDdddeVWB0PPvggAwYMoHHjxmRkZFC/fv0S27aIFA8FR4yKi4vjxhtvZMOGDXTt2pUJEyYwZswY0tPTS6yGBQsWMGTIEJo2bcqcOXOoW7duiW1bRIpP1ASHmaWZ2ZNm9r2ZOTNb4XdNpV2nTp246KKLeP311+nduze33nrrIcvceeedNGvWjPj4eFq3bh2xbd9xxx2MHDmSyy67jDlz5lCnTp2IrVtE/BVNgxxmA78A/wVq+FtKbPjHP/7BkiVLAKhatWqBF9jVqVOHqVOn8tFHH/Hee+9FZLt/+tOfmDRpEi1btmT69OnUqlUrIusVkegQTcFxhnPuewAz+wKo4nM9pdrChQsZMGAA3bp1o0KFCtx///2MHz/+kIvtunfvDsCqVasist3s7GymT59OYmIiU6dO5YQTTojIekUkekTNqar9oSHH7oMPPqB79+784Q9/4JFHHiErK4ty5cqRlpZWbNt0zjFnzhymT59OcnIy06ZNU2iIxKioCQ6JjKVLl9KxY0fOPvtsnn32WSpVqsQZZ5zB0KFDee6551i0aFHEt+mcY/r06cyePZt27doxdepUatasGfHtiEh0KPXBYWYjzGyxmS3esGGD3+X4atWqVbRt25bq1avz8ssvU61atQPz0tPTSUhIIDU1NaLbdM4xefJk5s6dS6dOnZgyZQo1atSI6DZEJLpEUxvHUXHOLQAWADRt2tT5XI6v6tevzw8//FDgvDp16rBjx46Ibs85x9ixY7n99tvp2rUrY8eOpWrVqhHdhohEn1IfHHJscnJyDjxyc3PZtWsX5cqVo2LFiod9XW5uLqNGjWLBggX07NmT0aNHU6WK+jOIlAUKjjIuKyuLOXPmHPg5ISGBVq1a8dZbbxX6mn379jFs2DAefPBBUlJSGDVqFJUrVy6BakUkGpT6Ng45NrNnz8Y5d9DjcKGRk5PDwIEDDwwlct111yk0RMoYHXFIke3du5d+/frx5JNPMnjwYIYNG0Z8fLzfZYlICYua4DCzAcD+YVNrARXNbEbo55XOuYf9qUwAdu/eTUpKCs8++yzDhw9n0KBBCg2RMipqggMYCrTKNy0z9Pw2oODwya5du+jRowcvvfQS1157Lf3791doiJRhURMczrnWftcgh9qxYwfdunVj4cKFjBkzhpSUFCpVquR3WSLio6gJDok+27Zt46qrruLtt99m3Lhx9OrV64jddEUk9ik4pEC//vorHTt25D//+Q8TJ06kR48eVKhQwe+yRCQKKDjkEJs3b6Z9+/Z8/PHHpKam0qVLF4WGiByg4JCD/PLLL7Rt25bPPvuMKVOmcNVVV1G+vD4mIvIbfSPIARs2bCA5OZlly5Yxbdo0rrzySoWGiBxC3woCwE8//URSUhLfffcd06dPp23btgoNESmQvhmE1atXEwgE+OGHH0hPTycpKUmhISKF0rdDGbdq1SoCgQA//fQTc+bMoVWrVsTFxfldlohEMQVHGfa///2PQCDAzz//TEZGBi1btlRoiMgRKTjKqOXLlxMIBNi2bRuZmZm0aNGCcuU0WLKIHJmCowxaunQpSUlJ7Nq1i4yMDJo3b67QEJEiU3CUMV988QVJSUns27ePYDBI06ZNFRoiEhZ9Y5QhS5YsoXXr1gBkZ2dzySWXKDREJGz61igjFi9eTCAQoEKFCgSDQS666CLMzO+yRKQUUnCUAe+99x5JSUkkJCQwd+5cGjdurNAQkaOm4Ihx77zzDm3btqV69erMnTuXCy64QKEhIsdEwRHD3njjDdq3b8+JJ55IdnY2559/vkJDRI6ZgiNGvfrqq3Ts2JE6deqQnZ3Nueee63dJIhIjFBwx6IUXXqBz587Ur1+f7Oxszj77bL9LEpEYouCIMU8//TTdu3fnjDPOIBgMcsYZZ/hdkojEGAVHDHniiSfo1asXDRs2JBgM0qBBA79LEpEYpOCIEQ8//DB9+/blggsuIDMzk/r16/tdkojEKAVHDLj//vsZNGgQjRs3JiMjg3r16vldkojEMAVHKXf33XczdOhQLrnkEjIzM6lbt67fJYlIjFNwlGK33XYbo0aN4rLLLmP27NmcdNJJfpckImWAgqOUuvnmmxk7diyXX3456enp1K5d2++SRKSMUHCUQsFgkNTUVBITE5kxYwa1atXyuyQRKUN0P45SxDnHrFmzyMzMpE2bNqSmplKzZk2/yxKRMkbBUUo450hLS+Omm26iffv2TJo0iRo1avhdloiUQQqOUsA5x4QJE5g3bx6dOnViwoQJVKtWze+yRKSMUnBEudzcXMaMGcNdd91F165dGTt2LFWrVvW7LBEpwxQcUSw3N5eRI0dy77330rNnT0aPHk2VKlX8LktEyjgFR5Tat28fQ4cO5W9/+xt9+vTh2muvpXLlyn6XJSKi4IhGOTk5DBw4kMcee4wBAwYwYsQIEhIS/C5LRARQcESdPXv20LdvX5566imGDBnC0KFDiY+P97ssEZEDFBxRZPfu3fTq1Yvnn3+e4cOHM2jQIIWGiEQdBUeU2LlzJ927d+eVV15h1KhR9O/fn0qVKvldlojIIRQcUWDHjh106dKF119/nRtuuIHevXsrNEQkaik4fLZt2zY6derEO++8w/jx4+nZsycVK1b0uywRkUIpOHy0ZcsWOnTowAcffMDEiRPp3r07FSpU8LssEZHDiprRcc2snJmNN7OvzWyXmf1gZn8ys5i8eGHTpk20bduWDz/8kNTUVIWGiJQaURMcwF+APwNfAWOAJ4EbgBfMLJrqPGY///wzSUlJLFmyhLS0NLp06aLQEJFSIypOVZnZ+Xhh8bRzrkee6f8DbgNSgEd9Ki+i1q9fT3JyMt988w3Tpk2jffv2lC8fFb8GEZEiiZa/5PsABszLN/0eYAfQv6QLKg5r166ldevWLF++nBkzZig0RKRUipZvrUuAXODDvBOdc7vMbElofqn2448/EggEWL16NbNmzSIQCBAXF+d3WSIiYYuW4DgF2Oic213AvNVACzOr6JzbU8J1RcTPP/9Mq1atWLduHTNmzKBFixbs3buXvXv3+l2aiAh4Z3yKvrBzrrgKKXoRZt8BFZxz9QuY9xAwAKjpnNtcwPwRwIjQjxcAXxRjqccqgTB/QfnUBDZFqJZoE8v7Btq/0i7W9+9059xxRV04Wo44dgC1C5kXn2eZQzjnFgALAMxssXOuaeTLiw6xvH+xvG+g/SvtysL+hbN8tDSOrwFONLOCxtmoi3caq1SephIRiTXREhwf4dXSLO9EM4sHGgNhpaGIiBSfaAmOJwAHjMs3fThwHPBIEdezIII1RaNY3r9Y3jfQ/pV22r88oqJxHMDMbgdGA88ALwHn4l05vggIOOdyfSxPRERCoik44vCOOEYApwMb8Y5E0p1z2/yrTERE8oqa4BARkdIhWto4IsrM6ppZmpm9bWZrzWy7mX1pZjeb2Ql+1xcJZjbSzB4JjSa8z8xK3V8AsTwicujz96SZfW9mzsxW+F1TJJnZ2WaWYWbvm9kGM9tqZkvMbHpp//2Z2Tmh/1tLzWyLme0IfUb/bGZ1/K6vOJjZcWb2v9Bn9Y4jLh+LRxxmdi1wK/Ai8C6wFa/H1mBgLdDMOfeTbwVGQOiL6ATgE6ABcKpz7lguLixxZnYrXjvWM8DLeO1aY4B3gOTS3K4VCvJfgP8CFwO/OudO97WoCDKzG4HrgeeB94G9QCLQC/gMaO6c2+lfhUfPzJKA6Xj79SOQAzQChgC/Ao2dc+v9qzDyzOwWYCRQBbjTOTf6sC9wzsXcAzgfOLmA6cPwem/d4neNEdjH04FyoX//0/tV+l9XmL+jXOCpfNPHhH5Hff2u8Rj373d5/v0FsMLvmiK8f02B6gVMzwr9/kb7XWMx7PPVoX1L9buWCO/XRXjhOCG0f3cc6TUxearKOfelK/iI4onQ8wUlWU9xcM6tcKX4L3JifERk59z3ftdQnJxzi51zWwqYFTP/xwqwMvRc09cqIijUKeke4BXg6aK+LlqGHCkpp4ae1/lahUAZGBG5jIqZ/2OhC5Cr4A17dB5wU2jWS74VFXnjgYZAjyMtmFdMHnEcxpzQ8998rULgyCMin2hmFUu4JjkGob9e0/FOe8TCjdeGARuAH4BXgRpAf+fcO34WFSlm1gDvOzHDObcinNdG9RGHmdXg0KvJD+c259wvhaxrIt45ygXOuTeOvbpjF8n9K4WOAwoKDYBdeZbRGGWlxzygOTDNObfM51oi4Vnga7yjjiZAZ6CWnwVF2Hzgf3i37A5LVAcHXsLPCmP5v+P1ZDmImQ0DbsbrZXX43gIlqwYR2L9S6qhHRJboY2aZeP+3Fjjn5vpdTyQ4537E61UF8KyZPQV8ZGYJpX0fzaw/0Ba4wjkX9o2Bojo4QodPx9TF1MyuwRuHZSHQ42jepOISif0rxdYA55lZpQJOV2lE5FLEzGYDM4AHgGv9rab4OOc+M7NPgOuAUhscoVHI/4zXVvOTmZ0ZmlU39Fw9NG2jK+AeSBDjbRxmNgSvx8BrQNdCzqeLPzQicgwws1l4R80PAcNcqH9nDEsAjve7iGOUgHfKrSOwPM/jrdD8/qGfhxW2gqg+4jgWZjYYuBd4E+jinNt1+FdICXsCmIbXxpO3sTHcEZHFJ2aWDswGHgaGlPLu4QeY2ckFdec3s0S8bsZvlXhRkbUdr703v1rAXXhdc+/Du5CzQLF65XhnvKuRfwVSgfxXsG5zzj1b0nVFkpldBfw+9GN/4BxgZujnzc65Iw4b4LdYHhHZzAYAp4V+HANUBP4U+nmlc+5hXwqLEDO7HrgDWIX3ucv/u1rnnPtXiRcWAWb2DFAHeAPv2o14vKv/U/Da3Vo755b4VmAxMbPT8RrLj3jleKwGx2wO3+i80pXy4R/M7EFgUCGzS8X+xfKIyGb2FtCqkNlvO+dal1w1kXeEzx+U4n00s154+3Yh3l/hDi9A/gXc7Jxb5WN5xabMB4eIiBSfmG4cFxGRyFNwiIhIWBQcIiISFgWHiIiERcEhIiJhUXCIiEhYFBwiIhIWBYeID8zsdDNzoYtVRUoVBYcUmZm1Dn3ZOTMrcEgTM6ttZntCy7xVwiXGJDMbnOd9n1TIMo3zLPNgCZcoZYyCQ47GLqBvaHjm/AbgDRWfU7IllQm7gCGFzBvKbzfAEilWCg45Gs8ANYEuBcwbgjdgYcwNYW9mVX0u4Rm8e5jkH4q+EtAXeNqXqqTMUXDI0fgv8Cn5/voNfaGdj3dDnwKZWVMze8bMNprZbjNbZmbTzax8vuWamdmDZvaNme0ws61mtsjMuhWwznpmdr+ZrQytc72Z/cfMBuVZZv/pntYFvP4tM1uRb9qK0PQmZvaqmW0hzzDTZnaWmT1sZmtDp+ZWmNnNZla5gPW3DNW+08zWhU7zVSnsPTqMF/DugZ3/qKML3j0iDve+J5vZQjPbbGa7zOwzMzvkpktm1tbMnjCz70P1bg697pABG/e/b2Z2ipk9ZmabzGx76P06+0g7E/q9/Wxmn5tZQr55j5hZrpklH2k9UvIUHHK0HgDamtmpeaZdA6wH/lnQC8ysA96Q6WfjDTF+A/AekAE8lm/xbkBD4B/AWCCI9+X4tJn1zbPO8nijll4NPI53d7YbgW+Ay49pD6E+vw2tPRm4PbTNi/FuNHUF8Ffgerx9vgH4l5lVyFPfpXg3EjsbuAnvznFN8W58FK69ePcp6ZPvi/Ya4BNgSUEvMrMReHfArIL3Pk4AvgPmm9nN+RYfjPc+P4Q3HPxf8Ia7f93MCno/KwP/Bvbh3V/lTqA18Fxo9ONCOed+wAvBC/DuV76/3mvwjqBucs69drh1iE+cc3roUaQH3heCAyYBJ+CdjpoWmpcAbAZuCf28DXgrz2vjgZ/wvmTK51vv+NB6W+eZVrmA7R8HLAO+yjPtwtBrU49Q++D828gz7y1gRb5pK0LLDytg+U+Br4Gq+aZ3C71mcJ5p/wH2AGfnmVYR+DC07OwivO/7a+8JNAr9u29o3ql4X9qjgRND8x7M89o6eG0fjxaw3ltDrz3jCO/7SXhD3r9UwPt2yHuPF7IOaFfEz9VtefavYeiz817+z4ke0fPQEYccFefcz8DzeF9qAN2B6sD9hbykDd4X0ANADTM7cf8Dr00EoG2e9W/f/28zO87MTsALjjeAc82sWmj2ltBzopnVPuYdO9gv5Dv9Y2aN8MLqUaBSvv14F+/uam1Dy9YGLgOec859k2ff9uD9JR8259zneEc7+09XDcI7Enm0kJf0BCoB9+WtNVTvC3hnHZLyrD/v+14l9L7vAz4ALi1g/bl4X/x5vRF6PquIuzUZ74jpHuD/8DpW9HXOqYNFlIrZW8dKiXgAeNHMWuKdLvnQOfdVIcueG3ouLFjACxbgwJduFt75+4ICoQbwq3NupZkFgTRgrZktAV4HnnTOfRTGvhTkO+fcvnzT9u/HnNCjIPv343eh568LWKaw96koHgDuMLPT8IL7OefcL6EwyG9/vYc75ZP3fT8D73RWO7z3OK+Cbt6zxh16W+afQ88nHGabv63Uud1m1gf4Eq+NrJ9z7n9Fea34Q8Ehx+JVYDXe3RYTgVGHWdZCz5Mp5Fw8sAbAzAzvnPy5eH/NfoR3ZLEP7y/tvuRpn3POzTCz+4GOeO0aw4DJZvZH59yU/YsdprbC/h/sOMx+/Anv3swF2ZRv2YK2bQVMK6pHQ9u/BzgT7zRVYfZvZyCwtpBlvgfvCAPvVGJlvDaHz4GteEcVaUCggNfmD9aCtl0UHYH9bSJNKPwISqKAgkOOmnNun5k9hPelshOvcbowy0PP292RGzwvxLufeoZz7qBbAJvZsEJq+R6v8fp2M4vHC7VUM/uTc2493mkn8Bp+82uAd7qnKPbvx74i7Md3oedzC5hX0LQicc5tNu++2H2AH/A6BxRmf70bi1BvEnAKcI1zLv8puqyjrfdIQp0N5uLtx0Zgopn9yzm3sLi2KcdGbRxyrO7GO2VzrXNuy2GWexWvx9VUMzvky9vMEuy36yT2/xVr+Za5AK8BOu+06nl7MQGETp0sDf1YM/S8v43hoO6doVMkpxym7vw+Ab4ArjWz3+WfaWbl9+9fKLDeB7rk7Z5qZhXxOgQcixvx3vfRzrncwyz3D7xODHPyd3kN1VLdfruQs7D3vS0Ft28cs9BRzuN4HSsGACPx7nv9UDG0WUmE6IhDjolzbhUwuwjLbTezgcCzwLLQqaVv8c6jN8RrXO+G11NnKd757lQz29+T6my8L5UvgIvyrDoRWGBmT4WW2wZcjHe66gPn3LLQ9peZ2WvAyNCpsCVA49A2vwUOCp/D7IczswF4DcCfhfbjS7yG+zND+5EGPBh6yYTQPi0yszvxviBTOMb/e865z8hzXclhlvvRzEYB9wJLzexhvO7FtfB6aHUFzsPrRfYuXs+3P5nZ6cCPeO/RALzTVo2OpeZCzAfOANo759YBmFkKXrftv5lZB+fc4U4zih/87talR+l5kKc7bhGWPag7bp7pFwB/x2sb2QOsw+uyOhM4Ps9ypwFP4l3wtgOv+2o3vJBywOmh5RrgHfUsBX7F69W0FO/akOr5tn1yaJ2/hup7Ge+U0VsU3B33kPrz1Xd3aLk9eA3CH+OdcqmXb9krQvu4C++o687Q+xB2d9wjLHdId9w88/6Ad+X5+lC9a4A3gYlAfJ7lLsRru9mE177xFl670YPe18VB6zzkfQtNP70o+4bX7uLwrtfIP29/l96Jfn/u9Tj0YaFfkoiISJGojUNERMKi4BARkbAoOEREJCwKDhERCYuCQ0REwqLgEBGRsCg4REQkLAoOEREJi4JDRETCouAQEZGw/D87B5PcGcyKbQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fig. 2\n",
    "\n",
    "std = 1\n",
    "alpha = 0.9\n",
    "\n",
    "lower_CL =  (1 - alpha)                                # lower limit for central confidence intervals\n",
    "\n",
    "ymin, ymax = 0, 6                                      # only positive values of mean\n",
    "mean = np.linspace(ymin, ymax, 100)\n",
    "x1 = norm.ppf(lower_CL, mean, std)                     # lower limit of x for central confidence intervals\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "plt.plot(x1, mean, color = 'k')\n",
    "plt.fill_between(                                      # shade acceptance region for 90% central CL for x > x1\n",
    "        x= x1, \n",
    "        y1= mean, \n",
    "        color= \"k\",\n",
    "        alpha= 0.2,\n",
    "        label = \"90% CL\")\n",
    "\n",
    "plt.text(-0.5, 1, r'$x_1$', horizontalalignment='right')\n",
    "plt.xlabel('Measured Mean x')\n",
    "plt.ylabel(r'Mean $\\mu$')\n",
    "plt.xlim([-2, 4])\n",
    "plt.ylim([ymin, ymax])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d395024",
   "metadata": {},
   "source": [
    "## Confidence interval based on flip-flopping\n",
    "\n",
    "Let us suppose, for example, that Physicist X takes the following attitude in an experiment designed to measure a small quantity: “If the result $x$ is less then $3\\sigma$, I will state an upper limit from the standard tables. If the result is greater than $3\\sigma$, I will state a central confidence interval from the standard tables.” We call this policy “flip-flopping” based on the data. Furthermore, Physicist X may say, “If my measured value of a physically positive quantity is negative, I will pretend that I measured zero when quoting a confidence interval”,\n",
    "which introduces some conservatism."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "da72be24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fig. 4\n",
    "\n",
    "std = 1\n",
    "alpha = 0.9\n",
    "\n",
    "\n",
    "ymin, ymax = 0, 6\n",
    "mean = np.linspace(ymin, ymax, 100)\n",
    "\n",
    "lower_UL =  (1 - alpha)                               # lower limit for upper confidence intervals\n",
    "x1_UL= norm.ppf(lower_UL, mean, std)                  # lower limit for x for upper confidence intervals\n",
    "\n",
    "lower_central_CL =  0.5*(1 - alpha)                   # lower limit for central confidence intervals\n",
    "upper_central_CL =  alpha + 0.5*(1 - alpha)           # upper limit for central confidence intervals\n",
    "x1_central = norm.ppf(lower_central_CL, mean, std)    # lower limit of x for central confidence intervals\n",
    "x2_central = norm.ppf(upper_central_CL, mean, std)    # upper limit of x for central confidence intervals\n",
    "\n",
    "## selecting interval  based on flip-flopping\n",
    "\n",
    "x1_FF = []                                            # x based on flip-flopping\n",
    "mean1_FF = []                                         # mean1 based on flip-flopping \n",
    "mean2_FF = []                                         # mean1 based on flip-flopping \n",
    "for x in np.arange(-2, 4.01, 0.01):\n",
    "    if x <= 0:                                        # For negative measurements, pretending it to be zero\n",
    "        y1 = np.interp(0, x1_UL, mean)\n",
    "        y2 = 0\n",
    "        x1_FF.append(x)\n",
    "        mean1_FF.append(y1)\n",
    "        mean2_FF.append(y2)\n",
    "        \n",
    "    if (x >= 0) & (x <= 3):                           # For small signals, selecting upper confidence intervals\n",
    "        y1 = np.interp(x, x1_UL, mean) \n",
    "        y2 = 0\n",
    "        x1_FF.append(x)\n",
    "        mean1_FF.append(y1)\n",
    "        mean2_FF.append(y2)\n",
    "        \n",
    "    if (x >= 3):                                      # For large enough signals, selecting central confidence intervals\n",
    "        x1_FF.append(x)\n",
    "        y1 = np.interp(x, x1_central, mean) \n",
    "        y2 = np.interp(x, x2_central, mean) \n",
    "        mean1_FF.append(y1)\n",
    "        mean2_FF.append(y2)\n",
    "    \n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "plt.plot(x1_FF, mean1_FF, color='k')                  # upper bound for mean, based on flip-flopping\n",
    "plt.plot(x1_FF, mean2_FF, color='k')                  # lower bound for mean, based on flip-flopping\n",
    "plt.fill_between(                                     # Shading 90% confidence interval based on flip-flopping\n",
    "        x= x1_FF, \n",
    "        y1= mean1_FF, \n",
    "        y2= mean2_FF,\n",
    "        color= \"k\",\n",
    "        alpha= 0.2,\n",
    "        label = \"90% CL\")\n",
    "\n",
    "plt.text(-0.5, 1.5, r'$x_1$', horizontalalignment='right')\n",
    "plt.text(3.5, 1.5, r'$x_2$', horizontalalignment='left')\n",
    "\n",
    "plt.xlabel('Measured Mean x')\n",
    "plt.ylabel(r'Mean $\\mu$')\n",
    "plt.xlim([-2, 4])\n",
    "plt.ylim([0, 6])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8710ee3",
   "metadata": {},
   "source": [
    "## Feldmann-Cousins confidence interval\n",
    "\n",
    "For a particular $x$, we let $\\mu_{\\rm best}$ be the physically allowed value of $\\mu$ for which $P(x|\\mu)$ is maximum. For Gaussian distribution $\\mu_{\\rm best} = max(0, x)$, and\n",
    "\n",
    "\\begin{equation}\n",
    "P(x|\\mu_{\\rm best}) = \n",
    "\\begin{cases}\n",
    "1/\\sqrt{2\\pi}, & x >0 \\\\\n",
    "\\exp{(-x^2/2)/\\sqrt{2\\pi}}, & x<0\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "We then compute $R$ \n",
    "\n",
    "\\begin{equation}\n",
    "R(x) = \\frac{P(x|\\mu)}{P(x|\\mu_{\\rm best})}\n",
    "\\end{equation}\n",
    "\n",
    "During our Neymann construction of confidence intervals, the values of $x$ are added to the acceptance region at a particular value of $\\mu$ in the decreasing order of $R$. In practice, this means that for a given value of $\\mu$, one finds the interval $[x_1, x_2]$ such that $R(x_1) = R(x_2)$ and \n",
    "\n",
    "\\begin{equation}\n",
    "\\int_{x_1}^{x_2} P(x|\\mu) dx = \\alpha\n",
    "\\end{equation}\n",
    "\n",
