What_a_confidence_interval_really_is.ipynb

{
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  {
   "cell_type": "markdown",
   "id": "c5e63dad-5dc0-4f47-a91c-7a84d2b271a3",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# What a confidence interval really is"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "f06723e2-15f3-4601-8e0b-2027bd06e2ba",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "<img src=\"attachment:42f75f7b-4f80-4cd9-872c-7a5770f87d48.png\" style=\"margin:auto\">\n",
    "\n",
    "Talk by François Durand (Nokia Bell Labs France). Above strip: https://xkcd.com/1132/."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a271bbdd-417e-4182-889a-ec782a035c80",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b14a149d-d2d1-4ccc-b71c-3fd30edd33be",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Why I did not prepare the talk I was planning..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffd8bac6-a9da-42a0-a106-787d188bcf3c",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "* My initial plan: talk on confidence intervals for the Monte Carlo method with a Bernouilli variable.\n",
    "* But in passing, I wanted to show the **traps** in interpreting the confidence intervals.\n",
    "* I also wanted to illustrate the difference between:\n",
    "  * **Frequentist** statistics with **confidence intervals** and\n",
    "  * **Bayesian** statistics with **credible regions**.\n",
    "* Working on this, in https://en.wikipedia.org/wiki/Confidence_interval, I rediscovered an illuminating counterexample that had helped me a lot, a while ago, to understand **what a confidence interval really is**...\n",
    "* I started to prepare material to present this counterexample, and quickly realized that I would have no time to cover anything else in one hour.\n",
    "* And this is how I ended up preparing a session based on less than 30 lines in Wikipedia... 😅"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da578c37-098f-49ef-90be-e29b631cf03b",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Spoiler alert: Moral of the story"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71392a9b-c522-4e41-bbcd-694f5851cac9",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "* Probabilities are full of traps.\n",
    "* Statistics are worse.\n",
    "* Frequentist statistics are even worse.\n",
    "\n",
    "In particular, confidence intervals are very misleading in terms of interpretation.\n",
    " \n",
    "**Main take-away: Do not interpret confidence levels as probabilities *a posteriori*!**\n",
    "\n",
    "(If this sentence is not clear for you, I hope it will be at the end of the talk!)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f235c434-28ef-4d3d-956d-8110b5e476f4",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Roadmap"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93a94003-19a8-4f4f-b3da-e350a00bcff8",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "* A bit of theory\n",
    "* In-depth analysis of the example\n",
    "* Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3774d862-7e85-4802-b589-4a63025bd45e",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "### Code tests (skipped in the presentation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6cb07580-65ed-46b3-9b6f-e85a31126533",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Rectangle, Polygon, Circle, Arc\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import interact"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "690a5d36-f207-4e86-88bf-df35495b46c1",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "#### CiulPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f50158ae-c707-41ad-bb68-65bf71f21807",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "class CiulPlot:\n",
    "    # Confidence interval for uniform location\n",
    "    def __init__(self, ax=None):\n",
    "        if ax is None:\n",
    "            ax = plt.figure(figsize=(7, 7)).add_subplot()\n",
    "        self.ax = ax\n",
    "        self.ax.set_axis_off()\n",
    "        self.ax.axis('equal')\n",
    "        self.e = .03  # Epsilon: Small space (typically between visual item and text)\n",
    "        self.be = .1  # Big epsilon: Larger space\n",
    "        self.color_forbidden_zone = 'gray'\n",
    "        self.color_in_ci = 'purple'\n",
    "        self.color_in_ci_fill = 'thistle'\n",
    "        self.draw()\n",
    "\n",
    "    def draw(self):\n",
    "        self.fill_forbidden_zone()\n",
    "        self.draw_axes()\n",
    "    \n",
    "    def fill_forbidden_zone(self):\n",
    "        self.ax.add_patch(Polygon(xy=((-1/2, -1/2), (1/2, -1/2), (1/2, 1/2)), edgecolor='k', facecolor=self.color_forbidden_zone))\n",
    "        self.ax.add_patch(Polygon(xy=((-1/2, -1/2), (-1/2, 1/2), (1/2, 1/2)), edgecolor='k', fill=False))\n",
    "    \n",
    "    def draw_axes(self):\n",
    "        self.ax.arrow(x=-1/2, y=-1/2 - self.be, dx=0, dy=1 + 2 * self.be, head_width=.01)\n",
    "        self.ax.arrow(x=-1/2 - self.be, y=-1/2, dx=1 + 2 * self.be, dy=0, head_width=.01)\n",
    "        self.ax.vlines(x=[0, 1/2], ymin=-1/2-self.e/2, ymax=-1/2+self.e/2, color='k')\n",
    "        self.ax.hlines(y=[0, 1/2], xmin=-1/2-self.e/2, xmax=-1/2+self.e/2, color='k')\n",
    "        self.ax.text(x=1/2 + self.be + self.e, y=-1/2, s=\"m\", va='center', ha='left')\n",
    "        self.ax.text(x=-1/2, y=1/2 + self.be + self.e, s=\"M\", ha='center', va='bottom')\n",
    "        self.ax.text(x=-1/2 - self.e, y=-1/2 - self.e, s=r\"$\\theta - \\frac{1}{2}$\", ha='right', va='top')\n",
    "        self.ax.text(x=0, y=-1/2-self.e, s=r\"$\\theta$\", ha='center', va='top')\n",
    "        self.ax.text(x=1/2, y=-1/2-self.e, s=r\"$\\theta + \\frac{1}{2}$\", ha='center', va='top')\n",
    "        self.ax.text(x=-1/2 - self.e, y=0, s=r\"$\\theta$\", va='center', ha='right')\n",
    "        self.ax.text(x=-1/2 - self.e, y=1/2, s=r\"$\\theta + \\frac{1}{2}$\", va='center', ha='right')\n",
    "\n",
    "    def draw_diagonal_plus_one_half(self):\n",
    "        self.ax.plot([-1/2 - self.e, 0 + self.be], [0 - self.e, 1/2 + self.be])\n",
    "        self.ax.text(x=0 + self.be + self.e, y=1/2 + self.e, s=r\"$M-m < \\frac{1}{2}$\", va='bottom', ha='left')\n",
    "        self.ax.text(x=0 - self.e, y=1/2 + self.e, s=r\"$M-m > \\frac{1}{2}$\", va='bottom', ha='right')\n",
    "\n",
    "    def show_point(self, x, y, color, xlabel=None, ylabel=None, xguide=True, yguide=True, show_point=True):\n",
    "        if xlabel is not None:\n",
    "            self.ax.text(x=x, y=-1/2-self.e, s=xlabel, va=\"top\", ha=\"center\", color=color)\n",
    "            if xguide:\n",
    "                self.ax.vlines(x=x, ymin=-1/2, ymax=y, linestyles ='dashed', color=color)\n",
    "        if ylabel is not None:\n",
    "            self.ax.text(x=-1/2-self.e, y=y, s=ylabel, va=\"center\", ha=\"right\", color=color)\n",
    "            if yguide:\n",
    "                self.ax.hlines(y=y, xmin=-1/2, xmax=x, linestyles ='dashed', color=color)\n",
    "        if show_point:\n",
    "            self.ax.add_patch(Circle(xy=(x, y), radius=.01, edgecolor=color, facecolor=color))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e16f6cc4-013b-4aaf-ac4d-66e8c850cf75",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TMZBdDvsChVYaMatWrYrGxsa0xwK6ScgAhZUkSdx+++3xwx/+UMRARnm0BBSSiIF8EDJA4YgYyA8hAxSKiIF8ETJAYYgYyB+HfYFC6BoxAwYMiFWrVsXIkSPTHgvoIxsZIPdEDOSXkAFyTcRAvgkZILdEDOSfkAFyScRAMTjsC+ROacS0tbXFiBEj0h4LqAAbGSBXRAwUi5ABckPEQPF4tATkQteIGThwYKxatUrEQAHYyACZJ2KguIQMkGkiBorNoyUgs5IkiTlz5sS//Mu/xMCBA6OtrS0aGhrSHguoIhsZIJNEDBAhZIAMEjHAMUIGyBQRA3QlZIDMEDFAKYd9gUwojZj29va44IIL0h4LSJmNDFDzRAxwKjYyQE3rGjGDBg2KtrY2EQN0spEBapaIAc5EyAA1ScQA3SFkgJojYoDuckYGqClJksTs2bPjRz/6kYgBzkjIADWjNGLa29tj+PDhaY8F1DAhA9SErhFTX18fbW1tIgY4I2dkgNSJGKC3hAyQKhED9IWQAVIjYoC+EjJAKkQMUA4O+wJVVxox7e3tMWzYsLTHAjJIyABV1TViBg8eHG1tbSIG6DWPloCqETFAuQkZoCpEDFAJuQ+Zjo6OWLt2bYwfPz4GDRoUzc3NsX///rTHgkI52cFeEQOUQ+5DZs2aNbFu3bp48sknY/PmzbFjx4546KGH0h4LCiNJkrjttts6NzEO9gLllOuQ2bZtW6xduzY2bNgQN954Y0ybNi3uueeeePbZZ9MeDQrhWMRs2rRJxAAVkeuQeeyxx2LmzJkxderUzmuNjY3x7rvvpjgVFMPJIub8889PeywgZ3IbMkmSxDPPPBNz58497vqhQ4di6NChKU0FxSBigGrJ7feR2blzZxw8eDDuv//+eOCBBzqvHzlyJG666abTvvbAgQMnXOvo6IiIiN/97ncn/Hx9fX0ZJoZ8EDFANeU2ZPbs2RP19fWxa9eu467PmTMnrr/++tO+dvDgwaf8uauuuuqEa8ciB4pOxADVltuQee+996KhoSEmTJjQeW3v3r3xxhtvxPz581OcDPJJxABpyG3INDQ0xP79+6OjoyPq6uoiIuLhhx+O2bNnx+TJk0/72vfff/+Ea6NGjYr33nsvXnrppZg4cWJFZoasEjFAWnIbMjNmzIhDhw7Fo48+GosXL46nnnoqNm7cGNu3bz/ja0925uVYDA0aNMiZGOiiNGJWr17tQD1QNbn9qqXGxsZYv359rFu3LqZMmRJbt26NLVu2xJgxY9IeDXKja8QMGTJExABVl9uNTERES0tLtLS0pD0G5FJpxLS3t4sYoOpyu5EBKidJkrj11lvjRz/6kYgBUiVkgB45FjGbNm2K8847T8QAqRIyQLeJGKDW5PqMDFA+pRGzevXqOO+889IeCyg4IQOcUdeIGTp0aLS3t4sYoCZ4tASclogBapmQAU5JxAC1TsgAJ3Wyg70iBqg1zsgAJ0iSJG655Zb48Y9/bBMD1DQbGeA4IgbIEhsZoFNpxKxevTqGDBmS9lgAp2QjA0SEiAGyyUYGOC5izj///GhvbxcxQCbYyEDBiRggy4QMFJiIAbJOyEBBiRggD4QMFJCIAfLCYV8omNKIWb16dQwePDjtsQB6xUYGCkTEAHkjZKAgRAyQR0IGCkDEAHnljAzkXJIkcfPNN8e//uu/ihggd2xkIMdEDJB3QgZySsQAReDREuRQ14gZNmxYtLe3ixggl4QM5ExpxKxevTrq6+vTHgugIjxaghwRMUDRCBnICREDFJGQgRwQMUBROSMDGZckSXzuc5+LzZs3ixigcIQMZFjXiBk+fHi0t7eLGKBQPFqCjBIxAEIGMknEAPyeR0uQMaURs3r16hg0aFDaYwGkwkYGMkTEABxPyEBGiBiAEwkZyAARA3ByQgZqnIgBODUhAzVMxACcnq9aghrVNWIuuOCCaG9vFzEAJYQM1KAkSWLWrFmxZcsWEQNwGh4tQY0RMQDdZyMDNaQ0YlavXh0DBw5MeyyAmmUjAzVCxAD0nI0M1ICuEdPQ0BDt7e0iBqAbbGQgZSIGoPeEDKRIxAD0jZCBlIgYgL5zRgZSkCRJzJw5M1588UURA9AHQgaqrGvEjBgxItra2kQMQC8JGaii0ohpb2+PAQMGpD0WQGY5IwNVImIAyk/IQBWIGIDKEDJQYSIGoHKEDFSQiAGoLCEDFSJiACpPyEAFiBiA6vDl11BmSZLEjBkz4ic/+YmIAagwIQNl1DViRo4cGW1tbSIGoII8WoIyETEA1WcjA2VQGjHt7e1x7rnnpj0WQO7ZyEAfiRiA9AgZ6AMRA5AuIQO9JGIA0idkoBdEDEBtcNgXeihJkrjpppvipz/9qYgBSJmQgR7oGjGNjY3R1tYmYgBS5NESdJOIAag9Qga6QcQA1CYhA2cgYgBqlzMycBqlEdPe3h7nnHNO2mMB8BEhA6fQNWIuvPDCaGtrEzEANUbIwEkkSRLTp0+PrVu3ihiAGuaMDJQQMQDZIWSgCxEDkC1CBj4iYgCyR8hAiBiArBIyFJ6IAcguIUOhiRiAbPPl1xRW14i56KKLYtWqVSIGIGNsZCgkEQOQDzYyFE6SJPEHf/AHsW3bNhEDkHFChkIpjZi2trY4++yz0x4LgF7yaInCEDEA+SNkKAQRA5BPHi2Re10jZtSoUbFq1SoRA5ATNjLkmogByDcbGXIrSZK48cYbY/v27SIGIKdsZMglEQNQDEKG3BExAMUhZMgVEQNQLEKG3BAxAMXjsC+50DViPvaxj0Vra6uIASgAGxkyT8QAFJeQIdNEDECxebREZpVGzKpVq6J/f/+XBigSGxkyScQAEGEjQwYlSRKf/exn42c/+5mIASg4f/qTKV0jZvTo0dHa2ipiAArMoyUyQ8QAUErIkAkiBoCTETLUPBEDwKkIGWqaiAHgdNwRqFlJksQNN9wQ//Zv/xZjxoyJlStXihgAjmMjQ00SMQB0h5Ch5ogYALpLyFBTRAwAPSFkqBkiBoCeEjLUBBEDQG+4U5C60ohpbW2Nfv36pT0WABlgI0OqRAwAfWEjQ2qSJInrr78+duzYEWPHjo2VK1eKGAB6xEaGVIgYAMpByFB1IgaAcvFoiarqGjEXX3xxrFixQsQA0Gs2MlSNiAGg3IQMVSFiAKgEj5aouCRJ4rrrroudO3eKGADKykaGihIxAFSSjQwV0zVixo0bF8uXLxcxAJSVjQwVIWIAqAYhQ9mJGACqRchQViIGgGoSMpSNiAGg2hz2pSySJIlrr702XnrpJREDQNXYyNBnIgaAtAgZ+kTEAJAmIUOviRgA0uaMDL3SNWLGjx8fy5cvj7PO0sUAVJc7Dz0mYgCoFe4+9IiIAaCWeLREt3WNmEsuuSSWLVsmYgBIlZChW5IkiWuuuSZ27dolYgCoGe5EnJGIAaBW2chwWl0j5tJLL42lS5eKGABqhjsSpyRiAKh1NjKcVJIk8ZnPfCZefvllEQNAzXJn4gQiBoCscHfiOCIGgCxxh6KTiAEga9yliAgRA0A2uVMhYgDILF+1VHBdI2bChAmxZMkSEQNAZrhjFZiIASDrbGQKKkmS+PSnPx0///nPRQwAmeXOVUAiBoC8cPcqGBEDQJ54tFQgXSNm4sSJcffdd4sYADLNXawgRAwAeWQjUwBJksSnPvWp2L17t4gBIFfczXJOxACQZ+5oOSZiAMg7d7WcEjEAFIE7Ww6JGACKwmHfnCmNmCVLlkRdXV3aYwFARQiZHEmSJK6++up45ZVXYtKkSXH33XeLGAByzfOGnBAxABSRkMkBEQNAUXm0lHFdI+ayyy6LxYsXixgACsNGJsNEDABFJ2QySsQAgEdLmdQ1Yj7+8Y9HS0uLiAGgkIRMxiRJEtOmTYtXX31VxABQeB4tZYiIAYDjCZmMEDEAcCIhkwEiBgBOTsjUOBEDAKcmZGqYiAGA0/NVSzUqSZKYOnVq/OIXv4hPfOITsWjRIhEDACVsZGqQiAGA7hEyNUbEAED3ebRUQ7pGzOTJk2PhwoUiBgBOw0amRogYAOg5IVMDRAwA9I5HSylLkiSuuuqqeO2112LKlCmxYMECEQMA3WQjkyIRAwB9I2RSImIAoO+ETApEDACUh5CpMhEDAOXjsG8VJUkSTU1N8ctf/lLEAEAZCJkq6Roxn/zkJ2P+/PkiBgD6yKOlKhAxAFAZQqbCRAwAVI6QqSARAwCV5YxMhXSNmMsvvzzmzZsnYgCgzIRMBSRJEldeeWW8/vrrIgYAKsijpTITMQBQPUKmjEQMAFSXR0tlUhox8+fPT3skAMg9G5kyEDEAkA4bmT5KkiSuuOKK2LNnj4gBgCoTMn0gYuB4hw8fjkceeSQiIv7oj/4ozjnnnJQngtp0+PDh+PrXvx4REQcPHkx5mmwTMr3UNWKuuOKKmDdvXtojAUDhOCPTCyIGAE5t+vTp8cUvfjHuu+++GDZsWDQ2NsYTTzwRBw4ciFWrVsWQIUNiwoQJ8f3vf7/P7yVkeujw4cMiBoBCOHToUPz2t7/t1WuffPLJaGhoiO3bt8cXv/jF+PznPx8LFy6M6667Lnbu3Bk333xzLF++PH73u9/1aUYh00O333577NmzJ6688koRA0CuXXP9DdEwYmQ0z50b3/zmN3sUNVdeeWX88R//cUycODG++tWvxoABA6KhoSHuueeemDhxYvzJn/xJ/OY3v4mf//znfZqxZs7IbNu2LV5++eW0xzilw4cPR0TE3r17Y/jw4XHeeefFD3/4w5Sngtpy9OjRzn/etGlT9OvXL8VpoHZ1/b3y9NNPx6uvvpriNKf22quvxlkXTornfvZaPP29JXHOuQPi1ltvicUtLbFo0aLT/h6/4oorOv+5X79+ccEFF8Tll1/eea2xsTEiIt55550+zVgTIfPBBx/ENddck/YY3bZv377YvHlz2mNATfvJT36S9giQCX/+53+e9gindf64qTH0mgVx6K3d8Zvv/2X809NPxz89/XTMnj07hg4desrXnX322cd9XFdXd9y1Y9/5/sMPP+zTfDURMv3794+tW7fW9EbmK1/5Svz3f/933HvvvXHBBRekPQ7UpMOHD3f+obxmzRpffg2n0PX3yl/91V/Fueeem/JEJ/fFL305Dr25M5I3fhIH/9+eOOfcAXFXc3MsbmmJwYMHpz1eRETUdXR0dKQ9RBaMHj063n777Xj99ddj0qRJaY8DNenAgQOdf7i9//77UV9fn/JEUJuy8nuladrV8dqrr8Ztt90ai1taYs6cOTFkyJAzvm769OnR1NQUjz/+eOe1cePGxX333Rf33Xdf57W6urr47ne/G83Nzb2esSY2MgBA7dn64pY4cuRIt+IlLUIGADipAQMGxIABA3r8uk2bNp1w7c033zzhWjkeCvnyawAgs4QMAJBZHi0BZVNfX1+WVTHknd8r5WMjAwBklpABADJLyAAAmSVkAIDMEjIAQGYJGQAgs3IfMnPnzo1hw4bFggUL0h4Fcq+joyPWrl0b48ePj0GDBkVzc3Ps378/7bEg89zLTi33IfPlL385vvGNb6Q9BhTCmjVrYt26dfHkk0/G5s2bY8eOHfHQQw+lPRZknnvZqeU+ZKZPn17Tf9kV5MW2bdti7dq1sWHDhrjxxhtj2rRpcc8998Szzz6b9miQee5lp5Z6yFhFQz489thjMXPmzJg6dWrntcbGxnj33XdTnAqqw70sPamHjFU0ZF+SJPHMM8/E3Llzj7t+6NChGDp0aEpTQfW4l6Un1ZCxioZ82LlzZxw8eDDuv//+GDx4cOePBx54ICZNmpT2eFBRfbmXTZ8+PdavX1/5IXMs1b800ioa8mHPnj1RX18fu3btOu76nDlz4vrrr09nKKgS97J0pRYyx1bRjz322HHXy72KnjVrVrz88stx4MCBGD16dHz729+Oa6+9tmyfH4h47733oqGhISZMmNB5be/evfHGG2/E/PnzU5wMKsu9LH2phUzXVfQDDzzQef3IkSNx0003le19XnjhhbJ9LuDkGhoaYv/+/dHR0RF1dXUREfHwww/H7NmzY/LkySlPB5XjXpa+1M7IHFtF7969O3bt2tX5Y9y4cSddRT/44INRV1d32h+//OUvU/iVADNmzIhDhw7Fo48+Gv/5n/8Zf/ZnfxYbN26MdevWpT0aVFRP72WPPPLIcefINm/eHPfee+9x1956660UfiXZldpGpqer6Pvvvz9aW1tP+zkvueSS4z4+9l+Gp9LR0dH9gYFTamxsjPXr18eaNWviT//0T2PGjBmxZcuWGDNmTNqjQUX19F527733xqJFizo/Xrp0acyfPz/mzZvXeW3UqFHHvca97PRSC5merqJHjBgRI0aM6NF7vPXWW7F8+fJ45513on///vG1r30tFi5cWJb5geO1tLRES0tL2mNAVfX0XjZ8+PAYPnx458cDBw6MkSNHHhdCpdzLTi+1kOm6il68eHE89dRTsXHjxti+fXvZ3qN///7x+OOPR1NTU/z617+OadOmxezZs6O+vr5s7wFAcbmXpS+1MzLHVtHr1q2LKVOmxNatW8u+ir7ooouiqakpIiIuvPDCaGhoiH379pXt8wNQbO5l6avrKMjDtR07dsTKlSvjlVde6dXrR48eHW+//Xa8/vrrvsEXAKno670sj1L9hnjVsm/fvlixYkU88cQTaY8CAL3iXnZyqf9dS5WWJEk0NzfHgw8+GNddd13a4wBAj7mXnVquQ6ajoyNaW1tjxowZsXz58rTHAYAecy87vVyHzIsvvhgbNmyI733ve9HU1BRNTU2xe/futMcCgG5zLzu9XJ+RueGGG+LDDz9MewwA6DX3stPL9UYGAMg3IQMAZJaQAQAyS8gAAJklZACAzBIyAEBmCZluOuss/1MBQK1xd+6mv/u7v4vFdy+Jiy++OO1RAICPFOZvvwYA8sdGBgDILCEDAGSWkAEAMkvIAACZJWQAgMwSMgBAZgkZACCzhAwAkFlCBgDILCEDAGSWkAEAMkvIAACZJWQAgMwSMgBAZgkZACCzhAwAkFlCBgDILCEDAGSWkAEAMkvIAACZJWQAgMwSMgBAZgkZACCzhAwAkFlCBgDILCEDAGSWkAEAMkvIAACZJWQAgMwSMgBAZgkZACCz/j/Q97dm06DjwgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "CiulPlot();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b87b0eb3-7671-4ac9-8ac2-1bb225763178",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "#### CiulPlotThetaInCI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9769f7e5-2fdf-4a42-9e2e-a4bf80ae4b58",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "class CiulPlotThetaInCI(CiulPlot):\n",
    "    def draw(self):\n",
    "        self.fill_theta_in_ci()\n",
    "        super().draw()\n",
    "        self.draw_diagonal_plus_one_half()\n",
    "        self.draw_theta_in_ci()\n",
    "\n",
    "    def fill_theta_in_ci(self): \n",
    "        self.ax.add_patch(Rectangle(xy=(-1/2, 0), width=1/2, height=1/2, edgecolor=self.color_in_ci, facecolor=self.color_in_ci_fill))\n",
    "    \n",
    "    def draw_theta_in_ci(self):\n",
    "        self.ax.text(x=-1/2+self.e, y=1/2-self.e, s=r\"$M - \\frac{1}{2} < \\theta < m + \\frac{1}{2}$\", va='top', ha='left')\n",
    "        self.ax.text(x=0-self.e, y=self.e, s=r\"$m < \\theta < M$\", va='bottom', ha='right')\n",
    "        self.ax.text(x=0+self.e, y=1/2-self.e, s=r\"$m, M > \\theta$\", va='top', ha='left')        \n",
    "        self.ax.text(x=-1/2+self.e, y=0-self.e, s=r\"$m, M < \\theta$\", va='top', ha='left')\n",
    "        self.show_point(x=0, y=0, color=self.color_in_ci)\n",
    "        # self.ax.text(x=0 + self.be + self.e, y=1/2 + self.be, s=r\"$\\text{CI} = [m, M]$\", va='bottom', ha='left')\n",
    "        # self.ax.text(x=0 - self.e, y=1/2 + self.be, s=r\"$\\text{CI} = [M - \\frac{1}{2}, m + \\frac{1}{2}]$\", va='bottom', ha='right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6b5c0a0c-5e26-4657-87ac-1e1b5e52c1df",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "CiulPlotThetaInCI();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b68e1875-aa95-4bb1-887d-cd179004542b",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "#### CiulPlotTheta1InCI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "83592abf-ad31-445f-9805-1e43e0a5b7dc",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "class CiulPlotTheta1InCI(CiulPlot):\n",
    "    def __init__(self, delta, ax=None):\n",
    "        self.delta = delta  # Defined by theta_1 = theta + delta\n",
    "        super().__init__(ax)\n",
    "        \n",
    "    def draw(self):\n",
    "        self.fill_theta_1_in_ci()\n",
    "        super().draw()\n",
    "        self.draw_diagonal_plus_one_half()\n",
    "        self.draw_theta_1_in_ci()\n",
    "\n",
    "    def fill_theta_1_in_ci(self): \n",
    "        if self.delta >= 0:\n",
    "            self.ax.add_patch(Rectangle(xy=(self.delta-1/2, self.delta), width=1/2, height=1/2-self.delta, edgecolor=self.color_in_ci, facecolor=self.color_in_ci_fill))\n",
    "        else:\n",
    "            self.ax.add_patch(Rectangle(xy=(-1/2, self.delta), width=1/2+self.delta, height=1/2, edgecolor=self.color_in_ci, facecolor=self.color_in_ci_fill))\n",
    "    \n",
    "    def draw_theta_1_in_ci(self):\n",
    "        self.show_point(x=self.delta, y=self.delta, xlabel=r\"$\\theta_1$\", color=self.color_in_ci)\n",
    "        if self.delta >= 0:\n",
    "            self.show_point(x=self.delta-1/2, y=self.delta, xlabel=r\"$\\theta_1 - \\frac{1}{2}$\", color=self.color_in_ci)\n",
    "            self.show_point(x=self.delta-1/2, y=self.delta, ylabel=r\"$\\theta_1$\", color=self.color_in_ci, show_point=False)\n",
    "        else:\n",
    "            self.show_point(x=-1/2, y=self.delta, ylabel=r\"$\\theta_1$\", color=self.color_in_ci, show_point=False)\n",
    "            self.show_point(x=-1/2, y=self.delta+1/2, ylabel=r\"$\\theta_1 + \\frac{1}{2}$\", color=self.color_in_ci, show_point=False)\n",
    "            self.show_point(x=self.delta, y=self.delta+1/2, color=self.color_in_ci)        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5b402855-ed3f-456a-b2cd-a9d69ddd0b34",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7b81a1b1f3c04c0d82f857de8cef4abd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.2, description='delta', max=0.5, min=-0.5, step=0.01), Output()), _d…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(delta=.2):\n",
    "    CiulPlotTheta1InCI(delta=delta)\n",
    "interact(f, delta=(-1/2, 1/2, .01));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e44d1f89-452e-4027-97bf-fbfe7b5d371c",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "#### CiulPlotCICondOnWidth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bc9376d6-2472-4ac5-acad-b32e11a6a171",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "class CiulPlotCICondOnWidth(CiulPlot):\n",
    "    def __init__(self, w, ax=None):\n",
    "        self.w = w  # Difference M - m\n",
    "        super().__init__(ax)\n",
    "\n",
    "    def draw(self):\n",
    "        self.fill_theta_in_ci()\n",
    "        super().draw()\n",
    "        # self.draw_diagonal_plus_one_half()\n",
    "        self.draw_theta_in_ci()\n",
    "        self.draw_cond()\n",
    "\n",
    "    def fill_theta_in_ci(self): \n",
    "        self.ax.add_patch(Rectangle(xy=(-1/2, 0), width=1/2, height=1/2, edgecolor=self.color_in_ci, facecolor=self.color_in_ci_fill))\n",
    "    \n",
    "    def draw_theta_in_ci(self):\n",
    "        self.show_point(x=0, y=0, color=self.color_in_ci)\n",
    "\n",
    "    def draw_cond(self):\n",
    "        self.ax.plot([-1/2 - self.e, 1/2 + self.e - self.w], [-1/2 - self.e + self.w, 1/2 + self.e], color=u'#1f77b4')\n",
    "        p = min(1., self.w / (1 - self.w))\n",
    "        self.ax.text(x=1/2 + self.e - self.w, y=1/2 + self.e, s=r\"$\\mathbb{P}[\\theta \\in \\text{CI} \\mid M-m = w] = \" + f\"{p:.2}$\", va='bottom', ha='center', color=u'#1f77b4')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8a36a259-e05a-452c-8dbb-ae69b69c336e",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bed490dec9354463b225e2bc439a7d26",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.2, description='w', max=1.0, step=0.01), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(w=.2): CiulPlotCICondOnWidth(w=w)\n",
    "interact(f, w=(0, 1, .01));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0f07820-a3e5-42e4-b0f9-76275fe05399",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "#### CiulPlotThetaInCR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2dfd3691-d619-43f7-8aa0-1c577fd9626a",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "class CiulPlotThetaInCR(CiulPlot):\n",
    "    def draw(self):\n",
    "        self.fill_theta_in_bi()\n",
    "        super().draw()\n",
    "        self.draw_theta_in_bi()\n",
    "\n",
    "    def fill_theta_in_bi(self): \n",
    "        self.ax.add_patch(Polygon(xy=((-1/2, 1/2), (-1/4, -1/4), (1/4, 1/4)), edgecolor=self.color_in_ci, facecolor=self.color_in_ci_fill))\n",
    "\n",
    "    def draw_theta_in_bi(self):\n",
    "        self.show_point(x=-1/4, y=-1/4, xlabel=r\"$\\theta - \\frac{1}{4}$\", ylabel=r\"$\\theta - \\frac{1}{4}$\", color=self.color_in_ci)\n",