    "We solve for $x_1$ and $x_2$ numerically to the desired precision, for each $\\mu$ in a grid. With the acceptance regions all constructed, we then read off the confidence intervals $[\\mu_1, \\mu_2]$ for each $x_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "81c8d799",
   "metadata": {},
   "outputs": [],
   "source": [
    "# defining a fuction to calculate FC confidence intervals [x_1, x_2] for a given mean\n",
    "\n",
    "def FC_range(mean, std = 1, alpha = 0.9):\n",
    "    \n",
    "    dx = 0.01                                           # step size for x\n",
    "    x_list = []\n",
    "    R_list = []\n",
    "    pdf_list = []\n",
    "    for x in np.arange(mean - 5*std, mean + 5*std, dx):\n",
    "        pdf = norm.pdf(x, mean, std)                    # probability distribution function at x for a given mean and sigma\n",
    "        mean_best = max(0,x)                            # For Gaussian, the maximum pdf occur at this\n",
    "        pdf_best = norm.pdf(x, mean_best, std)          # maximum probability distribution function at x_best\n",
    "        R = pdf/pdf_best                                # Feldmann-Cousins ordering ratio\n",
    "        x_list.append(x)\n",
    "        R_list.append(R)\n",
    "        pdf_list.append(pdf)\n",
    "\n",
    "    df = pd.DataFrame({'x': x_list, 'P': pdf_list, 'R': R_list} ) \n",
    "    df_sorted = df.sort_values(by='R', ascending=False) # sorting the R in decreasing order\n",
    "\n",
    "    x1, x2 = None, None\n",
    "    \n",
    "    # finding x_1 and x_2 for 90% CL where x with highest R are accepted first\n",
    "    \n",
    "    Prob_sum = 0                                          \n",
    "    for index, row in df_sorted.iterrows():             # Loop index progresses in decreasing order of R  \n",
    "        x = row[\"x\"]\n",
    "        P = row[\"P\"]\n",
    "        R = row[\"R\"]\n",
    "        Prob_sum += P*dx                                # integration over pdf\n",
    "        if x <= mean :\n",
    "            x1 = x                                      # lower CL\n",
    "        else:\n",
    "            x2 = x                                      # upper CL\n",
    "        if Prob_sum >= alpha:                           # stop when total probability is equal to or \n",
    "            print(f'{mean:6.3f} {x1:6.3f} {x2:6.3f}')   # greater than desired CL\n",
    "            break\n",
    "            \n",
    "    return x1, x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "70e3f32f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean \t x1 \t x2\n",
      " 0.000 -3.410  1.280\n",
      " 0.100 -4.900  1.380\n",
      " 0.200 -3.990  1.480\n",
      " 0.300 -2.620  1.590\n",
      " 0.400 -2.010  1.730\n",
      " 0.500 -1.650  1.880\n",
      " 0.600 -1.400  2.020\n",
      " 0.700 -1.190  2.170\n",
      " 0.800 -1.020  2.310\n",
      " 0.900 -0.860  2.440\n",
      " 1.000 -0.730  2.570\n",
      " 1.100 -0.600  2.690\n",
      " 1.200 -0.480  2.810\n",
      " 1.300 -0.370  2.920\n",
      " 1.400 -0.250  3.030\n",
      " 1.500 -0.140  3.140\n",
      " 1.600 -0.040  3.240\n",
      " 1.700  0.060  3.340\n",
      " 1.800  0.160  3.440\n",
      " 1.900  0.260  3.540\n",
      " 2.000  0.360  3.640\n",
      " 2.100  0.460  3.740\n",
      " 2.200  0.560  3.840\n",
      " 2.300  0.660  3.940\n",
      " 2.400  0.760  4.040\n",
      " 2.500  0.860  4.140\n",
      " 2.600  0.960  4.240\n",
      " 2.700  1.060  4.340\n",
      " 2.800  1.160  4.440\n",
      " 2.900  1.260  4.540\n",
      " 3.000  1.360  4.640\n",
      " 3.100  1.460  4.740\n",
      " 3.200  1.560  4.840\n",
      " 3.300  1.660  4.940\n",
      " 3.400  1.760  5.040\n",
      " 3.500  1.860  5.140\n",
      " 3.600  1.960  5.240\n",
      " 3.700  2.060  5.340\n",
      " 3.800  2.160  5.440\n",
      " 3.900  2.260  5.540\n",
      " 4.000  2.360  5.640\n",
      " 4.100  2.460  5.740\n",
      " 4.200  2.560  5.840\n",
      " 4.300  2.660  5.940\n",
      " 4.400  2.760  6.040\n",
      " 4.500  2.860  6.140\n",
      " 4.600  2.960  6.240\n",
      " 4.700  3.060  6.340\n",
      " 4.800  3.160  6.440\n",
      " 4.900  3.260  6.540\n",
      " 5.000  3.360  6.640\n",
      " 5.100  3.460  6.740\n",
      " 5.200  3.560  6.840\n",
      " 5.300  3.660  6.940\n",
      " 5.400  3.760  7.040\n",
      " 5.500  3.860  7.140\n",
      " 5.600  3.960  7.240\n",
      " 5.700  4.060  7.340\n",
      " 5.800  4.160  7.440\n",
      " 5.900  4.260  7.540\n"
     ]
    }
   ],
   "source": [
    "# calculating FC confidence intervals [x_1, x_2] for a list of means\n",
    "\n",
    "mean_list = []\n",
    "FC_x_range = []\n",
    "\n",
    "print(f'mean \\t x1 \\t x2')\n",
    "for mean in np.arange(0, 6, 0.1):\n",
    "    x_range = FC_range(mean)\n",
    "    mean_list.append(mean)\n",
    "    FC_x_range.append(list(x_range))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2cedb2b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Uy7l48SJVq1blp59+YsSIEdSqVcvqSPfFFZuqUpoEXAfqWB1EKaUcdf78efz8/Pj5558ZM2aM2xcNcLEjjtQYY+JF5CRQwOosSinliLNnz+Lv788ff/zBuHHjqFKlitWRnMLljzhExAsoCpyxOotSSqXVmTNnqFixIocOHWLSpEkeUzTAhQqHiOS/zV2jsB0ZrczAOEopdc9OnTpFhQoVOHz4MFOmTKFSpUpWR3IqV2qqGiwirwGbgWOAD7ZRVVWA/wOCLcymlFJp8vfff1OpUiWioqKYMWMGvr6+VkdyOlcqHFuA54A2QH4gETgIDAKmGmNirYumlFJ3d/jwYfz8/Dh37hwzZszgxRdftDpSunCZwmGMWQ4stzqHUkrdi0OHDuHv78/FixeZNWsWZcqUsTpSunGZwqGUUu7qwIED+Pv7ExsbS2hoKKVKlbI6UrrSwqGUUvdh3759+Pv7k5CQQGhoKM8884zVkdKdy4yqUkopd7Nnzx78/PwwxhAeHp4pigZo4VBKqXuya9cuKleuTJYsWQgPD+fJJ5+0OlKG0cKhlFIO+u6773jjjTfImTMnERERPP7441ZHylBaOJRSygFbt26levXq+Pj4EBkZSdGiRa2OlOG0cCilVBp9/fXX1KpViwcffJDIyEgeeeQRqyNZQguHUkqlwdq1a6lTpw4FCxYkIiKCQoUKWR3JMlo4lFLqLlauXElAQACPPvookZGRFCiQuSfr1sKhlFJ38MUXX9CgQQMee+wxwsPDefDBB62OZDktHEopdRsLFy6kSZMmPP3004SHh5MvXz6rI7kELRxKKZWKTz/9lJYtW/Lss88SGhpK7ty5rY7kMrRwKKVUChEREbRt25bnn3+ekJAQfHx8rI7kUrRwKKVUMrNmzaJjx46ULVuWmTNn8sADD1gdyeVo4VBKKbtp06bRtWtXXnnlFYKDg/Hy8rI6kkvSwqGUUsDEiRPp1asX5cuXZ9q0aeTMmdPqSC5LC4dSKtMbOXIk/fr1w8/Pj6lTp5IjRw6rI7k0LRxKqUzLGMPgwYMZNmwYVatWZeLEiWTLppcpuht9hZRSmZIxhqCgICZPnkzNmjUZOXIkWbNmtTqWW9DCoZTKdIwxvP/++wQHB/PWW28xdOhQsmTRBpi00sKhlMpUjDEEBgYye/Zs3n77bQYOHKhFw0FaOJRSmUZSUhLt27dn7ty5NG7cmA8++AARsTqW29HCoZTKFBITE2nTpg3z58+nZcuWvP/++1o07pEWDqWUx0tISKBFixYsXryYtm3b0qVLFy0a90ELh1LKo8XHx9OoUSOWL19Ox44d6dixo9WR3J4WDqWUx7p+/Tr169dn9erVdO3albZt21odySNo4VBKeaTY2Fjq1avHhg0b6NmzJy1btrQ6ksfQwqGU8jhXr16lTp06bNmyhaCgIBo3bmx1JI+ihUMp5VFiYmKoWbMm3377LQMHDqRBgwZWR/I4WjiUUh7j0qVLVK9enV27djF06FDq1q1rdSSPpIVDKeURLly4QNWqVdmzZw8jRoygVq1aVkfyWFo4lFJu79y5c1SuXJn9+/czbtw4qlatanUkj6aFQynl1qKjo6lcuTIHDx5kwoQJ+Pv7Wx3J42nhUEq5rTNnzuDn58eRI0eYPHkyFSpUsDpSpqCFQynllk6cOIGfnx8nTpzgww8/pFy5clZHyjS0cCil3M6xY8eoVKkS0dHRTJ8+HV9fX6sjZSpaOJRSbuWvv/7C39+f8+fPExwcTNmyZa2OlOlo4VBKuY2DBw/i7+/P5cuXmTVrFqVLl7Y6UqakhUMp5Rb279+Pv78/cXFxhIaG8uyzz1odKdPSwqGUcnm//vorVapUITExkbCwMJ5++mmrI2VqLnuhXRF5QEQOi4gRkY+szqOUssaPP/6In58fxhjCw8O1aLgAly0cwEiggNUhlFLW+f7776lSpQrZs2cnIiKC4sWLWx1J4aKFQ0ReAnoCwyyOopSyyLfffkvVqlXx9vYmPDycxx57zOpIys7lCoeIZAXCgbXAlxbHUUpZYOvWrVSvXp3cuXMTGRlJ0aJFrY6kknHFzvFewLPAO1YHUUplvI0bN1K3bl0KFChAeHg4BQsWtDqSSsGljjhEpDgwAhhpjDmSxsd0FJFdIrIrOjo6XfMppdLXmjVreOutt3j44YeJjIzUouGiXKpwACHAYWBqWh9gjAkzxvgaY3z1TaaU+1qxYgUBAQEUKVKEiIgI8ufPb3UkdRsu01QlIi2BGoCfMSbe6jxKqYyzZMkSmjdvTvHixQkNDSVv3rxWR1J34BJHHCKSE9tRxmrgtIg8LSJPA4/bV8lrX5bPqoxKqfSxYMECmjVrRokSJQgLC9Oi4QZconAA3kBBoA5wMNnPFvv9Le2/t7cinFIqfXz88ce0atWKUqVKERoaSu7cua2OpNLAVZqqYoBGqSwvCMzCNjQ3EvglI0MppdJPWFgYnTt35oUXXiA4OBhvb2+rI6k0conCYe/T+G/K5SLyhP2ffxpj/nW/Uso9ffTRR3Tv3p2XX36Z6dOn4+XlZXUk5QBXaapSSmUSU6dOpXv37pQrV44ZM2Zo0XBDLnHEcTv2cznE6hxKKecYP348AwYMoGLFikyaNIns2bNbHUndAz3iUEpliBEjRjBgwAAqV67M5MmTtWi4MZc+4lBKuT9jDIMGDWLcuHFUq1aN0aNHky2bfvS4M/3fU0qlG2MMH3zwAVOmTOHNN99kxIgRZM2a1epY6j5p4VBKpQtjDD169OCjjz6ibt26DBkyhCxZtHXcE2jhUEo5XVJSEoGBgYSFhdGgQQMGDBiAiI5z8RRaOJRSTpWUlES7du345JNPaNKkCX379tWi4WG0cCilnCYxMZFWrVqxcOFCWrVqRY8ePbRoeCAtHEopp0hISKBZs2b897//pV27dgQGBmrR8FBaOJRS9y0+Pp5GjRqxfPlyOnXqRIcOHayOpNKRFg6l1H2Ji4ujfv36rFmzhu7du9OmTRurI6l0poVDKXXPYmNjqVu3Lhs3bqR37940b97c6kgqA2jhUErdk6tXr1KrVi22bdtGv379aNQotSsjKE+khUMp5bArV65Qs2ZNvvvuOwYOHEj9+vWtjqQykBYOpZRDLl26RLVq1di9ezfDhg3jrbfesjqSymBaOJRSaXbhwgXeeOMNfvnlF0aNGkXNmjWtjqQs4FDhEJHJwE/Aj8ABY4xJcX8R4Jwx5przIiqlXMG5c+eoXLky+/fvZ9y4cbzxxhtWR1IWcfSIozdwo1hcE5FfsBWRn+w/TYEqwCtOS6iUslx0dDT+/v4cOnSIiRMn4ufnZ3UkZSFHC8dDwEspfjpjuyDUjYJy1WnplFKWO336NH5+fhw9epTJkydToUIFqyMpizlUOIwxF4BN9h8ARCQ3UBsYDhQAujsvnlLKSidOnMDPz48TJ07w4YcfUq5cOasjKRdw35PjG2MuG2MWYWueisFWPJRSbu7o0aOUL1+eU6dOMWPGDC0a6ianXVXFGHMF+BTo5axtKqWs8ddff1GxYkX++ecfZs6cycsvv2x1JOVCnD0cNxp4xMnbVEploD/++AN/f39iYmKYNWsWpUuXtjqScjGODseN5n/DcX8EfjTGHLLfJ0AdYJezQyqlMsZvv/1G5cqViYuLIyQkhGeffdbqSMoFOXrE8S3wAlDN/rsRkcvAAaCg/aeNiGQ3xsQ7L6ZSKr39+uuvVKlShcTERMLCwnj66aetjqRclKOjqgIARCQfUBZ40X5bFihm395/gQQR+QP4FfjZGDPBWYGVUs63e/duqlWrRtasWQkPD6d48eJWR1Iu7J76OOzDcrfYfwAQkRxAGf5XSF7E1nTVBNDCoZSL+r//+z+qV6+Ol5cXYWFhFCtWzOpIysU5rXPcGHOd//V93CQiTznrOZRSzrV9+3Zq1apFrly5CAsLo0iRIlZHUm7AacNxb8cY82d6P4dSynGbN2+mZs2a5MmTh8jISC0aKs3SvXAopVzPhg0bqF27Nvnz5ycyMpLChQtbHUm5ES0cSmUyq1evpm7dujz88MNERERQsGBBqyMpN6OFQ6lMZNmyZbz99tsULVqUyMhI8ufPb3Uk5Ya0cCiVSSxZsoRGjRpRvHhxwsLCyJcvn9WRlJvSwqFUJjB//nyaNWtGiRIlCAsLI2/evFZHUm7M4eG4IvI60A0oAeQHJMUqxhijQ3CVchEff/wx7733Hs899xwzZ84kV65cVkdSbs7RuapaA3OBeOAP4Fh6hFJKOcfs2bMJDAzkhRdeIDg4GG9vb6sjKQ/g6BHHIOB3oJox5mQ65FFKOUlwcDA9evTA19eXadOm4eXlZXUk5SEc7eN4HAjRoqGUa5syZQo9evTgtddeY/r06Vo0lFM5WjiOAznTI4hSyjnGjh1L3759qVixIh9++CE5c+qfrHIuRwtHKNBCRLKmRxil1P0ZPnw4gwYNokqVKkyePJns2bNbHUl5IEf7OHYD7wDfi8hM4DCQmHIlY8w3TsimlEojYwwDBw5k/PjxVK9enVGjRpEtm7Mv8KmUjaPvrK+T/TsCMCnuF/syh49IRKQkMBR4CXgUyI5t1NZqYJIx5pSj21QqMzDG0KdPHz788ENq167NsGHDyJpVGwVU+nG0cLRNlxQ2RbFdr3wptr6UBOB5oCPQVETKGmOi0vH5lXI7xhi6devGrFmzCAgIYNCgQWTJouf1qvTl6BUAP0mvIMaYr7n1iAYAEfkGWAy8C0xMr+dXyt0kJSXRqVMnIiIiaNiwIf369UMk5fm4SjmfOzSCHrXfPmhpCqVcSFJSEm3btuXTTz+lWbNm9O7dW4uGyjD3VDhExBcoh+3DPOVxsTHGjLrXQCLiBfgAXsBz/O+ys6vvdZtKeZLExERatWrFwoULadOmDd26ddOioTKUo1OOeANfAjX4X0f4jXesSbbsngsH0B4ITvb7EaClMWbbfWxTKY+QkJBA06ZN+eKLL2jfvj2dO3e2OpLKhBw94hiKrWiMwdYfsRloA0QBAwBvoPV9ZloGHMB21PEiUA+47ZVmRKQjtg50Hnvssft8aqVc1/Xr12nYsCErV66kc+fOtG/f3upIKpNytHA0BJYYY4aKyI0rwJwwxmwSka+BH7B1Yg+410DGmOPYRlUBLBORL4AfRMTbGDMulfXDgDAAX1/flMODlfIIcXFxBAQEsG7dOnr06EHr1vf7/Uype+fouL1iwFb7v2+c+JcDwBiTACwEmjonmo0x5hfgJ6CLM7erlLu4du0atWvXZt26dfTp00eLhrKco0ccl5M95jKQhO1kvRsuAulx1Xtv4KF02K5SLu3q1au8+eabbN++nf79+9OwYUOrIynl8BHHn8AzAMaYRGAftuYrxDasowHw970EEZFUC46IVAHKADvvZbtKuasrV65QrVo1duzYweDBg7VoKJfh6BHHRqCdiPS0F47ZwEci8ie20VTFgYH3mCVERB4BNmE7d8MLeBlb09dloM89blcpt3Px4kWqVavGjz/+yLBhw6hTp47VkZS6ydHCMR74DPsQXGPMLPt5Fy2x9XmEc+9ndy/ENkKrFbZRVAZbAZmNba4qvdqgyhTOnz9PlSpV2Lt3L6NHj6ZGjRpWR1LqFo5OOXIF2xUAky+bCky93yDGmMXYphZRKtM6e/YsVapU4cCBA4wbN4433njD6khK/cs9TzkiIjmBAkC0Mea68yIplTlFRUXh7+/Pn3/+yaRJk6hUqZLVkZRKlcPTaIrISyKyCVu/wzGgon15IRH5WkSqOTmjUh7v1KlTVKhQgcOHDzN16lQtGsqlOVQ4RKQssA14Cvg0+X32Kc+9sfVTKKXS6Pjx45QvX57jx48zbdo0Xn/9dasjKXVHjh5xjAROAqWB/vxvnqobvgZedUIupTKFI0eOUL58ec6cOcOMGTN45ZVXrI6k1F05WjgqAeH2TvLUpvc4xq0nBCqlbuPPP/+kQoUKnDt3jlmzZvHSSy9ZHUmpNHG0c9wL29nht5PnPrIolWn8/vvv+Pv7c/XqVUJCQnjuueesjqRUmjlaOP7EdlLe7bwB/HbvcZTyfL/99hv+/v7Ex8cTGhpKyZIlrY6klEMcbapaALRKMXLKAIhIH+BNbCcIKqVS8fPPP1OpUiUSExMJCwvToqHckqNHHJOB6sA6bNfMMMCHIlIQ2+SGG4BZTk2olIfYvXs31apVI2vWrMyePZvixYtbHUmpe+LQEYf9RL/qQF/gGhCLbdLDs0AQ8JYxJsnZIZVydzt37qRKlSpkz56diIgILRrKrTl85rj9uhsf2n+UUnexbds2atWqRe7cuQkLC+PRR3XgoXJvDp85rpRKu02bNlGzZk3y5ctHZGSkFg3lEe56xGGfXsQRxhhT9R7zKOUx1q1bR0BAAA8//DBhYWEUKFDA6khKOUVamqoqA/FAWicy1Ot+q0zvq6++4p133uHRRx8lLCyMhx7SC1gqz5GWwpGAbWqRjcBc4CvtAFfq9r788kuaNm3K448/TmhoKPny5bM6klJOlZY+jiLAAOBpYClwQkQmiIgOQFcqhUWLFtG4cWOefPJJwsLCtGgoj3TXwmGMiTbGTDHGPA+8DiwHOgK/ich3ItJeRHKnd1ClXN28efNo0aIFJUuWZPbs2eTJozPwKM/k6Hkc3xtjOgOPAK2BGGyXdj0pIi3TIZ9SbiEyMpI2bdrw3HPPERISgo+Pj9WRlEo393QFQGNMLDBfRI4ASUA14Ekn5lLKbYSGhtKlSxfKli3LjBkz8Pb2tjqSUunqXq4A+KiI9BeRA8A3QClgHLaOc6UylenTpxMYGIivry/BwcFaNFSmkKYjDhHJDgQAbYEaQCKwAugFrNNRViozmjRpEkFBQbz++utMmTKFHDlyWB1JqQyRlhMAZwDNgQeBX4A+wDxjzLl0zqaUyxo9ejRDhgyhUqVKTJw4kezZs1sdSakMk5Yjjm7YJjRcCPxof8y7IimvGnuTMcboPFbKYw0dOpRRo0ZRpUoVxo0bR7Zs99RVqJTbSus73hvbUUfzNKxr0AkQlQcyxtCvXz8mTZpEjRo1GDVqFFmzZrU6llIZLi2Fo0q6p1DKxRlj6NWrF9OnT6d27doMHz6cLFl0jlDl/oxxfJaouxYOY8zWe0qjlIcwxtC1a1dCQkIICAhg0KBBWjSURzDGMGPGDPLkyZPLkcdp46xSd5CUlESHDh2YM2cOjRo1IigoiDv07ynlNowxTJ06lYULF/LSSy8948hj9WuTUreRmJhImzZtmDNnDs2bN9eioTxGUlIS48ePZ+HChfTo0QMRcagWaOFQKhUJCQm0aNGCefPm8e6779KrVy8tGsojJCYmMnr0aL744guCgoKYNm2aw9vQpiqlUoiPj6dJkyYsXbqU9u3b07lzZ6sjKeUUCQkJjBgxgjVr1jB48GBGjhx5T1+ItHAolcz169dp0KABq1atokuXLrRr187qSEo5RUJCAkOGDGHDhg2MGjWKwYMH3/O2tHAoZRcXF0e9evVYv349PXr0oHXr1lZHUsop4uPjGThwIJs3b2bChAkEBQXd1/a0cCgFXLt2jTp16rB582b69u1L06ZNrY6klFPExcXRv39/tm3bxrRp03j//ffve5taOFSmFxMTw5tvvsmOHTsYOHAgDRo0sDqSUk4RGxtL37592blzJ7NmzSIwMNAp29XCoTK1y5cvU6NGDb7//nuGDh1K3bp1rY6klFNcu3aN3r17s2vXLsLDw2nfvr3Ttq2FQ2VaFy9epGrVqvz0008MHz6c2rVrWx1JKaeIiYmhZ8+e/Pzzz8ydO5c2bdo4dftaOFSmdP78eSpXrsxvv/3GmDFjqF69utWRlHKKK1eu0L17d3777TfmzZtHs2bNnP4cWjhUpnP27Fn8/f35448/GD9+PJUrV7Y6klJOcfHiRbp3787BgwdZtGgR77zzTro8jxYOlamcOXMGf39/Dh8+zOTJk6lYsaLVkZRyigsXLtClSxeOHDnCkiVLCAgISLfn0sKhMo2TJ0/i5+fH8ePHmTp1Kq+99prVkZRyin/++YfAwEBOnjzJ0qVL072/TguHyhT+/vtvKlWqRFRUFNOnT8fX19fqSEo5RXR0NIGBgURFRbFixYoM6a9zmUkOReQZERkpIjtFJFpELovIHhEZJCIOzRWvVHKHDx+mfPnyREdHExwcrEVDeYzTp0/TsWNHoqOjWbVqVYYN8nClI452QFdgBTAfiMd29cHRQGMRec0Yc83CfMoNHTp0CH9/fy5evMisWbMoU6aM1ZGUcoqTJ08SGBjIpUuXWLt2bYb217lS4fgvMM4YczHZslAROQgMAt4DPrIkmXJLBw4cwN/fn9jYWGbPns2zzz5rdSSlnOLvv/+mc+fOxMXFsWHDBsqVK5ehz+8yTVXGmF0pisYNi+y3+lVRpdnevXupWLEi169f16KhPMqRI0fo2LEj8fHxbNy4McOLBrhQ4biDovbbM5amUG7jp59+ws/PD2MMYWFhlChRwupISjnFn3/+SadOnQDYtGkTL7/8siU5XLpwiEhWYCiQACy4zTodRWSXiOyKjo7O0HzK9fzwww9UrlyZrFmzEh4ezpNPPml1JKWc4o8//qBTp05kz56dzZs388ILL1iWxaULBzANeA0Yaoz5PbUVjDFhxhhfY4xvwYIFMzScci3fffcdVatWxcvLi4iICB5//HGrIynlFPv376dz587kypWLzZs3U7p0aUvzuGzhEJFRQDcgzBgzzuo8yrV98803VK9enVy5chEZGUnRokXv/iCl3MDevXsJDAwkX758bN261SX661yycIjIcGAwMBfQCz6rO/r666958803yZcvH3PmzOGRRx6xOpJSTrFnzx66du1KoUKF2Lp1K0899ZTVkQAXLBwiMgwYBnwKtDfGGIsjKRe2bt066tSpQ8GCBYmMjKRQoUJWR1LKKXbt2kX37t0pUqQIW7Zs4YknnrA60k0uVThEZCgwHPgMaGuMSbI2kXJlK1eupF69ejz66KNERkZSoEABqyMp5RQ7d+6kZ8+ePPHEE2zevJlixYpZHekWLnMCoIh0BUYAx4CNQHMRSb7KGWPMBiuyKdfzxRdf0LRpU5544glCQ0PJly+f1ZGUcort27cTFBREyZIl2bBhAw8//LDVkf7FZQoH8Ir99jHgk1Tu3wpo4VAsXLiQVq1a8fTTTxMaGkru3LmtjqSUU2zZsoX+/fvz/PPPs27dOlx1pKjLNFUZY941xsgdfipbnVFZ79NPP6Vly5Y8++yzzJ49W4uG8hgbN26kf//+vPTSS2zcuNFliwa4UOFQ6m7Cw8N59913ef755wkJCcHHx8fqSEo5xdq1axk4cCDlypVj3bp1PPTQQ1ZHuiMtHMotzJo1i44dO/LSSy8xc+ZMHnjgAasjKeUUX331FUOGDMHPz4/Vq1e7RX+dFg7l8qZNm0bXrl159dVXmTFjBl5eXlZHUsopli5dyogRI6hatSpfffUVefLksTpSmmjhUC5twoQJ9OrVi/LlyzNt2jRy5sxpdSSlnGLx4sWMGTOGWrVqsWLFCnLlcp/r1WnhUC5r5MiR9O/fH39/f6ZOnUqOHDmsjqSUU8ybN4+JEycSEBDAl19+ibe3t9WRHKKFQ7kcYwxDhgxh2LBhVK1alQkTJpAtmyuNHFfq3s2dO5dp06bRsGFDFi9e7JZH0frXqFyKMYZ+/foxadIkatasyciRI8maNavVsZS6b8YYwsPDCQsLo1mzZnz66adu+4XIPVMrj2SM4f333yc4OJi33nqLoUOHkiWLHhQr92eMYdasWcydO5fWrVszZ84ct/5CpIVDuQRjDIGBgcyePZv69eszYMAALRrKIxhjmD59OvPmzaNDhw6Ehoa6/XvbvdOrVF27do2iRYvy2GOPERcXd8t97du3J2vWrHz++ecWpfu3pKQk2rVrx+zZs2ncuDEDBw50+z8spcBWNCZPnsy8efPo2rUrs2fPdui97ap/y/rX6YG8vb0ZMWIEf//9N7Nmzbq5fMCAAURGRhIcHEzTpk0tTPg/iYmJtGrVio8//piWLVvywQcfkGJyS6XcUlJSEmPHjmXRokX07NmT4OBgh9/brvq3LJ50uQtfX1+za9cuq2O4hMTERF544QWioqL466+/iIiIoFevXowYMYKhQ4daHQ+AhIQEmjVrxn//+1/atWtHYGCgFg3lERITExk9ejQrV66kX79+jBs37p7f2xnxt+zr68uuXbvSHFCPODxU1qxZGT9+PNHR0bz99tv07t2b7t27u0zRiI+Pp2HDhvz3v/+lU6dOdOnSRYuG8ggJCQkMHz6clStXMmzYsPsqGuCaf8taODzYW2+9xUsvvcTXX39NkyZNmD59+r/WmTlzJq+++ipeXl5Urlw5Q3LFxcXx9ttvs3z5crp27UqHDh0y5HmVSm8JCQkMHjyYNWvWMGbMGIYPH+6UL0R3+1uOi4ujQ4cOPPnkk/j4+FCiRAmmTZt23897OzqqyoMtXryYPXv2AJA7d+5U38CPPPII/fv354cffuC7775L90yxsbHUrVuXjRs30qtXL1q0aJHuz6lURrh+/ToDBw5ky5YtTJ48mT59+jht23f7W05ISKBw4cKsX7+eJ598kl9++YWaNWvyyCOP0KRJE6fluEH7ODzU+vXrqVu3LnXr1iV79uwsWbKEX3/9lVKlSqW6/rRp01i2bBlbtmxJt0xXr16ldu3abN26laCgIBo3bpxuz6VURoqLiyMoKIgdO3YwY8YMunfv7rRtO/q3fEO7du3w8fFhxowZd30O7eNQ/N///R8NGjSgQoUKzJ8/n9GjR5MlSxYGDBhgWaaYmBhq1KjBN998w8CBA7VoKI8RGxtL79692bFjByEhIU4tGvf6t5yQkMD27dv5z3/+47QsyWnh8DD79++nTp06PPPMMyxbtoycOXPy1FNP8d5777F8+XJ27NiR4ZkuXbrEG2+8wXfffcewYcNo0KBBhmdQKj3ExMTQs2dPvv/+eyIiIujcubPTtn0/f8s9evQgb968tG7d2ml5ktPC4UGOHTtGjRo1yJs3L2vWrLllbv+hQ4fi7e1NUFBQhmY6ceIEr732Grt372bEiBG89dZbGfr8SqWXs2fP0qlTJ3766Sc++eQT3nvvPadt+37+lvv06cP27dtZs2ZNus0orZ3jHuSxxx7j77//TvW+Rx55hKtXr2Zonr1791KjRg0uXLjA1KlTqVChQoY+v1Lp5ciRI/To0YMLFy6wdOlS6tat69Tt3+vfcs+ePfn666/ZtGkTBQoUcGqm5LRwZHIJCQk3f5KSkoiNjSVLliz3/U1l06ZNvP3222TLlo3w8HCeffZZJyVWylp79uyhT58+5MiRg02bNlGuXDmrIwG25qlNmzaxefNmChYsmK7PpU1Vmdzo0aPx9vbmgw8+YNu2bXh7e1OjRo372uaCBQt48803yZcvH5988okWDeUxNm3aRJcuXShYsCDffvutyxSNo0ePEhwczKFDhyhevDg+Pj74+PhQq1atdHk+HY6rnGrixIn069ePMmXKMH36dPLmzWt1JKWc4vPPP2fKlCm8+uqrrFixgkKFClkdyWkcHY6rTVXKKa5fv06XLl2IjIykUqVKjB8/3i2vbKZUSklJSQQHB/PZZ59Rr149FixY4FbXB08PWjjUfYuKiiIgIICdO3fStGlTevXq5dYXqVHqhuvXrzNixAjWrVtH586d+eijj/S9jRYOdZ92795NvXr1OHv2LMOHD9fhtspjXL58mQ8++IBdu3YxduxY+vfvrxNx2mnhUPds/vz5vPfee+TOnZvw8HBKly5tdSSlnOLMmTP06NGDo0eP8vHHH9OmTRurI7kUHVWlHJaYmEifPn1o2bIlTz/9NPPnz9eioTzGoUOHaNeuHWfOnOGrr77SopEKPeJQDrl8+TLvvPMOGzZsoG7dugwcOJDs2bNbHUspp9i1axd9+/bFx8eHLVu28PLLL1sdySVp4VBpdurUKapXr87+/fvp27evy1x+VilnWLduHcOHD+epp55i9erVFC9e3OpILksLh0qT/fv3U716dc6ePcvkyZPx8/OzOpJSTmGMYd68eUyfPp2KFSuybNky8ufPb3Usl6aFQ93VN998Q7169RARZs+eTZkyZayOpJRTJCYm8uGHH/L555/TsGFDPv30U7y9va2O5fK0c1zd0eLFi6levTo+Pj7MnTtXi4byGLGxsQwYMIDPP/+cHj16sGjRIi0aaaSFQ93W1KlTadq0KU899RSffPIJxYoVszqSUk5x8eJFunXrxubNm5kyZQrTp08nSxb9OEwrbapS/xIfH0/Xrl0JDw+nQoUKTJgwAS8vL6tjKeUUhw8fpnfv3pw5c4aFCxemyzW5PZ0WDnWL6Oho3n77bb799luaNGlC7969dYoF5TG++eYbhgwZwgMPPMCGDRt0kMc90sKhbvrpp5+oW7cuUVFRDBs2zOkXp1HKKsYY5syZQ2hoKC+++CJffvkljz/+uNWx3JYWDgXAwoULadeuHbly5SI8PFw7wZXHuHbtGiNGjGDjxo00b96c8PBwHnjgAatjuTXtDcrkkpKSCAoKonnz5jz55JPMnz9fi4byGCdPnqRdu3Zs2rSJiRMnMm/ePC0aTqBHHJnYuXPnaNasGevXr6dOnToMGjQo3S5ur1RG27VrF/369QNg5cqV1K5d2+JEnsNlCoeIDABeAl4GigNHjTFPWBrKg3377bc0atSIqKgo+vTpQ9OmTXXKaOURjDEsXryYqVOnUqJECZYuXaqXL3YylykcwFjgHPAjkM/aKJ7LGMPEiRMZNGgQBQoUICIiQpumlMe4fv06EyZMYPny5bz11lt89tln5MuXz+pYHseVCsdTxpi/AERkL+BjcR6Pc+7cOZo3b866deuoWLEio0aNInfu3FbHUsopzp49S1BQEL/88gsDBw5k1KhRelJfOnGZwnGjaKj0sWPHDho3bkxUVBQ9e/akRYsW2jSlPMa+ffv44IMPuHLlCosWLaJx48ZWR/JoWo49nDGG8ePH4+/vT1JSEhEREbRs2VKLhvIYq1atokOHDnh7e7Nt2zYtGhnAZY447pWIdAQ6Ajz22GMWp3Et//zzD82bN2f9+vVUqlSJkSNHatOU8hixsbFMmTKFpUuXUrlyZRYtWkShQoWsjpUpuP0RhzEmzBjja4zxLViwoNVxXMaOHTt4/vnn2bRpE7169WLq1KlaNJTHOHr0KG3btmXp0qUEBQWxfv16LRoZyO0Lh7pVUlIS48aNw9/fH2MMERER2p+hPMratWtp1aoV//zzDytWrGDChAl6+eIM5vZNVep/tGlKebLkTVPly5dn4cKF2jxtES0cHmLbtm00adKE6OhoevXqRfPmzfUoQ3mMI0eOMGDAAA4ePEi/fv0YPXo02bLpx5dV9JV3c9euXWP48OFMmTKFggULEhkZSenSpa2OpZTTrF27lrFjx+Ll5cXKlSt56623rI6U6blM4RCRVsCNeY4LAjlEZLD996PGmM+sSea6VqxYQdeuXTl+/DjVqlVj8ODB+PjoeZPKM2jTlOtymcIBvAf4p1g2yn67FdDCYXfs2DE6d+7MmjVrKFasGLNmzeLVV1+1OpZSTpO8aap///6MGjVKm6ZciMv8TxhjKludwdXdmIdn7NixGGMIDAykdevWOqJEeZQ1a9YwduxYvL29+eqrr6hTp47VkVQKLlM41J19/fXXdO7cmUOHDlGxYkX69+9P4cKFrY6llNPExsYyefJkli1bRoUKFViwYIE2TbkoLRwu7tSpU7z//vssWbKEwoULM2XKFPz9U7boKeXeDh8+zIABAzh06JA2TbkB/Z9xUbGxsUyYMIEJEyYQHx9PmzZt6NChA15eXlZHU8ppkpKSWLx4McHBwfj4+GjTlJvQwuFijDEsWrSIDz74gOPHj1OxYkX69OlDsWLFrI6mlFNFRUUxcuRIdu7cyZtvvklERARFihSxOpZKAy0cLmT37t1069aNnTt3Urx4cWbOnEm5cuWsjqWU023YsIFx48aRkJDAzJkzCQwM1BNW3YgWDhdw5swZ+vbty/z588mTJw9BQUG88847ZM2a1epoSjnV5cuXmThxImvWrOGVV17hk08+oVSpUlbHUg7SwmGhuLg4Jk6cyIQJE4iLi6Nx48YEBgbqSXzKI/3www8MHz6cs2fPMnz4cAYNGqQd4G5K/9csEBMTQ0hICB9++CEnT57k9ddfp2/fvjz++ON3f7BSbubq1at89NFHLF68mBIlSrBs2TJee+01q2Op+6CFIwNFR0czdepUQkJCuHjxImXKlGHAgAG8/vrrVkdTKl189913jBkzhjNnztCtWzfGjRunR9QeQAtHBjh8+DDjxo3js88+IzY2lgoVKtC2bVvKli1rdTSl0sXFixf58MMP+eqrryhZsiSLFy+mUqVKVsdSTqKFIx39+OOPjB49muXLl5MlSxaqV69Ou3btKF68uNXRlEo3GzduZOLEiVy6dImBAwcyePBgvL29rY6lnEgLh5MZY9iwYQNjx45l69ateHt706hRI9q0aaOXtlQe7ezZs0yYMIHNmzfz4osvEh4ezssvv2x1LJUOtHA4ybVr11i0aBFTp07l119/5cEHH6RTp040bdpUr8KnPJoxhlWrVjFlyhTi4+MZP348ffr00RFTHkz/Z+/Tjz/+yKxZs1i8eDGXL1+mSJEiBAUFERAQQM6cOa2Op1S6On/+PGPHjmXz5s1UrFiRsLAwPS8jE9DCcQ8uXLjAZ599RlhYGHv37iV79uz4+fnRsGFDXn75ZbJkyWJ1RKXS3fbt2xk1atTNk/p69+6tJ61mElo40sgYw9atWwkJCWH58uXExcXx5JNP0qtXL+rWrUuePHmsjqhUhrh27RrTpk3jiy++oEyZMmzYsIEXX3zR6lgqA2nhuIvTp08TERHBnDlzOHz4MA888AA1a9akYcOGlCpVSufXUZnK3r17GTJkCMePH6dv376MGjVKZ2zOhLRwpCI+Pp41a9YQGhrK+vXrSUxMpHTp0gwePJiaNWvq0EKV6SQkJBAZGcmcOXN49NFH2bhxI2+88YbVsZRFtHBga4b6448/WL16NevWrWP79u3ExMSQN29eGjVqRMOGDXniiSesjqmUJQ4cOMCoUaP4/fffadWqFdOnT+fBBx+0OpayUKYtHGfPnmX9+vWsWbOGTZs2cfLkSQAKFy7MG2+8QaVKlahUqZJez1tlWnFxcURERPDpp5+SP39+lixZQsOGDa2OpVxApikccXFxbNu2jdWrV7Nx40b27t2LMQYfHx/Kli1LixYtqFChAkWLFrU6qlKW27NnD6NGjeLo0aO8++67TJ48mfz581sdS7kIjy0cxhj27t3LqlWrWL9+Pd999x2xsbFkzZqVUqVK0a5dOypUqMBzzz2nJyopZRcTE8PMmTNZsmQJxYoVY/Xq1dSqVcvqWMrFeNQnZnx8PHPnzmXt2rVs3ryZ6OhoAIoVK0atWrWoUKECr7zyCrly5bI4qVKuJ+VMtmPGjNFZD1SqxBhjdQanEREDkCdPHl5++WVef/11ypcvT+HCha2OppTLunLlClOmTGHlypWULFmSsLAw/Pz8rI6lMpCvry+7du1K87kFHnXEUbBgQaZOnUrJkiX17G2l0mD37t0MGzaMqKgo+vfvz9ChQ3W4uborjyocBQoU0HlylEqD69evExISwrx583jyySf55ptvqFChgtWxlJvwqMKhlLq7gwcPMmTIEA4dOkTHjh2ZPHmy9mUoh2jhUCqTSExMZP78+YSEhPDggw+yfPly6tWrZ3Us5Ya0cCiVCZw6dYphw4bx448/EhAQwOzZs3n44YetjqXclBYOpTzc3r176dWrF/Hx8URGRtK2bVudnFPdFy0cSnmwbdu2MWDAAAoXLszq1at18IhyCh2zqpSH+vLLL+nTpw/PPfcc3377rRYN5TR6xKGUhzHGMHv2bCIiInjzzTdZtGiRXmhMOZUWDqU8SEJCAmPGjGHlypW0a9eO0NBQneFZOZ02VSnlIWJjY+nduzcrV65k6NChREREaNFQ6UKPOJTyANeuXaNXr17s3r2b0NBQOnXqZHUk5cG0cCjl5mJiYujZsyc///wzH3/8Ma1bt7Y6kvJwWjiUcmNXrlyhR48e7Nu3j/nz59O0aVOrI6lMQAuHUm7q4sWLdO/enYMHD7Jo0SLeeecdqyOpTEILh1Ju6MKFC3Tp0oUjR46wZMkSAgICrI6kMhGXGVUlIllEpJeIHBCRWBH5W0SmiIherk+pZP755x86duzIsWPHWLp0qRYNleFcpnAAHwJTgd+A7sASoAewUkRcKadSlomOjqZTp06cPn2aFStWULt2basjqUzIJZqqRKQ0tmLxpTHmnWTLDwMzgKbAAoviKeUSTp8+TWBgIOfOnWPVqlVUrlzZ6kgqk3KVb/LNAAGmpVgeDlwFWmZ0IKVcycmTJ+nUqRMXLlxg7dq1WjSUpVziiAN4BUgCvk++0BgTKyJ77PcrlSn9/fffdO7cmbi4ODZs2EC5cuWsjqQyOVcpHI8CZ40xcancdwIoLyI5jDHX77SRhIQEoqOj0yWgUlY4e/YsPXv2xBjD119/zUsvvWR1JKUQY4zVGRCRP4HsxpjHUrnvU6AV8KAx5kIq93cEOtp/LQPsTceoVisAnLU6RDrx5H2D+9i/nDlzZi9RokQJVx4kcu7cuawPPfRQotU50oun79+ff/6ZIyYmJs3vL1cpHL8ChYwx/7qWpYgsBhoBOe92xCEiu4wxvukU03KevH+evG+g++fudP9u5SrfYE4CBUQkZyr3FcHWjHXHoqGUUipjuErh+AFblleTLxQRL6AssMuCTEoppVLhKoVjEWCAnimWdwAeAOancTthTszkijx5/zx530D3z93p/iXjEn0cACISDHQDlgKrgVLYzhzfAbxhjEmyMJ5SSik7VyocWbEdcXQEnsA2AmURMNQYc8W6ZEoppZJzmcKhlFLKPbhKH4dTiUgRERkgIltF5JSIxIjIPhGZJCL5rc7nDCLSSUTm22cTThQRt/sG4MkzItvff0tE5C8RMSJyxOpMziQiz4jISBHZKSLRInJZRPaIyCB3//8TkZL2v639InJRRK7a36NTReQRq/OlBxF5QEQO29+rH911fU884hCRzsB0YBWwHbiMbcTWu8Ap4FVjzGnLAjqB/YMoP/ATUBwoaowRS0M5SESmY+vHWgqswdav1R3YBlRz534teyE/B/wIvAxcMsY8YWkoJxKR8UBXYAWwE4gHqgCNgV+A14wx16xLeO9EpCowCNt+HQcSgOeBtsAloKwxJsq6hM4nIpOBToAPMNMY0+2ODzDGeNwPUBoonMry9thGb022OqMT9vEJIIv931/Z/iutz+Xg/1ES8EWK5d3t/0fNrc54n/v3ZLJ/7wWOWJ3JyfvnC+RNZflo+/9fN6szpsM+N7LvW5DVWZy8Xy9hK4697fv30d0e45FNVcaYfSb1I4pF9tsyGZknPRhjjhg3/kaOh8+IbIz5y+oM6ckYs8sYczGVuzzmbywVR+23D1qawonsg5LCgbXAl2l9nKtMcphRitpvz1iaQoHOiOypPOZvzH4Csg/gBTwHTLDftdqyUM7XC3gWcOiC9R55xHEHI+y3n1iaQsHdZ0QuICI5MjiTug/2b69DsTV7eMKF19oD0cDfwDogH9DSGLPNylDOIiLFsX0mjjTGHHHksS59xCEi+fj32eR3MsMYc+422+qDrY0yzBiz6f7T3T9n7p8begBIrWgAxCZbR+cocx/TgNeAgcaY3y3O4gzLgAPYjjpeBOoBBa0M5GQhwGFsl+x2iEsXDmwVfpgD68/DNpLlFiLSHpiEbZTVnUcLZKx8OGH/3NRVoNBt7vNKto5yAyIyCtvfVpgxZpzVeZzBGHMc26gqgGUi8gXwg4h4u/s+ikhLoAbgZ4yJd/TxLl047IdP9zXEVETaYZuHZT3wzr28SOnFGfvnxk4Cz4lIzlSaq3RGZDciIsOBwcBcoLO1adKPMeYXEfkJ6AK4beGwz0I+FVtfzWkRedp+VxH7bV77srMmlWsggYf3cYhIW2wjBjYCb9+mPV1ZQ2dE9gAiMgzbUfOnQHtjH9/pwbyBh6wOcZ+8sTW51QEOJvvZYr+/pf339rfbgEsfcdwPEXkXiAA2AwHGmNg7P0JlsEXAQGx9PMk7Gx2dEVlZRESGAsOBz4C2bj48/CYRKZzacH4RqYJtmPGWDA/lXDHY+ntTKgjMwjY0NxLbiZyp8tQzx+thOxv5EhAEpDyD9YoxZllG53ImEakLvGD/tSVQEhhi//2CMeau0wZYzZNnRBaRVsDj9l+7AzmAKfbfjxpjPrMkmJOISFfgI+AYtvddyv+rM8aYDRkezAlEZCnwCLAJ27kbXtjO/m+Krd+tsjFmj2UB04mIPIGts/yuZ457auEYzp07nY8aN5/+QUQ+Btrc5m632D9PnhFZRLYA/re5e6sxpnLGpXG+u7z/wI33UUQaY9u3/2D7Fm6wFZANwCRjzDEL46WbTF84lFJKpR+P7hxXSinlfFo4lFJKOUQLh1JKKYdo4VBKKeUQLRxKKaUcooVDKaWUQ7RwKKWUcogWDqUsICJPiIixn6yqlFvRwqHSTEQq2z/sjIikOqWJiBQSkev2dbZkcESPJCLvJnvd+95mnbLJ1vk4gyOqTEYLh7oXsUBz+/TMKbXCNlV8QsZGyhRigba3ue89/ncBLKXSlRYOdS+WAg8CAanc1xbbhIUeN4W9iOS2OMJSbNcwSTkVfU6gOfClJalUpqOFQ92LH4GfSfHt1/6BVhrbBX1SJSK+IrJURM6KSJyI/C4ig0QkW4r1XhWRj0XkDxG5KiKXRWSHiNRPZZvFRGSOiBy1bzNKRL4VkTbJ1rnR3FM5lcdvEZEjKZYdsS9/UUTWichFkk0zLSIlROQzETllb5o7IiKTRCRXKtuvaM9+TUTO2Jv5fG73Gt3BSmzXwE551BGA7RoRd3rdq4nIehG5ICKxIvKLiPzroksiUkNEFonIX/a8F+yP+9eEjTdeNxF5VEQWish5EYmxv17P3G1n7P9v/4jIryLineK++SKSJCLV7rYdlfG0cKh7NReoISJFky1rB0QBX6X2ABGpjW3K9GewTTHeA/gOGAksTLF6feBZYDHwPjAG24fjlyLSPNk2s2GbtbQR8Dm2q7ONB/4AKt3XHsJj/G9q7Q+AYPtzvoztQlN+wGygK7Z97gFsEJHsyfKVw3YhsWeACdiuHOeL7cJHjorHdp2SZik+aNsBPwF7UnuQiHTEdgVMH2yvY2/gTyBERCalWP1dbK/zp9img/8Q23T3X4tIaq9nLuAbIBHb9VVmApWB5fbZj2/LGPM3tiJYBtv1ym/kbYftCGqCMWbjnbahLGKM0R/9SdMPtg8EA/QF8mNrjhpov88buABMtv9+BdiS7LFewGlsHzLZUmy3l327lZMty5XK8z8A/A78lmzZf+yPDbpL9ndTPkey+7YAR1IsO2Jfv30q6/8MHAByp1he3/6Yd5Mt+xa4DjyTbFkO4Hv7usPT8LrfyN4QeN7+7+b2+4pi+9DuBhSw3/dxssc+gq3vY0Eq251uf+xTd3ndH8Y25f3qVF63f7322IqsAWqm8X01I9n+PWt/73yX8n2iP67zo0cc6p4YY/4BVmD7UANoAOQF5tzmIdWxfQDNBfKJSIEbP9j6RABqJNt+zI1/i8gDIpIfW+HYBJQSkTz2uy/ab6uISKH73rFbnSNF84+IPI+tWC0AcqbYj+3Yrq5Ww75uIeB1YLkx5o9k+3Yd2zd5hxljfsV2tHOjuaoNtiORBbd5SEMgJxCZPKs970psrQ5Vk20/+evuY3/dE4H/A8qlsv0kbB/8yW2y35ZI4259gO2IKRz4L7aBFc2NMTrAwkV57KVjVYaYC6wSkYrYmku+N8b8dpt1S9lvb1dYwFZYgJsfuqOxtd+nVhDyAZeMMUdFZAwwADglInuAr4ElxpgfHNiX1PxpjElMsezGfoyw/6Tmxn48ab89kMo6t3ud0mIu8JGIPI6tcC83xpyzF4OUbuS9U5NP8tf9KWzNWTWxvcbJpXbxnpPm35dl/sd+m/8Oz/m/jRoTJyLNgH3Y+shaGGMOp+WxyhpaONT9WAecwHa1xSpA4B3WFfvtB9ymLR44CSAigq1NvhS2b7M/YDuySMT2Tbs5yfrnjDGDRWQOUAdbv0Z74AMRmWiM6XdjtTtku93fwdU77McUbNdmTs35FOum9tySyrK0WmB//nDgaWzNVLdz43laA6dus85fYDvCwNaUmAtbn8OvwGVsRxUDgDdSeWzKwprac6dFHeBGn8iL3P4ISrkALRzqnhljEkXkU2wfKtewdU7fzkH7bYy5e4fnf7BdT32kMeaWSwCLSPvbZPkLW+d1sIh4YStqQSIyxRgTha3ZCWwdvykVx9bckxY39iMxDfvxp/22VCr3pbYsTYwxF8R2XexmwN/YBgfczo28Z9OQtyrwKNDOGJOyiW70vea9G/tgg3HY9uMs0EdENhhj1qfXc6r7o30c6n6FYmuy6WyMuXiH9dZhG3HVX0T+9eEtIt7yv/MkbnyLlRTrlMHWAZ18Wd7ko5gA7E0n++2/Pmi/vdHHcMvwTnsTyaN3yJ3ST8BeoLOIPJnyThHJdmP/7AVrJxCQfHiqiOTANiDgfozH9rp3M8Yk3WG9xdgGMYxIOeTVniWv/O9Eztu97jVIvX/jvtmPcj7HNrCiFdAJ23WvP02HPivlJHrEoe6LMeYYMDwN68WISGtgGfC7vWnpELZ29Gexda7XxzZSZz+29u4gEbkxkuoZbB8qe4GXkm26ChAmIl/Y17sCvIytuer/jDG/25//dxHZCHSyN4XtAcran/MQcEvxucN+GBFpha0D+Bf7fuzD1nH/tH0/BgAf2x/S275PO0RkJrYPyKbc59+eMeYXkp1Xcof1jotIIBAB7BeRz7ANLy6IbYTW28Bz2EaRbcc28m2KiDwBHMf2GrXC1mz1/P1kvo0Q4CngTWPMGQARaYpt2PYnIlLbGHOnZkZlBauHdemP+/yQbDhuGta9ZThusuVlgHnY+kauA2ewDVkdAjyUbL3HgSXYTni7im34an1sRcoAT9jXK47tqGc/cAnbqKb92M4NyZviuQvbt3nJnm8NtiajLaQ+HPdf+VPkC7Wvdx1bh/BubE0uxVKs62ffx1hsR10z7a+Dw8Nx77Lev4bjJruvArYzz6PseU8Cm4E+gFey9f6Dre/mPLb+jS3Y+o0+tn1c3LLNf71u9uVPpGXfsPW7GGzna6S878aQ3j5Wv+/1598/Yv9PUkoppdJE+ziUUko5RAuHUkoph2jhUEop5RAtHEoppRyihUMppZRDtHAopZRyiBYOpZRSDtHCoZRSyiFaOJRSSjlEC4dSSimH/D9wsU/tnWMpHAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting FC confidence intervals\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "plt.plot(np.array(FC_x_range)[:, 0], mean_list, color ='k')        # plotting x1 for FC confidence interval\n",
    "plt.plot(np.array(FC_x_range)[:, 1], mean_list, color ='k')        # plotting x2 for FC confidence interval\n",
    "\n",
    "plt.fill_between(                                                  # shading 90% confidence interval\n",
    "        x= np.array(FC_x_range)[:, 0], \n",
    "        y1= mean_list, \n",
    "        color= \"k\",\n",
    "        alpha= 0.2,\n",
    "        label = \"90% CL\")\n",
    "\n",
    "plt.fill_between(                                                  # shading 90% confidence interval                           \n",
    "        x= np.array(FC_x_range)[:, 1], \n",
    "        y1= mean_list, \n",
    "        color= \"w\",\n",
    "        alpha= 1,\n",
    ")\n",
    "\n",
    "plt.text(-0.5, 1.5, r'$x_1$', horizontalalignment='right')\n",
    "plt.text(3.5, 1.5, r'$x_2$', horizontalalignment='left')\n",
    "\n",
    "plt.xlabel('Measured Mean x')\n",
    "plt.ylabel(r'Mean $\\mu$')\n",
    "plt.xlim([-2, 4])\n",
    "plt.ylim([0, 6])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5de53e7e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x0 \t mu1 \t mu2\n",
      "-3.00  0.00  0.27\n",
      "-2.90  0.00  0.28\n",
      "-2.80  0.00  0.29\n",
      "-2.70  0.00  0.29\n",
      "-2.60  0.00  0.30\n",
      "-2.50  0.00  0.32\n",
      "-2.40  0.00  0.34\n",
      "-2.30  0.00  0.35\n",
      "-2.20  0.00  0.37\n",
      "-2.10  0.00  0.39\n",
      "-2.00  0.00  0.40\n",
      "-1.90  0.00  0.43\n",
      "-1.80  0.00  0.46\n",
      "-1.70  0.00  0.49\n",
      "-1.60  0.00  0.52\n",
      "-1.50  0.00  0.56\n",
      "-1.40  0.00  0.60\n",
      "-1.30  0.00  0.65\n",