    "        self.show_point(x=1/4, y=1/4, xlabel=r\"$\\theta + \\frac{1}{4}$\", ylabel=r\"$\\theta + \\frac{1}{4}$\", color=self.color_in_ci)\n",
    "        self.show_point(x=0, y=0, color='black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "56d5e52e-ffc7-42d3-bd9f-1e38327b7d1a",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "CiulPlotThetaInCR();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77d9a44d-805f-4317-83c3-b3f92374e918",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "#### CiulPlotTheta1InCR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e80eabd0-12e4-40a4-8769-fa7353819b92",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "class CiulPlotTheta1InCR(CiulPlot):\n",
    "    def __init__(self, delta, ax=None):\n",
    "        self.delta = delta  # Defined by theta_1 = theta + delta\n",
    "        super().__init__(ax)\n",
    "        \n",
    "    def draw(self):\n",
    "        self.fill_theta_1_in_bi()\n",
    "        super().draw()\n",
    "        self.draw_theta_1_in_bi()\n",
    "\n",
    "    def fill_theta_1_in_bi(self): \n",
    "        d = self.delta\n",
    "        if d > 1/4:\n",
    "            xy = [(d - 1/4, d - 1/4), (1/2, 1/2), (4 * d / 3 - 1/2, 1/2)]\n",
    "        elif d > 0:\n",
    "            xy = [(d - 1/4, d - 1/4), (d + 1/4, d + 1/4), (4 * d - 1/2, 1/2), (4 * d / 3 - 1/2, 1/2)]\n",
    "        elif d > -1/4:\n",
    "            xy = [(d - 1/4, d - 1/4), (d + 1/4, d + 1/4), (-1/2, 4 * d / 3 + 1/2), (-1/2, 4 * d + 1/2)]\n",
    "        else:\n",
    "            xy = [(-1/2, -1/2), (d + 1/4, d + 1/4), (-1/2, 4 * d / 3 + 1/2)]\n",
    "        self.ax.add_patch(Polygon(xy=xy, edgecolor=self.color_in_ci, facecolor=self.color_in_ci_fill))\n",
    "\n",
    "    def draw_theta_1_in_bi(self):\n",
    "        d = self.delta\n",
    "        if self.delta < 1/4:\n",
    "            self.show_point(x=self.delta+1/4, y=self.delta+1/4, xlabel=r\"$\\theta_1 + \\frac{1}{4}$\", ylabel=r\"$\\theta_1 + \\frac{1}{4}$\", color=self.color_in_ci)\n",
    "        if self.delta > -1/4:\n",
    "            self.show_point(x=self.delta-1/4, y=self.delta-1/4, xlabel=r\"$\\theta_1 - \\frac{1}{4}$\", ylabel=r\"$\\theta_1 - \\frac{1}{4}$\", color=self.color_in_ci)\n",
    "        if 0 < d < 1/4:\n",
    "            self.ax.text(x=4 * d - 1/2, y=1/2+self.e, s=r\"$\\theta + 4 \\delta - \\frac{1}{2}$\", ha='center', va='bottom', color=self.color_in_ci)    \n",
    "        if 0 < d < 3/4:\n",
    "            self.ax.text(x=4 * d / 3 - 1/2, y=1/2+self.e, s=r\"$\\theta + \\frac{4}{3} \\delta - \\frac{1}{2}$\", ha='center', va='bottom', color=self.color_in_ci)    \n",
    "        if -1/4 < d < 0:\n",
    "            self.ax.text(x=-1/2 - self.e, y=4 * d + 1/2, s=r\"$\\theta + 4 \\delta + \\frac{1}{2}$\", ha='right', va='center', color=self.color_in_ci)\n",
    "        if -3/4 < d < 0:\n",
    "            self.ax.text(x=-1/2 - self.e, y=4 * d / 3 + 1/2, s=r\"$\\theta + \\frac{4}{3} \\delta + \\frac{1}{2}$\", ha='right', va='center', color=self.color_in_ci)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "81a355d4-bda0-4614-a536-9a4d3219df1b",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "13348bf1a10c467cbabbceff16545d40",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.12, description='delta', max=0.75, min=-0.75, step=0.01), Output()),…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(delta=.12):\n",
    "    CiulPlotTheta1InCR(delta=delta)\n",
    "interact(f, delta=(-3/4, 3/4, .01));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ba4e86b-c875-4e14-8426-6a600961995d",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "#### CiulPlotCRCondOnWidth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "bcadd1c6-d177-4ec7-838a-d2dfe4096b38",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "class CiulPlotCRCondOnWidth(CiulPlot):\n",
    "    def __init__(self, w, ax=None):\n",
    "        self.w = w  # Difference M - m\n",
    "        super().__init__(ax)\n",
    "\n",
    "    def draw(self):\n",
    "        self.fill_theta_in_bi()\n",
    "        super().draw()\n",
    "        self.draw_theta_in_bi()\n",
    "        self.draw_cond()\n",
    "\n",
    "    def fill_theta_in_bi(self): \n",
    "        self.ax.add_patch(Polygon(xy=((-1/2, 1/2), (-1/4, -1/4), (1/4, 1/4)), edgecolor=self.color_in_ci, facecolor=self.color_in_ci_fill))\n",
    "\n",
    "    def draw_theta_in_bi(self):\n",
    "        self.show_point(x=-1/4, y=-1/4, xlabel=r\"$\\theta - \\frac{1}{4}$\", ylabel=r\"$\\theta - \\frac{1}{4}$\", color=self.color_in_ci)\n",
    "        self.show_point(x=1/4, y=1/4, xlabel=r\"$\\theta + \\frac{1}{4}$\", ylabel=r\"$\\theta + \\frac{1}{4}$\", color=self.color_in_ci)\n",
    "        self.show_point(x=0, y=0, color='black')\n",
    "    \n",
    "    def draw_cond(self):\n",
    "        self.ax.plot([-1/2 - self.e, 1/2 + self.e - self.w], [-1/2 - self.e + self.w, 1/2 + self.e], color=u'#1f77b4')\n",
    "        self.ax.text(x=1/2 + self.e - self.w, y=1/2 + self.e, s=r\"$\\mathbb{P}[\\theta \\in \\text{CR} \\mid M-m = w] = \\frac{1}{2}$\", va='bottom', ha='center', color=u'#1f77b4')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "473be1af-6c7e-431d-be85-6ac411fbe7de",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ab8e5b016cf44d34b11114865610819c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.2, description='w', max=1.0, step=0.01), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(w=.2): CiulPlotCRCondOnWidth(w=w)\n",
    "interact(f, w=(0, 1, .01));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e021f3c-1e05-4228-b0f5-62911ad19dc3",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "#### plot_compare_theta_1_in_interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5558b946-741b-4a80-b2f6-bb6173f7fa5a",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def plot_compare_theta_1_in_interval():\n",
    "    deltas = np.linspace(-3/4, 3/4, 61)\n",
    "    plt.plot(deltas, [\n",
    "        1/2 - 8 / 3 * delta**2 if abs(delta) < 1/4 else 4/3 * (3/4 - abs(delta))**2\n",
    "        for delta in deltas\n",
    "    ], label=r\"$\\mathbb{P}[\\theta_1 \\in \\text{CR}]$\")\n",
    "    plt.plot(deltas, [\n",
    "        1/2 - abs(delta) if abs(delta) < 1/2 else 0 for delta in deltas\n",
    "    ], label=r\"$\\mathbb{P}[\\theta_1 \\in \\text{CI}]$\")\n",
    "    plt.xlabel(r\"$\\delta$\")\n",
    "    plt.ylabel(\"Probability\")\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "eb117269-f863-43f3-9c15-1a9f3aaf8ccf",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_compare_theta_1_in_interval();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d148b0db-2f18-469c-a6f3-725b3ad1a360",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "source": [
    "#### Monte Carlo estimation of pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "9fa0000a-da28-445c-93a5-f301ce2e2e67",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def plot_mc_estimation_of_pi():\n",
    "    ax = plt.figure(figsize=(5, 5)).add_subplot()\n",
    "    x = np.linspace(0, 1, 50)\n",
    "    ax.add_patch(Rectangle(xy=(0, 0), width=1, height=1, edgecolor='black', fill=False))\n",
    "    ax.add_patch(Arc(xy=(0, 0), width=2, height=2, theta1=0., theta2=90., edgecolor=u'#1f77b4', fill=False))\n",
    "    ax.axis(\"equal\")\n",
    "    xs = np.random.random(100)\n",
    "    ys = np.random.random(100)\n",
    "    is_in = (xs**2 + ys**2 < 1)\n",
    "    ax.scatter(xs[is_in], ys[is_in])\n",
    "    ax.scatter(xs[~is_in], ys[~is_in])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7ee4288d-19fb-4abb-be02-c7ac81c4d42f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mc_estimation_of_pi()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6f9788d-5887-4aec-8d4d-b98d33f5c18f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Theory"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d298d67d-95fd-47b2-baa3-395d49b67329",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Confidence interval: Definition"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c419f85a-f61e-4edb-8636-23be57b9d7ee",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "* $X$ random variable. Example: $X = (X_1, \\ldots, X_n)$, where the $X_i$'s are some iid variables.\n",
    "* $\\theta \\in \\mathbb{R}$ unknown parameter of the distribution that we want to estimate. Example: mean.\n",
    "* $\\phi$ other parameters of the distribution, generally also unknown. Example: standard dev.\n",
    "* $\\gamma \\in [0, 1]$ a confidence level. Example: 95%.\n",
    "\n",
    "A confidence interval for $\\theta$ with confidence level $\\gamma$ is a **random** interval $\\text{CI} = [u(X), v(X)]$ such that, <font color='red'>**for any value of $\\theta$ and $\\phi$**:</font>\n",
    "\n",
    "$$\\mathbb{P}\\big( u(X) \\leq \\theta \\leq v(X) \\big) \\geq \\gamma.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "034327fd-34dc-4095-985d-d862a6e20b8d",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "**Remark:** instead of $\\mathbb{P}[\\theta \\in \\text{CI}]$, it is probably better to think $\\mathbb{P}[\\text{CI} \\ni \\theta]$ because the random variable is $\\text{CI}$ here, not $\\theta$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85dc7fd7-ecd6-4f95-b0a7-781a6baf31f9",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Which confidence interval does always work?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51ddc687-2e46-46ac-9d6c-c1a6242623b0",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "$\\mathbb{R}$ does. But generally, we want the confidence interval to be as **\"small\"** as possible."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb4a2144-6937-4c93-9039-3f4ba64ea5da",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Confidence interval: Interpretation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac703266-d9cc-4773-9472-ac54b78ed47e",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Reminder in a nutshell: $\\forall \\theta, \\mathbb{P}\\big( u(X) \\leq \\theta \\leq v(X) \\big) \\geq \\gamma.$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1681568-6013-47c8-874f-46fefbabf089",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "What can I say **before** applying the procedure?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82c58aa1-cdce-4331-85bf-797b50e046ff",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "* The probability that the confidence interval **will** contain the true value is at least $\\gamma$.\n",
    "* If I repeat the procedure several times, then **on the long run**, a proportion at least $\\gamma$ of the generated confidence intervals will contain the true value."