      "-1.20  0.00  0.70\n",
      "-1.10  0.00  0.75\n",
      "-1.00  0.00  0.81\n",
      "-0.90  0.00  0.88\n",
      "-0.80  0.00  0.95\n",
      "-0.70  0.00  1.02\n",
      "-0.60  0.00  1.10\n",
      "-0.50  0.00  1.18\n",
      "-0.40  0.00  1.27\n",
      "-0.30  0.00  1.36\n",
      "-0.20  0.00  1.45\n",
      "-0.10  0.00  1.54\n",
      " 0.00  0.00  1.64\n",
      " 0.10  0.00  1.74\n",
      " 0.20  0.00  1.84\n",
      " 0.30  0.00  1.94\n",
      " 0.40  0.00  2.04\n",
      " 0.50  0.00  2.14\n",
      " 0.60  0.00  2.24\n",
      " 0.70  0.00  2.34\n",
      " 0.80  0.00  2.44\n",
      " 0.90  0.00  2.54\n",
      " 1.00  0.00  2.64\n",
      " 1.10  0.00  2.74\n",
      " 1.20  0.00  2.84\n",
      " 1.30  0.02  2.94\n",
      " 1.40  0.12  3.04\n",
      " 1.50  0.22  3.14\n",
      " 1.60  0.31  3.24\n",
      " 1.70  0.38  3.34\n",
      " 1.80  0.45  3.44\n",
      " 1.90  0.51  3.54\n",
      " 2.00  0.59  3.64\n",
      " 2.10  0.65  3.74\n",
      " 2.20  0.72  3.84\n",
      " 2.30  0.79  3.94\n",
      " 2.40  0.87  4.04\n",
      " 2.50  0.95  4.14\n",
      " 2.60  1.03  4.24\n",
      " 2.70  1.11  4.34\n",
      " 2.80  1.19  4.44\n",
      " 2.90  1.28  4.54\n",
      " 3.00  1.37  4.64\n"
     ]
    }
   ],
   "source": [
    "# calculating FC confidence intervals [\\mu_1, \\mu_2] for a list of measured x_0 (same as in Table X)\n",
    "\n",
    "x0_list = np.arange(-3, 3.1, 0.1)\n",
    "mu1_list = np.interp(x0_list, np.array(FC_x_range)[:, 1], mean_list) \n",
    "mu2_list = np.interp(x0_list, np.array(FC_x_range)[:, 0], mean_list)\n",
    "\n",
    "print('x0 \\t mu1 \\t mu2')\n",
    "for (x0, mu1, mu2) in zip(x0_list, mu1_list, mu2_list):\n",
    "    print(f'{x0: 5.2f} {mu1: 5.2f} {mu2: 5.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26d67049",
   "metadata": {},
   "source": [
    "## Feldmann-Cousins intervals using Toy Monte Carlo method\n",
    "\n",
    "### Example: Gaussian with Boundary at Origin\n",
    "\n",
    "Ref.: Feldman-Cousins Confidence Levels - Toy MC Method, Till Moritz Karbach, [arXiv:1109.0714](https://arxiv.org/abs/1109.0714v1)\n",
    "\n",
    "The method is based on toy Monte Carlo (MC) experiments, which are datasets drawn from the assumed pdf. Here, we shall use it to compute the confidence belt for the trivial example of a unit Gaussian bound to positive values, $\\mu > 0$.\n",
    "\n",
    "Feldmann-Cousins method uses ratio of likelihood: \n",
    "\n",
    "\\begin{equation}\n",
    "R(x, \\mu) = \\frac{P(x|\\mu)}{P(x|\\mu_{\\rm best})}\n",
    "\\end{equation}\n",
    "\n",
    "In pratice, it is convenient to take the logarithm of the likelihood ratio \n",
    "\n",
    "\\begin{align}\n",
    "-2\\ln{R} \\equiv \\Delta \\chi^2 &= \\chi^2 - \\chi^2_{\\rm best}\\\\\n",
    "&= \\chi^2(x,\\mu) - \\chi^2(x, \\mu_{\\rm best}),\n",
    "\\end{align}\n",
    "\n",
    "because one often prefers to minimize $-2\\ln{R}$ rather than to maximize $P$. The algorithm to contruct FC intervals is as following:\n",
    "\n",
    "- At the considered value of the true parameter $\\mu_0$, generate a toy experiment by drawing a value of $x_{\\rm toy}$ from the pdf. That is, draw from the unit Gaussian $G(\\sigma = 1, \\mu = \\mu_0)$.\n",
    "- Compute $\\Delta\\chi^2_{\\rm toy}$ for the toy experiment. For $\\chi^2(x,\\mu)$, $x$ is set to $x_{\\rm toy}$ and $\\mu$ is set to $\\mu_0$. For $\\chi^2(x,\\mu_{\\rm best})$, $x = x_{\\rm toy}$ and $\\mu_{\\rm best} = max(0, x_{\\rm toy})$ implementing the boundary at zero. \n",
    "- Find the value $\\Delta \\chi^2_c$, such that $\\alpha$ of the toy experiment have $\\Delta\\chi^2_{\\rm toy} < \\Delta \\chi^2_c$.\n",
    "- The interval $[x_1, x_2]$ is given by all values of $x$ such that $\\Delta\\chi^2(x,\\mu_0) < \\Delta\\chi^2_c$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d714570f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_FC_x_range(mean):\n",
    "    std = 1                                            # sigma of Gaussian pdf\n",
    "    alpha = 0.9                                        # 90% CL\n",
    "    total_events = 10000                               # Total number of pseudo experiments\n",
    "    \n",
    "    x_toy = norm.rvs(mean, std , size = total_events)  # Randomly generated events following Gaussian distribution\n",
    "\n",
    "    P = norm.pdf(x_toy, mean,std)                      # P(x|u) = P(x_toy | u)\n",
    "    chi2 = -2*np.log(P)                                # converting P(x|u) to chi^2(x,u)\n",
    "\n",
    "    mean_best = np.maximum(np.zeros(len(x_toy)), x_toy)# calculating the best mean [max(0,x_toy)] for which P(x|u) is maximum\n",
    "    P_best = norm.pdf(x_toy, mean_best, std)           # maximum pdf = P(x_toy|u_best)\n",
    "    chi2_best = -2*np.log(P_best)                      # converting P(x_toy|u_best) to chi^2(x_toy,u_best)\n",
    "\n",
    "    delta_chi2 = chi2 - chi2_best                      # Delta_chisq = chi^2(x_toy,u) - chi^2(x_toy,u_best)\n",
    "\n",
    "    df = pd.DataFrame({'x_toy': x_toy, 'delta_chi2': delta_chi2} ) \n",
    "    df_sorted_delta_chi2 = df.sort_values(by='delta_chi2') # sorting the delta_chi2 in increasing order\n",
    "    \n",
    "    # finding x_1 and x_2 for 90% CL where x with highest R are accepted first\n",
    "    \n",
    "    count = 0                                          \n",
    "    for index, row in df_sorted_delta_chi2.iterrows():  # Loop index progresses in increasing order of delta_chi2  \n",
    "        x = row[\"x_toy\"]\n",
    "        d = row[\"delta_chi2\"]\n",
    "        count += 1                                      # integration over pdf\n",
    "        if x <= mean :\n",
    "            x1 = x                                      # lower CL\n",
    "        else:\n",
    "            x2 = x                                      # upper CL\n",
    "        if count/total_events >= alpha:                 # stop when total probability is equal to or \n",
    "            print(f'u = {mean:6.3f}, x1 = {x1:6.3f}, x2 = {x2:6.3f}, delta_chi2_c = {d:6.3f}')   # greater than desired CL\n",
    "            break\n",
    "\n",
    "    return x1, x2, d, df_sorted_delta_chi2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e674eddf",
   "metadata": {},
   "source": [
    "### Toy experiment with Gaussian pdf\n",
    "\n",
    "- Distribution of $x_{\\rm toy}$ for Gaussian pdf $G(\\sigma = 1, \\mu = \\mu_0)$ with $\\mu_0 = 0.5$.\n",
    "- Solid blue curve showing likelihood ratio in terms of $\\Delta\\chi^2$ as a function $x_{\\rm toy}$\n",
    "- Dashed blue curve showing $\\Delta\\chi^2_c$ at 90% CL\n",
    "- The intersection of solid and dashed curve gives $x_1$ and $x_2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e0f79069",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u =  0.500, x1 = -1.629, x2 =  1.871, delta_chi2_c =  1.880\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.0, 14.688740025570441)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean = 0.5\n",