   ]
  },
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   "source": [
    "And **after**?"
   ]
  },
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   "source": [
    "* I **cannot** say that the probability that the confidence interval **does** contain the true value is at least $\\gamma$. Since $\\theta$ is fixed (although unknown), either the confidence interval contains it, or it does not!"
   ]
  },
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   "source": [
    "In other words, **the confidence level applies to a procedure, not to its end result.**"
   ]
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   "source": [
    "### Credible region: Definition"
   ]
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    "* $\\Theta$ random parameter, which can be seen as drawn according to a prior distribution.\n",
    "* $\\Phi$ other random parameters.\n",
    "* Draw $X$ according to a distribution that depends on $(\\Theta, \\Phi)$.\n",
    "* $\\gamma \\in [0, 1]$ a credibility level. Example: 95%."
   ]
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   "source": [
    "<font color='red'>**Given a value $x$,**</font> a credible region (or credible interval) for $\\Theta$ with credibility level $\\gamma$ is an interval $\\text{CR} = [u, v]$ such that:\n",
    "\n",
    "$$\\mathbb{P}[u \\leq \\Theta \\leq v \\textcolor{red}{\\mid X = x}] \\geq \\gamma.$$"
   ]
  },
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   "source": [
    "**Remark:** Here it really makes sense to think of $\\mathbb{P}[\\Theta \\in \\text{CR}]$, because $\\Theta$ is a random variable and $\\text{CR}$ is fixed (now that you have your data $X = x$)."
   ]
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   "source": [
    "Here again, $\\mathbb{R}$ always works. Is it possible to give a smaller interval without looking at $x$?"
   ]
  },
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   "source": [
    "The support of the prior distribution of $\\Theta$. It may be smaller than $\\mathbb{R}$."
   ]
  },
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   "source": [
    "### Credible region: Interpretation"
   ]
  },
  {
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   "source": [
    "Reminder in a nutshell: With $x$ given, $\\mathbb{P}[u \\leq \\Theta \\leq v \\mid X = x] \\geq \\gamma$."
   ]
  },
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   "source": [
    "Interpretation?"
   ]
  },
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   "source": [
    "* If you accept the prior on $\\Theta$, then $\\gamma$ **actually is** a probability *a posteriori* (by definition!).\n",
    "* Unlike the confidence interval, the credibility level concerns the **end result**: You can really say that there $\\theta$ is in the credible region with probability at least $\\gamma$.\n",
    "* In practice, we generally define a whole procedure, i.e. $[u(x), v(x)]$ for each possible value of $x$. But this is not necessary: for a given $x$, you can say whether $[u, v]$ is a credible region without defining the whole procedure.\n",
    "* But all this comes at the price of accepting the prior!"
   ]
  },
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   "source": [
    "### Frequentists vs Bayesians: Differences of interpretation"
   ]
  },
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   "source": [
    "[Almost verbatim from https://jakevdp.github.io/blog/2014/06/12/frequentism-and-bayesianism-3-confidence-credibility/]\n",
    "\n",
    "* Frequentists consider probability a measure of **the frequency of (perhaps hypothetical) repeated events**.\n",
    "* Bayesians consider probability as a measure of **the degree of certainty about values**.\n",
    "\n",
    "As a result of this:\n",
    "* Frequentists consider **model parameters to be fixed and data to be random**,\n",
    "* Bayesians consider **model parameters to be random and data to be fixed**."
   ]
  },
  {
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   },
   "source": [
    "### Frequentists vs Bayesians: Differences of interpretation (2)"
   ]
  },
  {
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   "id": "9bbb6831-a98c-4b52-a53a-6969d08fda30",
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   "source": [
    "[Still from https://jakevdp.github.io/blog/2014/06/12/frequentism-and-bayesianism-3-confidence-credibility/]"
   ]
  },
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   "source": [
    " \"*Given our observed data,* there is a 95% probability that the true value of $\\theta$ falls within the credible region\" - Bayesians"
   ]
  },
  {
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   "source": [
    "\"There is a 95% probability that when I compute a confidence interval from data of this sort, the true value of $\\theta$ will fall within it.\" - Frequentists"
   ]
  },
  {
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   },
   "source": [
    "Which leads to..."
   ]
  },
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   "source": [
    "\"*Given this observed data,* the true value of $\\theta$ is either in our confidence interval or it isn't\" - Frequentists"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6df9f33b-4526-4c3a-9734-615cfefe3deb",
   "metadata": {
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   },
   "source": [
    "### Frequentists vs Bayesians: Who wins?"
   ]
  },
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   "source": [
    "* The frequentist approach is indisputable, i.e. it is right for any value of $\\theta$. This also implies that if $\\theta$ happens to be random, it is also true for any distribution on $\\theta$.\n",
    "* The Bayesian conclusions may be wrong if the prior is wrong.\n",
    "\n",
    "However, for *your particular data*:\n",
    "* Frequentism tells you... essentially nothing (which helps in being indisputable),\n",
    "* Bayesianism gives you some information."
   ]
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   "source": [
    "## Presentation of the example and first approaches"
   ]
  },
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   "source": [
    "### Presentation of the example"
   ]
  },
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   "source": [
    "Assumption: $X_1$ and $X_2$ iid, uniformly drawn in $[\\theta - \\frac{1}{2}, \\theta + \\frac{1}{2}]$.\n",
    "\n",
    "Goal: Estimate $\\theta$. For the sake of the exercise, we are looking for a **50% confidence interval**.\n",
    "\n",
    "In other words: we have a uniform distribution on an interval of known width 1, and we want to estimate its mean, along with a 50% confidence interval.\n",
    "\n",
    "It will be convenient to define $m = \\min(X_1, X_2)$ and $M = \\max(X_1, X_2)$, which are random variables themselves."
   ]
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   "source": [
    "### Common sense approach: 100% confidence interval"
   ]
  },
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   "source": [
    "**General tip in math / science / life:** It is always a good idea to start by a common sense approach, which will serve as a sanity check for future thoughts. Even more important in statistics because they are especially tricky."
   ]
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   "source": [
    "Reminders:\n",
    "* $X_1$ and $X_2$ iid, uniformly drawn in $[\\theta - \\frac{1}{2}, \\theta + \\frac{1}{2}]$.\n",
    "* $m = \\min(X_1, X_2)$ and $M = \\max(X_1, X_2)$.\n",
    "* We want to estimate the unknown parameter $\\theta$.\n",
    "\n",
    "Let us warm up: Any ideas for a **100%** confidence interval on $\\theta$?"
   ]
  },
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   "source": [
    "$$\\theta \\in A = [M - \\frac{1}{2}, m + \\frac{1}{2}].$$\n",
    "\n",
    "This is trivial because $m, M \\in [\\theta - \\frac{1}{2}, \\theta + \\frac{1}{2}]$. In particular, $M \\leq \\theta + \\frac{1}{2}$ and $m \\geq \\theta - \\frac{1}{2}$."
   ]
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   "source": [
    "### Still warming up"
   ]
  },
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   "source": [
    "I ran an experiment and found $m = 0.001, M = 0.499$. As we noticed, we know with certainty that $\\theta \\in A = [-0.001, 0.501]$.\n",
    "\n",
    "What is the probability that $\\theta \\in [m, M] = [0.001, 0.499]$?"
   ]
  },
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   "source": [
    "Actually, it is 0%, because $\\theta = 0.00001$ and I did not tell you."
   ]
  },
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   "source": [
    "... Or it is 100%, because $\\theta = 0.35673$ and I did not tell you."
   ]
  },
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   "source": [
    "Do you think I'm cheating? Those are actually perfectly normal frequentist interpretations."
   ]
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   "source": [
    "### A stupid (but instructive) 50% confidence interval"
   ]
  },
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    "Let $B$ be a random bit defined by $B = 1$ if $X_1 \\leq X_2$ and $0$ otherwise. It provides a fair coin flip that is independent of $(m, M)$.\n",
    "\n",
    "Define $\\text{SCI}$ by:\n",
    "* If $B=0$, let $\\text{SCI} = A = [M - \\frac{1}{2}, m + \\frac{1}{2}]$ ,\n",
    "* If $B=1$, let $\\text{SCI}$ be a single-point interval, for example $\\text{SCI} = [\\frac{M+m}{2}, \\frac{M+m}{2}]$. Or even more nonsensical, $\\text{SCI} = [42, 42]$. Or even $\\text{SCI} = \\emptyset$ if you consider that it is a valid (degenerated) interval.\n",
    "\n",
    "Then $\\text{SCI}$ **is a 50% confidence interval**. Could you prove it?"
   ]
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   "source": [
    "$\\mathbb{P}[\\theta \\in \\text{CI}] = \\mathbb{P}[B = 0] = \\frac{1}{2}$."
   ]
  },
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   "source": [
    "Do you see its very counterintuitive properties?"
   ]
  },
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   "source": [
    "* If the procedure returns an interval of positive length, we know that $\\theta \\in \\text{CI}$ with certainty.\n",
    "* Otherwise, we know that $\\theta \\notin \\text{CI}$ with (almost) certainty."
   ]
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   "source": [
    "### Interpretation of our stupid 50% confidence interval"
   ]
  },
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   "source": [
    "This example illustrates what we have already said before:"
   ]
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    "* If I repeat the procedure several times, then **on the long run**, 50% of the generated confidence intervals will contain the true value.\n",
    "* **Before** I apply the procedure, I **can** say that the probability that the confidence interval **will** contain the true value is 50%.\n",
    "* However, **after** applying the procedure, I **cannot** say that the probability that the confidence interval **does** contain the true value is 50%. "
   ]
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   "source": [
    "Specificity of this example: After applying the procedure, I can even know with certainty if it contains the true value or not.\n",
    "\n",
    "Generality of this example: The confidence level cannot be interpreted as a probability **a posteriori**."
   ]
  },
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   "source": [
    "### Another stupid 50% interval (?)"
   ]
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   "source": [
    "Let $B$ be a random bit defined by the first fractional bit of $X_1$. Define $\\text{SCI}'$ by:\n",
    "\n",
    "$$\\text{SCI}' = A = [M - \\frac{1}{2}, m + \\frac{1}{2}] \\text{ if } B=0 \\text{ and } [42, 42] \\text{ otherwise}.$$"
   ]
  },
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   "source": [
    "Is $B$ a fair coin flip?"
   ]
  },
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   "source": [
    "Yes because $X_1$ is drawn uniformly on $[\\theta - \\frac{1}{2}, \\theta + \\frac{1}{2}]$."
   ]
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   },
   "source": [
    "Is $B$ independent of $(m, M)$?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c925aa68-0da0-4c9c-8bcf-dceae9ff285a",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "No. For exemple, if $m, M \\in [0, \\frac{1}{2}]$, then $B = 0$ with certainty."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82a1c560-29de-40e3-864d-594362649850",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "Is $\\text{SCI}'$ a 50% confidence interval?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6904976c-015e-4aff-bd30-f8134c1406b5",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "Yes because $\\mathbb{P}[\\theta \\in \\text{SCI}'] = \\mathbb{P}[B = 0] = 50\\%$. $\\Rightarrow$ In $\\text{SCI}$, the independence of $B$ and $(m, M)$ was intellectually comfortable but actually not necessary for our argument."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "597c8eb3-5391-4654-b106-f6f10dedba18",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## An \"optimal\" 50% confidence interval"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "542fdc26-0da1-4a50-b138-8ea5180e54b9",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Define CI"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7fd8b06-9b65-4fc4-9233-6d0d0f8819a1",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "* If $M - m \\geq \\frac{1}{2}$, let $\\text{CI} = A = [M - \\frac{1}{2}, m + \\frac{1}{2}]$.\n",
    "* If $M - m < \\frac{1}{2}$, let $\\text{CI} = [m, M]$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "669de14c-0e92-4917-8dc2-bd9c79b603b6",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "In other words, $\\text{CI} = [\\max(M - \\frac{1}{2}, m), \\min(m + \\frac{1}{2}, M)]$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4141e413-ae6d-47aa-bce4-356d0ef7d287",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Check that CI is a 50% confidence interval"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b8ba6b2-17bd-4aca-80af-9d7777ded703",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Reminder: $\\text{CI} = [M - \\frac{1}{2}, m + \\frac{1}{2}]$ if $M - m \\geq \\frac{1}{2}$ and $[m, M]$ if $M - m < \\frac{1}{2}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "bc3f21ef-4617-46ea-8347-1210bb1557f5",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "CiulPlotThetaInCI();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcf3066f-a33c-4aad-b8aa-0d5dd5e5ba8c",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Optimality of CI"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba8a1611-cc61-444d-81ef-ad3d34846dea",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "It can be shown that $\\text{CI}$ is optimal in the sense that it is \"uniformly most accurate unbiased and uniformly most accurate invariant at level [50%]\"[*] (honnestly, I did not delve into this.)\n",
    "\n",
    "[*] Pratt, J. W. (1961). \"Book Review: Testing Statistical Hypotheses. by E. L. Lehmann\". Journal of the American Statistical Association. 56 (293): 163–167.\n",
    "\n",
    "Roughly speaking, it is optimal in the sense of the usual theory of confidence intervals.\n",
    "\n",
    "We will not prove this, but we will at least show that it is \"better\" than another example of 50% confidence interval (still in the sense of the usual theory of confidence intervals)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb2d7590-3cf2-4603-867b-57d502166591",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Surprising properties"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2862e6f-45c4-464c-8415-cac31a84ed5f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "* If $M - m > \\frac{1}{2}$, then $\\text{CI}$ is *guaranteed* to contain the true value $\\theta$.\n",
    "* If $M - m = 0^+$, then note that we have very little information: $A = [M - \\frac{1}{2}, m + \\frac{1}{2}]$ (an interval of width almost 1). However $\\text{CI} = [m, M]$, which excludes almost all possible values.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2353b18-dc72-4091-8261-8a34a61f36de",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### $\\mathbb{P}[\\theta \\in \\text{CI} | M - m = w]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "03fd20c8-5311-4201-ba61-379a50f8d568",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f91975eb2ae54080ae001fd6f524e649",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.2, description='w', max=1.0, step=0.01), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(w=.2): CiulPlotCICondOnWidth(w=w)\n",
    "interact(f, w=(0, 1, .01));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e49275f-12c7-406f-8249-eb0af3abeada",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "All this averages out to have $\\mathbb{P}[\\theta \\in CI] = \\frac{1}{2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43d18ff0-dcbb-4542-9960-bc1f5c995b04",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Bayesian approach: Credible region"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cede091-182e-4490-87e4-ab1e3115c455",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Define CR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cabd9b5a-5f89-4a56-822b-891191ae3ef7",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "We know that $\\theta \\in A = [M - \\frac{1}{2}, m + \\frac{1}{2}] = [\\bar{X} - \\frac{1 - (M-m)}{2}, \\bar{X} + \\frac{1 - (M-m)}{2}]$, where $\\bar{X} = \\frac{M + m}{2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b211d0b-bd3f-4107-9b5c-4a9854e5f075",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Any idea for a 50% credible region?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19d05aa4-385f-431e-acdb-313967fec03e",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "* Uniform prior on this interval.\n",
    "* Whatever $\\theta$ in this interval, the (density of) probability for $(X_1, X_2) = (x_1, x_2)$ is the same.\n",
    "* So the posterior on this interval is also uniform.\n",
    "* 50% credible region: $\\text{CR} = [\\bar{X} - \\frac{1 - (M-m)}{4}, \\bar{X} + \\frac{1 - (M-m)}{4}]$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4146cdf-c363-46d6-9b7b-5d460a9b3e15",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Remark: Other 50% credible regions exist, for exemple $ [\\bar{X}, \\bar{X} + \\frac{1 - (M-m)}{2}]$. We simply chose the most natural one, which is centered on the empirical mean."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8107c0e-7cb6-4fbd-869b-ee591ca56a03",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### CR happens to be also a 50% confidence interval"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98c02eca-7775-481a-b5ea-28660e28a15a",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "... Whereas it was defined as a 50% **credible region** in the Bayesian sense."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91c7a42e-a5e8-4187-90bd-c1fdeebee3ea",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Reminder: $\\text{CR} = [\\frac{M + m}{2} - \\frac{1 - (M-m)}{4}, \\frac{M + m}{2} + \\frac{1 - (M-m)}{4}]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4c59c966-e99c-4b3e-9216-54860ee296df",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "CiulPlotThetaInCR();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dfa08a0-07fe-4f70-a173-16186909ee74",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Intuitive properties"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eed38750-e073-4d0c-bc2f-f5af345dd698",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "* If $m$ and $M$ are far, then $A$ is of length close to 0 and $\\text{CR}$ too.\n",
    "* If $m$ and $M$ are close (leaving more uncertainty on $\\theta$), then $A$ is of length close to 1 and $\\text{CR}$ is of length close to $\\frac{1}{2}$.\n",
    "\n",
    "Intuitively: the more information, the shorter the credible region."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1e2474c-6a3a-40d4-ac0d-fd7aa7e48dd0",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### $\\mathbb{P}[\\theta \\in \\text{CR} | M - m = w]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "927df958-eba8-4ae5-9c32-70f39a497d4f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9bc8ec881cd64e6bb5a7f32933c1d641",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.2, description='w', max=1.0, step=0.01), Output()), _dom_classes=('w…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(w=.2): CiulPlotCRCondOnWidth(w=w)\n",