    "x1, x2, delta_chi2_c, df_toy = get_FC_x_range(mean)        # Toy experiment based on Gaussian pdf with mean = 0.5\n",
    "\n",
    "fig, ax1 = plt.subplots(figsize=(6, 6))\n",
    "\n",
    "x_ = ax1.hist(df_toy[\"x_toy\"], bins = 20, histtype='step', color = 'k') # Histogram of x_toy\n",
    "ax1.set_ylabel(\"Number\")\n",
    "ax1.set_xlabel(\"Measured Mean x\")\n",
    "\n",
    "\n",
    "df_sorted_x_toy = df_toy.sort_values(by='x_toy')           # Sorting with increasing x_toy for plotting smooth curve\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "color = 'b'\n",
    "ax2.plot(df_sorted_x_toy[\"x_toy\"], df_sorted_x_toy[\"delta_chi2\"] , color = color) # plot delta_chi2 as a function of x_toy\n",
    "ax2.axhline(delta_chi2_c, color = color, linestyle='--')   # plot delta_chi2 at 90 %CK\n",
    "ax2.text(3.5, 2.3, r'$\\Delta\\chi^2_c$', color=color) \n",
    "\n",
    "ax2.text(1.1*x1, delta_chi2_c, r'$x_1$', horizontalalignment='right', verticalalignment=\"top\", color = color)\n",
    "ax2.text(x2, delta_chi2_c, r'$x_2$', horizontalalignment='left', verticalalignment=\"top\", color = color)\n",
    "\n",
    "ax2.set_ylabel(r'$\\Delta\\chi^2$', color=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "ax2.set_ylim(bottom=0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d6c73617",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u =  0.100, x1 = -3.908, x2 =  1.396, delta_chi2_c =  1.680\n",
      "u =  0.200, x1 = -3.542, x2 =  1.469, delta_chi2_c =  1.611\n",
      "u =  0.300, x1 = -2.653, x2 =  1.599, delta_chi2_c =  1.688\n",
      "u =  0.400, x1 = -2.101, x2 =  1.757, delta_chi2_c =  1.841\n",
      "u =  0.500, x1 = -1.658, x2 =  1.882, delta_chi2_c =  1.911\n",
      "u =  0.600, x1 = -1.359, x2 =  2.012, delta_chi2_c =  1.993\n",
      "u =  0.700, x1 = -1.185, x2 =  2.166, delta_chi2_c =  2.150\n",
      "u =  0.800, x1 = -1.045, x2 =  2.320, delta_chi2_c =  2.311\n",
      "u =  0.900, x1 = -0.926, x2 =  2.474, delta_chi2_c =  2.478\n",
      "u =  1.000, x1 = -0.744, x2 =  2.577, delta_chi2_c =  2.488\n",
      "u =  1.100, x1 = -0.615, x2 =  2.694, delta_chi2_c =  2.562\n",
      "u =  1.200, x1 = -0.456, x2 =  2.793, delta_chi2_c =  2.537\n",
      "u =  1.300, x1 = -0.347, x2 =  2.913, delta_chi2_c =  2.601\n",
      "u =  1.400, x1 = -0.247, x2 =  3.027, delta_chi2_c =  2.651\n",
      "u =  1.500, x1 = -0.159, x2 =  3.151, delta_chi2_c =  2.727\n",
      "u =  1.600, x1 = -0.028, x2 =  3.230, delta_chi2_c =  2.657\n",
      "u =  1.700, x1 =  0.057, x2 =  3.346, delta_chi2_c =  2.711\n",
      "u =  1.800, x1 =  0.167, x2 =  3.430, delta_chi2_c =  2.665\n",
      "u =  1.900, x1 =  0.250, x2 =  3.549, delta_chi2_c =  2.722\n",
      "u =  2.000, x1 =  0.326, x2 =  3.672, delta_chi2_c =  2.801\n",
      "u =  2.100, x1 =  0.448, x2 =  3.753, delta_chi2_c =  2.732\n",
      "u =  2.200, x1 =  0.538, x2 =  3.862, delta_chi2_c =  2.762\n",
      "u =  2.300, x1 =  0.644, x2 =  3.956, delta_chi2_c =  2.743\n",
      "u =  2.400, x1 =  0.764, x2 =  4.036, delta_chi2_c =  2.677\n",
      "u =  2.500, x1 =  0.864, x2 =  4.137, delta_chi2_c =  2.680\n",
      "u =  2.600, x1 =  0.945, x2 =  4.255, delta_chi2_c =  2.740\n",
      "u =  2.700, x1 =  1.073, x2 =  4.325, delta_chi2_c =  2.648\n",
      "u =  2.800, x1 =  1.161, x2 =  4.441, delta_chi2_c =  2.693\n",
      "u =  2.900, x1 =  1.252, x2 =  4.549, delta_chi2_c =  2.719\n",
      "u =  3.000, x1 =  1.365, x2 =  4.636, delta_chi2_c =  2.677\n",
      "u =  3.100, x1 =  1.450, x2 =  4.749, delta_chi2_c =  2.722\n",
      "u =  3.200, x1 =  1.553, x2 =  4.845, delta_chi2_c =  2.712\n",
      "u =  3.300, x1 =  1.655, x2 =  4.948, delta_chi2_c =  2.715\n",
      "u =  3.400, x1 =  1.740, x2 =  5.060, delta_chi2_c =  2.754\n",
      "u =  3.500, x1 =  1.856, x2 =  5.144, delta_chi2_c =  2.704\n",
      "u =  3.600, x1 =  1.946, x2 =  5.254, delta_chi2_c =  2.737\n",
      "u =  3.700, x1 =  2.068, x2 =  5.331, delta_chi2_c =  2.662\n",
      "u =  3.800, x1 =  2.128, x2 =  5.474, delta_chi2_c =  2.803\n",
      "u =  3.900, x1 =  2.255, x2 =  5.545, delta_chi2_c =  2.707\n",
      "u =  4.000, x1 =  2.346, x2 =  5.654, delta_chi2_c =  2.735\n",
      "u =  4.100, x1 =  2.438, x2 =  5.760, delta_chi2_c =  2.761\n",
      "u =  4.200, x1 =  2.543, x2 =  5.857, delta_chi2_c =  2.747\n",
      "u =  4.300, x1 =  2.672, x2 =  5.928, delta_chi2_c =  2.649\n",
      "u =  4.400, x1 =  2.739, x2 =  6.062, delta_chi2_c =  2.762\n",
      "u =  4.500, x1 =  2.848, x2 =  6.152, delta_chi2_c =  2.729\n",
      "u =  4.600, x1 =  2.935, x2 =  6.266, delta_chi2_c =  2.774\n",
      "u =  4.700, x1 =  3.069, x2 =  6.331, delta_chi2_c =  2.660\n",
      "u =  4.800, x1 =  3.147, x2 =  6.453, delta_chi2_c =  2.733\n",
      "u =  4.900, x1 =  3.257, x2 =  6.544, delta_chi2_c =  2.702\n",
      "u =  5.000, x1 =  3.342, x2 =  6.656, delta_chi2_c =  2.748\n",
      "u =  5.100, x1 =  3.471, x2 =  6.729, delta_chi2_c =  2.655\n",
      "u =  5.200, x1 =  3.556, x2 =  6.846, delta_chi2_c =  2.711\n",
      "u =  5.300, x1 =  3.656, x2 =  6.945, delta_chi2_c =  2.705\n",
      "u =  5.400, x1 =  3.743, x2 =  7.055, delta_chi2_c =  2.744\n",
      "u =  5.500, x1 =  3.873, x2 =  7.127, delta_chi2_c =  2.648\n",
      "u =  5.600, x1 =  3.946, x2 =  7.255, delta_chi2_c =  2.738\n",
      "u =  5.700, x1 =  4.062, x2 =  7.337, delta_chi2_c =  2.681\n",
      "u =  5.800, x1 =  4.145, x2 =  7.455, delta_chi2_c =  2.739\n",
      "u =  5.900, x1 =  4.253, x2 =  7.546, delta_chi2_c =  2.711\n"
     ]
    }
   ],
   "source": [
    "mean_list = np.arange(0.1, 6, 0.1)\n",
    "FC_x_range = []\n",
    "for u in mean_list:\n",
    "    x1, x2, _, _ = get_FC_x_range(u)\n",
    "    FC_x_range.append([x1, x2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "81805f6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "plt.plot(np.array(FC_x_range)[:, 0], mean_list, color = 'k')       # plotting x1 for FC confidence interval\n",
    "plt.plot(np.array(FC_x_range)[:, 1], mean_list, color = 'k')       # plotting x2 for FC confidence interval\n",
    "plt.fill_between(                                                  # shading 90% confidence interval\n",
    "        x= np.array(FC_x_range)[:, 0], \n",
    "        y1= mean_list, \n",
    "        color= \"k\",\n",
    "        alpha= 0.2,\n",
    "        label = \"90% CL\")\n",
    "\n",
    "plt.fill_between(                                                  # shading 90% confidence interval                           \n",
    "        x= np.array(FC_x_range)[:, 1], \n",
    "        y1= mean_list, \n",
    "        color= \"w\",\n",
    "        alpha= 1,\n",
    ")\n",
    "\n",
    "plt.text(-0.5, 1.5, r'$x_1$', horizontalalignment='right')\n",
    "plt.text(3.5, 1.5, r'$x_2$', horizontalalignment='left')\n",
    "\n",
    "plt.xlabel('Measured Mean x')\n",
    "plt.ylabel(r'Mean $\\mu$')\n",
    "plt.xlim([-2, 4])\n",
    "plt.ylim([0, 6])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "192282d6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}