    "interact(f, w=(0, 1, .01));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3df27a9b-946d-4ee3-87bf-a73ea74d1a74",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "* $\\mathbb{P}[\\theta \\in \\text{CR} \\mid M-m = w] = \\frac{1}{2}$ for any value of $w$, which is less disturbing than for $\\text{CI}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1b9331d-939b-49c3-9a3a-5876f494566a",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Probability that a given incorrect value is in the interval"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed86783f-a987-43c3-9e4a-07667355e932",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### $\\mathbb{P}[\\theta_1 \\in \\text{CI}]$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6387b2c5-1bd1-4511-9c62-d9fbbc384c7b",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Let $\\theta_1 = \\theta + \\delta$ a value that may be different from $\\theta$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cee85ec4-193c-4a07-8a48-b8d0716f2b06",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "$\\theta_1 \\in \\text{CI} = [\\max(M - \\frac{1}{2}, m), \\min(m + \\frac{1}{2}, M)]$\n",
    "\n",
    "$\\Leftrightarrow M - \\frac{1}{2} \\leq \\theta_1$ and $m \\leq \\theta_1$ and $\\theta_1 \\leq m + \\frac{1}{2}$ and $\\theta_1 \\leq M$\n",
    "\n",
    "$\\Leftrightarrow$ $\\theta_1 - \\frac{1}{2} \\leq m \\leq \\theta_1$ and $\\theta_1 \\leq M \\leq \\theta_1 + \\frac{1}{2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d84b1f87-47e4-4668-b6d2-3bdc97ec9d88",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### $\\mathbb{P}[\\theta_1 \\in \\text{CI}]$ (plot)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30d60c50-be9d-46c6-ac67-3ff5f577e5a8",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Reminder: $\\theta_1 \\in \\text{CI}$ $\\Leftrightarrow$ $\\theta_1 - \\frac{1}{2} \\leq m \\leq \\theta_1$ and $\\theta_1 \\leq M \\leq \\theta_1 + \\frac{1}{2}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "283fd9f0-5a1e-4595-bfe1-879a4c944b5e",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8ef77a5597904bf3a4ab8657da850d2f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.2, description='delta', max=0.5, min=-0.5, step=0.01), Output()), _d…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(delta=.2): CiulPlotTheta1InCI(delta=delta)\n",
    "interact(f, delta=(-1/2, 1/2, .01));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f199ffd-3b8a-419b-a129-be8ff5a65f14",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### $\\mathbb{P}[\\theta_1 \\in \\text{CR}]$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0766844-34a3-454a-b81a-be0f59ebc333",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "$\\theta_1 \\in \\text{CR} = [\\frac{M+m}{2} - \\frac{1 - (M-m)}{4}, \\frac{M+m}{2} + \\frac{1 - (M-m)}{4}]$\n",
    "\n",
    "$\\Leftrightarrow$ $\\frac{3}{4} M + \\frac{1}{4} m \\leq \\theta_1 + \\frac{1}{4}$ and $\\frac{1}{4} M + \\frac{3}{4} m \\geq \\theta_1 - \\frac{1}{4}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecef80f2-7582-4bec-8549-7283fe766224",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### $\\mathbb{P}[\\theta_1 \\in \\text{CR}]$ (plot)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9feb223-4120-4756-ae4b-8b3f71a33fe5",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Reminder: $\\theta_1 \\in \\text{CR}$ $\\Leftrightarrow$ $\\frac{1}{4} M + \\frac{3}{4} m \\geq \\theta_1 - \\frac{1}{4}$ and $\\frac{3}{4} M + \\frac{1}{4} m \\leq \\theta_1 + \\frac{1}{4}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a5104701-0087-43d9-aef1-9d80ed21db9e",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "48a1ae8c75a04f0fa9c1978cd96f33f2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.12, description='delta', max=0.75, min=-0.75, step=0.01), Output()),…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(delta=.12): CiulPlotTheta1InCR(delta=delta)\n",
    "interact(f, delta=(-3/4, 3/4, .01));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcb3de77-297d-47f8-8c1e-7ac78eb93f86",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### $\\mathbb{P}[\\theta_1 \\in \\text{CI}]$ vs $\\mathbb{P}[\\theta_1 \\in \\text{CR}]$: Formulas"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c02bd3f-a04c-4ec9-a07b-225ba8147e72",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "From what precedes, we can deduce that:\n",
    "* If $|\\delta| \\leq \\frac{1}{2}$, $\\mathbb{P}[\\theta_1 \\in \\text{CI}] = \\frac{1}{2} - |\\delta|$.\n",
    "* If $|\\delta| \\geq \\frac{1}{2}$, $\\mathbb{P}[\\theta_1 \\in \\text{CI}] = 0$.\n",
    "\n",
    "And:\n",
    "\n",
    "* If $|\\delta| \\leq \\frac{1}{4}$, $\\mathbb{P}[\\theta_1 \\in \\text{CR}] = \\frac{1}{2} - \\frac{8}{3} \\delta^2$.\n",
    "* If $|\\delta| \\in [\\frac{1}{4}, \\frac{3}{4}]$, $\\mathbb{P}[\\theta_1 \\in \\text{CR}] = \\frac{4}{3} \\left( \\frac{3}{4} - |\\delta| \\right)^2$.\n",
    "* If $|\\delta| \\geq \\frac{3}{4}$, $\\mathbb{P}[\\theta_1 \\in \\text{CR}] = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "436b461d-0076-4742-ab44-5413a8f655bd",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### $\\mathbb{P}[\\theta_1 \\in \\text{CI}]$ vs $\\mathbb{P}[\\theta_1 \\in \\text{CR}]$: Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "3af1ce25-a3ce-41c4-a5ad-a51fd59b9a1a",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_compare_theta_1_in_interval();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eff8ccbc-f0d7-417c-a40c-e82598620280",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "$\\Rightarrow$ $\\mathbb{P}[\\theta_1 \\in \\text{CI}] < \\mathbb{P}[\\theta_1 \\in \\text{CR}]$ for each $\\theta_1 \\neq \\theta$.\n",
    "\n",
    "$\\Rightarrow$ $\\text{CI}$ is better than $\\text{CR}$ according to the theory of confidence intervals."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0ccf305-b876-40b4-95c3-d9681c90da6f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e35b55c6-ec54-498d-8c34-ce0242869b1f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Final quiz: Monte Carlo estimation of $\\pi$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a84798a1-5fa8-4ebb-b686-811521f96a18",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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n5iuhVn/ce+VluGNwEj74/jAWf1mIa/72FW7ql4D7szojrm0z58vxlADvKFV16s6aKYuHZMXkJhNfVCJqidESenOs/mZMzEzEzZcn4J38Q3jli334eEcxbh+UiHuvTEHbwIDGD+ApAZ5TKnG4c7K6qyMyFg/5BJMbScZoCd0Zi58ZdwxJwk39O+D1r4vw+teFeHfLIUwbloIpgxM920JAjSlVderOyeruJELyGtfciGQSYvXHrOFd8OXDV+EPfTtg4bqfMeyvG/Hv/IM4V29TOjxtU7Lq1NU1UxYPyYrJjUhmkcEW/HlMd2z405UYclkknly1C8MXfIlPfjgCm0pOi9AcpRNH2hjggV3A5E+BP7xh//zAzkuLgVg8JBvOhxApJCE8EH8b1xt3X5GMv362F/e9ux2vfbUfD4/ohqGdIyEIxlmf9AlH4mh2g/R86ROHq2umLB6SBZMbkcJSY0Ox9PbLsaXoBJ7P3YNJS7cgMzkCs6/tht4JbZUOT1u0kjhYPCQ5JjcilRiQFI4Pp2ViXUEZ/vrZHoxd9A1Gdo/B7Gu7ISkySOnwtIOJg8A1NyJVEQQBw9Oi8d/7r8CLN/XCzuIKjPjbV/jrZ3twpu680uERaQaTG5EKmU0CbuzXAeuyh2HasGTkfF2E4Qu+Qu6uoxBFFp0QtYbJjUjF2gSYkX1NV/zvgSvQJToY05Ztw6SlW1B47LR3X9hWDxR9Dez80P6Z/QzlxddfclxzI9KAxMggLL39cqwrKMNTn/yEEQu/wtShyZh59WXubwLnkSvK4usvC47ciDTCsR63LnsY7r3yMry+qQhZL32JtTvdmKrkkSvK4usvGyY3Io2x+psxa3gXrJs1DGlxobj3nW2Y+MYW7Cv7baqy3iYib/9xrNpRjLz9x1FvE3nkitL4+suK05JEGtUxIhCvT74cG/aU4s+rd+Pal7/CHUOSkBoTiudz9zQ6kSE2zIqXM6owQInO+WSn1MkFBsXkRqRxV3eLxqCUSLz2ZSH+seEXnG+mhVdJRQ2WrfsOAwKa+QJN8cgVafDIG1lxWpJIB6z+Zsy8+jK0C2o+e4kAytDWtS92fL/P4qKLKHVygUExuRHpxJaiEzhWVev8323dcEQMh+i0c/4FG59jYYMUlDy5wICY3Ih0oqyqpsV/t8GEp85NcuErCSxskILSJxcYDJMbkU5EhVhbvc9ntgE43PP+Vu51UWED+RaPvJENC0qIdGJAUjhiw6woqahpttjc4T8HAjDLlS/IwgZpaOXkAo3jyI1IJ8wmAXNHpwFoftJLAJA9vAuKakNc+4IsbJCO4+SCHjfaPzOx+RyTG5GOjEyPxau39UVMWOMpypgwK169rS/++LvOmD/rHlT4R8H5od8sbCDt47Qkkc6MTI/F8LQYbCk6gbKqGkSFWDEgKRxmk308F2i1ADe8BPH9SbBBbHKFy8IGuoitvvnpU2e3qwiTG5EOmU0CMlMinN8hbQyEm9+G+N/ZQNVvXTPOB8fC7zo28CU4b/CcfiOw60PVN35mciMyqrQxMF0obPilcB/+saUK6ypS8OCJNNxuE2EytbIfjvTL0eC5aWlS5RFg898vvb+j8bOKKj655kZkZBcKGzr/bgrm/+le3Hx5Ip7+dDcmvJ6P0sqW982RTrXY4NkZ9TV+ZnK7oNku6kQGEhjghz+P6Y7lUzNQVF6Na1/+Ghv3likdFsmt1QbPzqhrfySnJQHk7jqKpz7ZfUkX9bmj0zAyPbaFRxLpz6CUSKz941D86YMfcPu/vsM9VyTjwRFd4W/mtbAheLu/USX7Iz36bV20aBESExNhtVqRkZGBLVu2tHj/hQsXomvXrmjTpg0SEhIwa9Ys1NSoY8ojd9dRTF+2rVFiA+xd1Kcv24bcXUcVioyMSC0zCBHBFiydfDnmXNsNb2wqws2v5eHwiTOKxEIy83Z/o0r2R7o9cnvvvfeQnZ2NxYsXIyMjAwsXLsSIESOwd+9eREVFXXL/5cuX45FHHsHSpUsxaNAg/Pzzz7j99tshCAIWLFjgk2/CU/U2EU99stvp0YECgKc+2Y3haTENZdTkW/U20WnJutGobQbBZBJwz7AUXJ4UjvuWb8eov3+NF27shZHpMbLHQjJyNHiuPAr31t0E++NUsj/S7ZHbggULMHXqVEyZMgVpaWlYvHgxAgMDsXTp0mbvv3nzZgwePBgTJkxAYmIirrnmGowfP77V0Z4cthSduGTEdjERwNGKGmwpOiFfUAaSu+sohjy/AeNz8nH/ih0Yn5OPIc9vMORoWc0zCH07tsPaPw7FoJRITFu2FXNX7ULNOXUUDSjKVg8UfQ3s/ND+WSWFFF5rscGzM+rbH+lWcqurq8PWrVuRlZX12xcwmZCVlYW8vLxmHzNo0CBs3bq1IZkVFhZi7dq1uO6665w+T21tLSorKxt9SKG1Luru3o9cp+Y3c7m1NoMA2GcQlCxyCgv0x6u39cUz13fHu1sO4//+uRmFx04rFo/idq8GFqYDb/0e+M+d9s8L0/VzVJDTBs/xwKA/Xji65+Lb1df42a1pyfLyctTX1yM6uvGcanR0NPbs2dPsYyZMmIDy8nIMGTIEoiji/PnzmDZtGh599FGnzzNv3jw89dRT7oTmEVe6qLtzP3INp4Mbc2cGocWN2RITBAETMxPRt1M73Ld8O0b/YxP+ckMPjO0Tr1hMinC6B0x9e7280lKD56w/q75DieTlTxs3bsRzzz2Hf/7zn9i2bRs++ugjrFmzBs8884zTx8yZMwcVFRUNH4cPH5YkNkcX9RaODkRsmH0diHyH08GNaW0GoXtcGFbfNwTXdI/BA+/twEMf/IAzdeeVDkseLe4BU99eL685a/CsgcbPbo3cIiMjYTabUVrauNSztLQUMTHNLzI/8cQTmDhxIu666y4AQI8ePVBdXY27774bjz32GEymS/OrxWKBxWJxJzSPOLqoT1+2DQIa/7o6Et7c0WmSjR6MWkyhtTdzqWlxBiHY4ocFN/fCoJQIPLnqJ2w/fAqLJvRF1xgXTxzQqlb3gF201ytpqGxh0aXcGrkFBASgX79+WL9+fcNtNpsN69evR2ZmZrOPOXPmzCUJzGy2Z3lRVH6jdGtd1KWqUjNyMYUW38ylpNUZBEEQcFP/BHxy32CYBQFjXtmED76XZpZFNVzdw6WSvV5G5vZWgOzsbEyePBn9+/fHgAEDsHDhQlRXV2PKlCkAgEmTJiE+Ph7z5s0DAIwePRoLFixAnz59kJGRgX379uGJJ57A6NGjG5Kc0lrrou5rjmKKpqndUUwhZVJVg9YO1RRgv7hQ25u5VJSeQfDWZVEhWDVzMOau+gkPffgj9pRUYc613eCnx03fru7hUsleLyNzO7mNGzcOx44dw5NPPomSkhL07t0bubm5DUUmhw4dajRSe/zxxyEIAh5//HEUFxejffv2GD16NP7yl7/47rvwgVa7qPsIiym0/2YuBccMQtN9bjEa6ZRj9Tdj/h96IC0uFE9/uhs/l1bhlfF9ERbor3RovtXqHjB17fUyMkFUw9xgKyorKxEWFoaKigqEhoZ69DW2bduGfv36YevWrejbt6+PI3Rd3v7jGJ+T3+r93p06UNHKODmobdOyGuhhHfabfeWYsXwb2gUGIGdSP1wWpbN1uIZqSaDZSzO9VEv6mC/eg93JBewtKTMWU/xG7ulgLZBrBkFKgy+LxKoZg3HXW9/jhkWb8ffxfXBVt0u7F2mWYw9Yc2edjZzPxKYSTG4yYzFFY3p4M6dLdYoIwkf3DsKs93bgjre+w+yR3XDPFckQBJ1cuLS0B8zXNHDqtRoxucmMxRRkFCFWfyyZ2B8LPv8Z8/+7B3uOVmL+H3rC6q+TN2bHXi8pOTsNW2WnXquRDsuZ1M1RTAFc2rXNqMUUpF8mk4AHR3TF38f3Qe5PJRj3Wh5KWtjATxdxrO013Vfn6ISil1ZfEmFyU4BSe+uIlDKmVxw+uGcQyqpqMeaVTdh+6KTSIamb0TqhSIDTkm7wZSUbiynIaHp0CMOqmYMxfdk2jFuSj3k39MAf+nVQOix1YicUrzG5uUiKsnU1FFPoofSctCMqxIrlUzPw+Me78KcPfsDe0irMHtlNnt85LRVmsBOK15jcXKDXjiLcZ0ZKsPiZ8cKNPZEaG4pn11zY8D2hL4ItEr4daa0wg51QvMY1t1Zo4awtT/A8NVKSIAi4Y0gS3rpjAL4/cBITcvJRfrpWmifTYmGGoxNKSx1HQ+PZCaUFTG6t0OPxLHpN2KQ9Qzu3x4q7B+LIqRrctDgPh0+c8e0TaLUwo8XTsNV36rUaMbm1Qo8dRfSYsEm70uPD8NH0QbCJIv7v1c3YfaTSd1/cncIMtXF6Grb6Tr1WI665tUKPHUX0mLBJ2zpGBOLDaYMw5c0tGPdaHpZM6u+bYiutF2bI2QlFZzhya4VWz9pqiRYSdr1NRN7+41i1oxh5+49zitQA2odYsOLuTPRMCMPkpVvw350+WPfVQ2GGBk69ViMmt1bosaOI2hO2kQ9yNbpgix+W3n45rukejXuXb8Oy/IPefUEWZhgWk5sL9NZRRM0Jm1WcZPEz4++39MHkzEQ8vnIX/vb5z/D4ZC4WZhgW19xcpLeOImo8HFOLB7lyE7w0TBcuwKJCLXghdy/Kqmrx7Nh0z15bHlFjSExublBDRxFfUlvCdqeKUw0/B26Cl5YgCLj3yssQGWzBnI924kR1LV6+pY9npwqwMMNwmNwMTk0JW0tVnHrtWqNGN/dPQHhgAGYs34ZJS7cgZ1J/hLXxd/8LyXFEDakG19xINbRQxQlwE7wSstKisXxqBvaWVGHca3korVT+AofUjcnNDSxPl5avqzil+nlxE7wy+nUKx4fTMlFx9hz+8Opm33czIV3htKSLuL4iPUcV5/Rl2yCgccMkd6s4pfx5aWn6VG86R4fgw+mDMCEnH7csyce7UweiY0Sg0mGRCnHk5gKWp8vHF9supP55aWX6VK/i27bBirsHIsDPhHFL8lBUXq10SKRCHLm1Qovl6VrnTRWnHD8vx/RpSUVNs88jwJ6MtdS1Rmtiw+wJbnxOPm5ZkoflUwcipX2w0mGRinDk1gquryjDUcV5fe94ZKZEuJyI5Ph5qXkTvJFEh1qx4u6BCLX645Yl+filtErpkEhFmNxawfUVbZHr56W3rjVaFRVixbt3D0R4YADG5+RjbwkTHNlxWrIVXF/RFjl/XmrbBG9UkcEWvHv3QNz6+rcYn5OP5VMz0C0mVOmwSGEcubVC7U2G1UyJrRNy/7w8nT4l3woPCsDyuzIQE2rFrTnfcoqSmNxaw/UVzyjV2Z8/L+NqFxSAZXdloH2IBeNzvsW+stNKh0QKYnJzAddX3KP01gn+vIwr/EKCaxfojwk5+dwmYGBcc3MR11dco5atE/x5GVdksAXLpw7ELUvyMH5JPt67ZyA6RQQpHRbJjMnNDWpqMqxWcnb2b+24GbX+vHhMjvTah1jw7tSBuGVJ/oUEl4mEcHYyMRImN/IpuUrxtdoOTatxa1FUqBXLpw7EuCV5uGVJPj6Ylom4tm2UDotkwjU38ik5SvGVXtPzlFbj1rKYMCvenToQADB56RacOlOncEQkFyY38impS/G1etyMVuPWg7i2bfD2nQNQfroWd771Pc7W1SsdEsmAyY18SupSfK22Q9Nq3HqR0j4Y/5oyALuPVGLm8m04X29TOiSSGJMb+ZyUpfhabYem1bj1pHdCW7x6W198+fMxzPloJ0SRo2Q9Y0GJj7ACrjGpSvG12g5Nq3HrzZVdo/DXm3pi1ns/oH2IBQ+P7KZ0SCQRJjcfYAVc86QoxdfqcTNajVuPbujTAeVVdfjL2gK0D7FgyuAkpUMiCXBa0kusgJOXVttraTVuvZp6RTLuviIZT3+6G6t/OKJ0OCQBJjcvsAJOGVptr6XVuPXqkZHdcEPvePzp/R3Y9Eu50uGQj3Fa0gtyduOgxrTaXkurceuRySTg+Rt74sSZOtzz7++x4u5M9OgQpnRY5CNMbl5gBZyy1NpeqzVajVuP/M0m/PPWvhif8y1u/9cWfDh9EJIi2YdSDww9LenteWOsgCPSvsAAP/zr9ssRFuiPSUu/5cWoThh25OaLCkdWwBHpQ3hQAN6+YwD+8Opm3L70O7x3z0CEWP2VDou8YMiRm68qHFkBR6QfHdoF4q07BuDwyTO4599bcY5dTDTNcMnN1xWOrIAj0o9uMaF4fVJ/fHfgBJ765CelwyEvGG5asqC8zucVjqyAI9KPjOQIPHN9Oh75aCe6xoRi4sBOSodEHjBccjtZ49pUg7uLyqyAI9KPWwZ0xJ6SKjy1+idc1j6Yf9saZLhpyXZW175lVjgSGdvjo1KRkRyOe9/ZisMnzigdDrnJcMktNTJA0vPGiEgf/MwmvDK+L0Ks/pj69veorj2vdEjkBsMlN1Y4EpGr2gUF4PXJ/XH4xBlkv78DNrbS0wzDJTeAFY5E5Lou0SF4+ZY++N/uUixc/4vS4ZCLDFdQ4sAKRyJyVVZaNB68piv++tledIsJwXU9eAGsdoZNbgArHJXCg11Ji+69MgUFRyvxp/d/QKeIQHSPY5NlNTN0ciP58WBX0ipBEPDXG3vhptc24+63t2LVzMGIDLYoHRY5Ycg1N1IGD3YlrWsTYMaSif1Re96G6cu2ou48W3SpFZMbOeXtqQlNvxYPdiU9iGvbBq9N7IsfDldg7updEEX+zqoRpyWpWb6ePuTBrqQn/TqF49mx6Xj4Pz+iW0woJg9KVDokaoIjN7qEFNOHPNiV9ObmyxMwZXAinvl0N7YdOql0ONQEkxs1ItX0IQ92JT169LpU9OwQhvuWb0fFmXNKh0MX8Si5LVq0CImJibBarcjIyMCWLVtavP+pU6cwY8YMxMbGwmKxoEuXLli7dq1HAZO03Jk+dIfjYFe2PSM98Teb8PfxfVBVcw6z//Mj199UxO3k9t577yE7Oxtz587Ftm3b0KtXL4wYMQJlZWXN3r+urg7Dhw/HgQMH8OGHH2Lv3r3IyclBfHy818GT70k1fci2Z6RXHdoF4q839ULuTyX4d/5BpcOhC9xObgsWLMDUqVMxZcoUpKWlYfHixQgMDMTSpUubvf/SpUtx4sQJrFy5EoMHD0ZiYiKGDRuGXr16eR08+Z6U04dse0Z6NaJ7DCZndsKznxbgpyMV9htt9UDR18DOD+2fbfXKBmkwblVL1tXVYevWrZgzZ07DbSaTCVlZWcjLy2v2MatXr0ZmZiZmzJiBVatWoX379pgwYQJmz54Ns9nc7GNqa2tRW1vb8P+VlZXuhElecEwfllTUNLvuJsCejDydPmTbM9KrOdel4vuDJzFz+XasveYk2qx7FKg88tsdQuOAkc8DaWOUC9JA3Bq5lZeXo76+HtHR0Y1uj46ORklJSbOPKSwsxIcffoj6+nqsXbsWTzzxBF566SU8++yzTp9n3rx5CAsLa/hISEhwJ0zyghzTh462Z9f3jkdmSgQTG+mC1d+MVyb0Rc/KL2H96HaIFyc2AKg8Crw/Cdi9WpkADUbyakmbzYaoqCgsWbIE/fr1w7hx4/DYY49h8eLFTh8zZ84cVFRUNHwcPnxY6jDpIpw+JPJMUrgV8wPfgSheenHYUG+c+winKGXg1rRkZGQkzGYzSktLG91eWlqKmJiYZh8TGxsLf3//RlOQqampKCkpQV1dHQICAi55jMVigcXCnm1K4vQhkQcObkabmtLmMtsFIlBZDBzcDCQNlTMy52z19nhOlwLB0UCnQYCp+SUjLXEruQUEBKBfv35Yv349xo4dC8A+Mlu/fj1mzpzZ7GMGDx6M5cuXw2azwWSyDxR//vlnxMbGNpvYSD14agIZndsnWJwudf5vntxPartXA7mzdbk26Hb7rezsbEyePBn9+/fHgAEDsHDhQlRXV2PKlCkAgEmTJiE+Ph7z5s0DAEyfPh2vvPIK7r//ftx333345Zdf8Nxzz+GPf/yjb78TIiIf8qgFXXB087d7ej8p7V5tXwNsWjrmWBu8+W1NJzi3k9u4ceNw7NgxPPnkkygpKUHv3r2Rm5vbUGRy6NChhhEaACQkJOCzzz7DrFmz0LNnT8THx+P+++/H7NmzffddEBH5kKMFXdOKYUcLOqdrz50G2Uc+lUdxSdIAAAj2f+80SIKo3WCrt4/YnPYiEuxrg91GaXaK0qPGyTNnznQ6Dblx48ZLbsvMzER+fr4nT0VEJKvWWtAJsLegG54Wc+kUpclsn9J7f9KFe4oXPVawL8WNnK98wji4ufFU5CVUuDboJvaWJCK6iNct6NLG2Kf0QhuP7MpNETh345vqmOrT2tqgB3jkDRHRRXzSgi5tjH1K70IVYuHZYFy76jymFnfGg+k+CtQbWlob9BCTGxFpktuVjC7yWQs6k7lhSi8ZwIyqX/Dy+l9wTfdo9OzQ1rsgvaWVtUEvMLkRkeb4+jDdi0nVgm76lSn47KcSPPjBD/jkviGw+Cm47tbC2mDDJj01rA16gWtuZCj1NhF5+49j1Y5i5O0/7va5dKQ8KQ7TvZhULej8zSa8eFMvFJVX4x/r93kVo084WRtEaJzmtwEAHLmRgUh5tU/y8KqS0Q2OFnRNf19ivPx9SY0NxX1Xd255elLOjiFN1gYN26GESKs83rdEquJOJaO33XWkakHX4vSkEh1DLlob1BNOS5LutXa1D9iv9jlF2Tw1TeVKdZiuM1KcYOF0etLRMYSnCfiEYUZu9TYRloQe+PrQWdSGHWcTYAOR82pfb9Q2lSvlYbpyumR6Mi5E9x1D5GaIkVvurqOYtqYMMRPm4W/5pzA+Jx9Dnt/g9cIzaYPcV/t6IXXhhicclYzOLksF2JOvp4fpymn6lSnoFhOChz74EXWFm1zvGOIJA54Krvvk5vgDPX7W1uh2Jf9ASV56udqXk5qmci+eFt1SdAJPjJL2MF25OKYn9x87jf99+4NrD/KkY8ju1cDCdOCt3wP/udP+eWG67qc5dT0tKVdlFambVPuW9EwtU7nOpkXvviIJq3846tNKRiU4pieXf7Ebv/d34QHudgzReef/lug6uanlD5SU5di3NH3ZNmfbVTVztS8XNUzltlThuuSrIiya0AftgiyaP0z33qtSsO6n/jh2KgKR4gkIvuoYYoDO/y3R9bSkGv5ASR0c+5ZiwhpPPcaEWbkNoBlKT+W6Mi36zJoCDEgK92kloxL8zSa8cHNfzK1zjLCcTLi62zHEnc7/OqTrkZurf3jlVbVYtaNY01d/WiFVP0BXSLVvSY+Unso12qxLamwoul51K+79Ani57QoEVF9UCxAaZ09s7k4fGqDzf0t0ndxa+wMFAJNgvwJ0YMcK6aihrNyxb4lapvRUrhFnXe69KgVjd/8OY+uH4ZOJZpjPlHnXMcQAnf9boutpyYt7xDnTtNiLVZTSUGNZObXM2VRueFAAFk2QdipX6WlRJfibTZj/fz1RUHYGbx1NAHrcaO8c4ul6mKPzf0sbJ0LjNd35vyW6Tm7Ab3+gEW0af6vOLjjZscL31FRWTu4ZmR6LJ0alIjzot1K+49V1eGbNbkkvSPS0n80dPTqEYcKAjvjb5z97Pyp1dP4H4LN1PA3RfXID7H+gi0dFoWT5HMwa2BZPjEq9ZMR2sVZP2iW3eH2yMSkmd9dRzFi+HSeqzzW6XeoRt1Sd+bXgoRFd4WcWMH/tHu+/mM47/7fEEMkNsP+x1B7eiaEd2yAyxOLSY/Q0n68kI66f6IHSI26jVri2DQzAwyO74aPtxfjugA8u+NLGAA/sAiZ/CvzhDfvnB3bqOrEBOi8occaI8/lKigxy7WLC1fuRPNRQsWjUCtdx/ROwYsshPLFyFz69bwj8zF6OQ3Ta+b8lhhm5Xcyo8/mKcfV9SN/vV5qjlhG3FJ351c5kEvD09enYW1qFZfkHlQ5HkwyZ3Iw8n6+E8tO1Pr0fyYMzHMrqldAWt1zeES99/jOOVfFvw12GTG6AcefzlcA3SW3iDIfyHh7RFWaTgOdzfVBcYjCGXHNzMOp8vtyU7nahVkp2a3GF0hu5CWgXFICHRnTFYx/vwvgBCejXyVh/I94wdHIDpOtYofY3LjnxTfJSaujW4grHDEfTWLXYgV+rbrm8I1ZsOYwnVv6ET+4bYqi/E28YPrlJQStvXHLim+RvWup2P33ZNtVNi3OGQ1lmk4Bnxqbjhn9+g3e+PYhJmYlKh6QJTG4+prU3LjnxTVK7ZwyyJ6eyeie0xbj+CXjxs70Y1SMWEYF+9m7+p0u96z+pY0xuPqTVNy45Gf1NUg17x0ibHh7ZDf/dVYI1772GSRWvNj7OJjTO3mpL5xuz3WHYakkpsM0UtUYte8dIe8KDAvByr8O47dATEJue0+Y4WXv3amWCUyEmNx/iGxe1htsiyGO2egwrfBGC0Fy/gwvzRbmP2E/gJiY3X+IbF7WGe8fIYwc3Q6g80kIjH32frO0uJjcfUuqNq94mIm//cazaUYy8/cdlPTpGyefWInbHIY8Z/GRtd7GgxIeU2M+l5LYDbnnwDLdFkEcMfrK2u5jcfEzONy4ltx1wy4N3uC2C3OY4WbvyKOCs109onG5P1nYXk5sE5HjjUnLbAbc8+IbRt0WQmxwna78/CXA2N6Tjk7XdxTU3iUh9TIeS2w645YFIIU5O1raF6P9kbXdx5KZRSm474JYHIgWljQG6jQIObkbFscO475Mj6JF2LR5K6650ZKrCkZtGKbntgFseiBR24WTtsAETkD7493hj8yGUVfJi8mJMbhql5H4p7tUiUo97hqXA4mfGy+t/UToUVWFy0ygl90txrxaReoS18ceMq1Kw4rvDKCqvVjoc1WBy0zAlTxPnSea+wU3w5AuTMhMRFWLBS//bq3QoqsGCEo1Tcr8U92p5h5vgyVes/mY8kNUZs/+zE/dcUYEeHcKUDklxHLnpgNTbDtT63Frm2ATfdEuFYxN87q6jCkVGWvWHvh2Q0j4IL3y2R+lQVIHJjUhmrW2CB+yb4H09RckpUH3zM5vw0Iiu+PqXcmzeV650OIrjtCSRzJQ4sJRToMYwonsMeie0xQuf7cXHKREQBOPOpHDkRiQzuTfBcwrUOARBwP1ZnbHj8CnkFR5XOhxFMbkRyUzOTfBKTYGScq7s0h5psaF4deN+pUNRFJMbkczk3ATPPqDGIwgCpl+Zgq9/KcfOXyuUDkcxTG5EMpNzEzz7gBrTdT1ikRgRiH9u3Kd0KIphciNSgFyb4PXcB5TVn86ZTQLuGZaC3J9KsK/stNLhKILVkkQKkWMTvGMKtKSixtnxlojRYB9QVn+27v/6xmPhup/x2pf78debeikdjuw4ciNSkNSb4PXYB1Tq6k+9jAgtfmbcNSQZH28vxpFTZ5UOR3ZMbkQ6p6c+oFJXf+buOoohz2/A+Jx83L9iB8bn5GPI8xs0u11ifEZHBFn8kPN1odKhyI7TkkQGoJc+oFJugHeMCJumRceI0BcXAvU2UdafQbDFD5MHJSLnq0Lcd3VnhAcFSPZcasPkRmQQjilQLZOq+rO1EaEA+4hweFqMx8lIqXXCKReS25vfFCH7mq6SPY/acFpSxfQy90/kK1JVf0q9H1DJLjHtggIwfkBHvLn5AE7XnpfsedSGIzeVYjUYNSX3lJYaSVX9KeV+QDlGha2ZekUS/p1/AMu/PYi7r0iR5DnUhiM3FWIvQGpKb4UOnpKq+lPK/YBq6BITG9YGN/SJx+tfF6H2fL1kz6MmHiW3RYsWITExEVarFRkZGdiyZYtLj1uxYgUEQcDYsWM9eVpDYC9AaooXO41JUf0pZUs0tXSJuWdYCo6drsV/thZL+jxq4fa05HvvvYfs7GwsXrwYGRkZWLhwIUaMGIG9e/ciKirK6eMOHDiABx98EEOHDvUqYL1T4jgUUi81TGmpka+rPx0jwunLtkEAGr3e3u4HVEuXmJT2wbg2PQavfbUfN/fvAD+zvifu3P7uFixYgKlTp2LKlClIS0vD4sWLERgYiKVLlzp9TH19PW699VY89dRTSE5O9ipgvVPLVR6pgxqmtNTK1xvgpdoPKNWo0JOCs2nDUnDw+Bls2FPm1nNpkVsjt7q6OmzduhVz5sxpuM1kMiErKwt5eXlOH/f0008jKioKd955J77++utWn6e2tha1tbUN/19ZWelOmJqmlqs8Ugde7MhLiv2AUowKPS0469mhLXontMW/8w/imu4x7n0jGuPWyK28vBz19fWIjo5udHt0dDRKSkqafcymTZvwxhtvICcnx+XnmTdvHsLCwho+EhIS3AlT0+Q8DoXUjxc78pOiJZovR4XersFOHNgJX/9SjqLyate/AQ2SdNK1qqoKEydORE5ODiIjI11+3Jw5c1BRUdHwcfjwYQmjVBc99gIkz/FiRz9Gpsdi0+yr8e7UgXj5lt54d+pAbJp9tVuJzRcFZ6N6xqJtoD/eyT/o3jegMW5NS0ZGRsJsNqO0tLTR7aWlpYiJuXSIu3//fhw4cACjR49uuM1ms9mf2M8Pe/fuRUrKpXsuLBYLLBaLO6HpiuMqr+m0Q4zG9rlxX5b3pCx0IPl52yXGFwVnVn8zxvVPwIrvDuNP13RFmwCzx/GomVvJLSAgAP369cP69esbyvltNhvWr1+PmTNnXnL/bt26YefOnY1ue/zxx1FVVYWXX37ZUNON7tJ6L0BuQvcdvVzskPd8tQY7IaMjlnxdiE9+PIKb++vzfdjtrQDZ2dmYPHky+vfvjwEDBmDhwoWorq7GlClTAACTJk1CfHw85s2bB6vVivT09EaPb9u2LQBccjtdSqu9AOVoQGs0Wr/YId/w1Rpsp4ggDOvSHsvyDzK5OYwbNw7Hjh3Dk08+iZKSEvTu3Ru5ubkNRSaHDh2CyaTv/RPkHPdlSUerFzvkO75sPzZxYCfc+db3+OHwKfRKaOvrUBXnUW/JmTNnNjsNCQAbN25s8bFvvvmmJ09JGsFN6ETS8eUa7JVdoxDftg3+nX9Ql8mNQyzyKe7LIpKWr7YVmE0Cbh3YEZ/8cAQnq+ukCFVRPBWAfIr7soik56s12Jv7J2Dh57/gw62/YuoV+uoexeRGPiXVkSRE1Jgv1mAjgy24rkcMln17EHcOSYJJR+vgnJYkn+ImdCJtmZjZCQePn8HX+8qVDsWnmNzI56RqQOsLPN2cqLG+HdshNTYU/87TV8cSTkuSJNS4L4sby4kuJQgCJg7shMdX7sSvJ8+gQ7tApUPyCY7cSDJSNKD1FA/8JHLu+t5xCArww/JvDykdis8wuZHu8XRzopYFWfxwfZ84fLStWDd/B0xupHs88JOodTf06YCSyhp8W3Rc6VB8gsmNdI8by4la17djW3QMD8TK7cVKh+ITTG6ke9xYTtQ6QRAwtncc/ruzBDXn6pUOx2tMbqR7PPCTyDXX94lHVe15bNhTpnQoXmNyI93jxnIi16S0D0avDmH4WAdTk0xuZAhq3lhOpCbX947Hxr1lOHVG282UuYmbDEONG8uJ1GZ0rzj8ZW0B1uw8ilszOikdjseY3HSi3ibyTdsFPPCTqGXtQywYclkkVm4vZnIjZam9rRQTL5G2jO0Th1nv/YDDJ84gIVyb7biY3DTO0VaqaU8BR1sppdeTPEm8TIZEyromLQZt/Hdh9Q9HMOOqy5QOxyNMbhrWWlspAfa2UsPTYhRJDp4kXrWPQomMIMjihxHdo/HRtl9x75UpEATtXVyyWlLD1NxWypN+jmxu3BiP5yElXd8nHvuPVeOnI5VKh+IRjtw0TM1tpdxJvJkpEaofhcqNI1hS2tDLIhERFICPtxcjPT5M6XDcxpGbhqm5rZS7iVfNo1C5cQRLauBnNmF0rzis/uGIJmcNmNw0pOk0Vb9O7VTbVsrdxKvmUaiceDwPqcnYPvE4VlWLzfvLlQ7FbZyW1Ahn01RjesViyVdFEIBGb4hKt5Vy9HMsqahp9o1agL07iCPxqnkUKid3p3OJpNSrQxg6RQRizY9HMbRze6XDcQtHbhrQ0jTVkq+KcPcVSaprK+VuP0c2N7bjCJbURBAEXJMWjfV7ymDT2GwBR24q50qhxeofjuLLh67C1oMnVbU3zNHPsemIM6aZwghHMpy+bJvqRqFycnVkWl5Vi3qbqPvXg5SXlRqNnK+L8GNxBXontFU6HJcxuamcq9NUWw+eVOU0lTv9HN1JhnrV2nSuwzNrCvD6piLDvC6knH6d2iGsjT/W7S5lciPf0cM0lTv9HI3e3LilEWxTaulCo0XsguM6P7MJV3eLwrqCUjw4oqvS4biMyU3ljFhoYfTmxs5GsE0Zcf+fL3APofuyUqPx8fZiTfWaZEGJyrHQwphGpsdi0+yr8cSo1BbvZ6T9f77APYSeuaJLJPzNAtYXlCodisuY3FSOp0gbl9kkIDLE4tJ91TwtrRbcQ+i5EKs/BiZHYF1BmdKhuIzJTQN4irRxGXFaWipKdsHRQ5/Q4WnRyC88jsqac0qH4hKuuWmE0QstjMrdzfDknFLFWXpZ4/tdajSeXPUTvtx7DKN7xSkdTqs4ctMQR6HF9b3jkZkSwcRmAJyW9h0lRsF6WuOLb9sGqbGhWKeRdTcmNyKV47S0b8hdnKXHNb7hqVH4Yk8ZztXblA6lVZyWJNIANU9Lq2nPWEuxyN0FR499QrPSovH3Dfvw/QF1No24GJMbkUaocf+fmtaTXIlFzi44emjA0FR6XBiiQy1YV1Cqut/FppjciMgjjvWkppNqSnROcScWuUbBeqx0NZkE/C41GusKSvH4qFQIgvIzB85wzY1II9RUTq6m9SRPYpGjOEuvDRiGp0bj4PEz2Fd2WulQWsSRG5EGqGn6D1DXepKaYrmYXk+6yEyJQBt/M9YVlKFzdIjS4TjFkRuRyqmxnFxN60lqiqUpPVa6Wv3NGJAUrvrTuTlyI1IxV87zU6JxsprWk9QUS3PUXOnqqcyUCLy87hecq7fB36zOMZI6oyJZqWkthxpTsmVUS9S0nqRELO7+zeitAcPA5AicPVePH389pXQoTnHkZnDerOWoaX+TXql1yk1N60lyx6K29U8lpMeFItjih/zCE+jXSZ0FMRy5GZg3azm5u45iyPMbMD4nH/ev2IHxOfkY8vwGTbUT0gI1T7mpaT1JrljUuP6pBD+zCZcntkN+4XGlQ3GKIzeD8mYtR037m/RO7Y2T1bSeJHUsal3/VMrA5AgsXPcL6s7bEOCnvnGS+iIiWXi6lqOm/U1G4G7jZCXWT9W0niRlLGpd/1RKZoq61904cjMoT9dy1LqnSM9cbRnFtSBpqXX9UylpsaEIsfghv/A4+ieqb92Nyc2gPF3LUeMfuBEKW1qbcuNUsfTUvP6pBD+zCQOSwpFXeBwzr+6sdDiXYHIzKE/XctT2B26k0YqzxslcC5KH2tc/lTAwOQIvfb4XtefrYfEzKx1OI1xzMyhPD8FU0/4mVq7ZcS1IHjw49lIDkyNQc86GHw5XKB3KJZjcDMyT8mm1/IGzsOU3apwq1is1bX9Qg7S4UIRY/VS5JYDTkgbnSfm0nGdiOcPClt+obapY79S0/UFpZpOAjKRw5Bcexx9/p651NyY38ugQTKX/wDla+Q3XguSnxoNjlTIwOQJ//Ux9626cliSPKbm/iaOV36hlqpiMaWByBGrP27Dj0CmlQ2mEyY00SU2FLWrAtSBSSmpsKEKt9j6TasJpSdIkNTXuVQulp4rJmMwmAQOSIrDlwHEA6ll348iNNIujlUupqRUWGUevDmHYVVwJUVRPdTJHbqRpHK0QKS+9Qxgqzp7D4RNn0TEiUOlwADC5kQ6wco1IWT3iwwAAPxafUk1y82hactGiRUhMTITVakVGRga2bNni9L45OTkYOnQo2rVrh3bt2iErK6vF+xMRkbZEBlsQF2bFzmL1dCpxO7m99957yM7Oxty5c7Ft2zb06tULI0aMQFlZWbP337hxI8aPH48vvvgCeXl5SEhIwDXXXIPi4mKvgyciInVIjw/DLi0ntwULFmDq1KmYMmUK0tLSsHjxYgQGBmLp0qXN3v+dd97Bvffei969e6Nbt254/fXXYbPZsH79eqfPUVtbi8rKykYfRESkXj3i1VVU4lZyq6urw9atW5GVlfXbFzCZkJWVhby8PJe+xpkzZ3Du3DmEhzvffzRv3jyEhYU1fCQkJLgTJhERyeziohI1cCu5lZeXo76+HtHR0Y1uj46ORklJiUtfY/bs2YiLi2uUIJuaM2cOKioqGj4OHz7sTphERCSzi4tK1EDWasn58+djxYoV2LhxI6xW522RLBYLLBaLjJEREWmPmg7qvbio5Pc94xSJ4WJuJbfIyEiYzWaUlpY2ur20tBQxMTEtPvbFF1/E/PnzsW7dOvTs2dP9SImIqIEaD+pVU1GJW9OSAQEB6NevX6NiEEdxSGZmptPHvfDCC3jmmWeQm5uL/v37ex4tERGp9qBeNRWVuF0tmZ2djZycHLz11lsoKCjA9OnTUV1djSlTpgAAJk2ahDlz5jTc//nnn8cTTzyBpUuXIjExESUlJSgpKcHp06d9910QERmEmg/qVVNRidtrbuPGjcOxY8fw5JNPoqSkBL1790Zubm5DkcmhQ4dgMv2WM1999VXU1dXhxhtvbPR15s6diz//+c/eRU9EZDBqPqjXUVSys7hC8U4lHhWUzJw5EzNnzmz23zZu3Njo/w8cOODJUxARUTPUfFCvo6jkx+JTGNVT2cblPBWAiEhD1H5Qr1qKSpjciIg0RO0H9aqlqITJjYhIQxwH9QK4JMGp4aDe7vGhqDh7DsWnlC0qYXIjItIYNR/Um9I+GABQVF6tWAwAz3MjItIktR7U26FdIPzNAorKqzG0c3vF4mByIyLSKDUe1Gs2CegUEYTCYxy5kQGoqQceEUkrKTKI05Kkf2rsgUfkKV6otS45MghrFWoB5sDkRpJy9MBrWhTs6IGn9OI3kTt4oeaapMgg/HryLGrP18PiZ1YkBlZLkmTU3AOPyF1qbVasRsntgyGKwKHjZxSLgcmNJONODzwiNeOFmnuSIoMAAIUKrrsxuZFk1NwDj8gdvFBzT2RwAEIsfopWTDK5kWTU3gOPyFW8UHOPIAhIah+EonLljjZjciPJqL0HHpGreKHmvmSFtwMwuZFk1N4Dj8hVvFBzX1JkMJMb6Zeae+ARuYoXau5Lah+E8tN1qDh7TpHn5z43kpxae+ARucNxodZ0n1sM97k1K/lCxWRReTV6J7SV/fmZ3DRMS50S1NgDj8hdvFBzXVJDcjvN5EauY6cEImXwQs01QRY/RIdaUKTQdgCuuWmQUTsl1NtE5O0/jlU7ipG3/zg3zBKpXGJEEIoU6lLCkZvGtNYpQYC9U8LwtBhdTZVwpEqAtqbiyb4e2dLmdykxuWmMO50S9DJ1wubLBPACR4uiQ6348dcKRZ6b05IaY7ROCezpR4Bxp+K1LirEgtJKZd6LmNw0xmidEtjTj3iBo13tQyw4U1eP07XnZX9uJjeNkbpTgtqKNow2UqVL8QJHu6JD7RfZSozeuOamMY5OCdOXbYMANLqa9bZTghrXNIw2UtUbXxSA8AJHu6JCLACAsspaWGR+biY3DZKiU4JaizYcI9WSippmp6UE2L9vPfb003ploK8ulniBo11RF0ZuZVU1SJD5uZncNMqXnRLUvL1AypGqmqlxFO0OX14s+foCR+sXDVoSbPFDUIAZZZW1SAiW97m55qZhjk4J1/eOR2ZKhMd/oGpf0zBa82WtVwb6ugDEl02Lc3cdxZDnN2B8Tj7uX7ED43PyMeT5Dap/TbUsOtSqyJQxR26kiTUNo/T0U/Mo2lVS7MX0xVS8Wqfe9a59iAWllbWAzC8tkxtpZk3DCD399LBJX6qLJW8ucPRw0aBVv43c5C0pYXIjQxdtqI0WRtGtkfJiydMLHD1cNGhVVIgFu45UQO7kxjU3halhXxkPYlQPrYyiW6LGU6v1cNGgVdGhVpRV1sr+vBy5KUhNFXE8iFEd9DCKVmOFqx4uGrQqKtSC07XncfacTdbnZXJTiBoXt41StKFmakwMnlDbxZIeLhq0qv2Fjdwna5jcdE/Ni9tGKNpQO7UlBk+p6WJJLxcNWuRowXWypl7W52VyU4BeF7e5OdZ31JQYvKGmiyW9XDRojaMF18mzHLnpnh4Xt9W0fqgXakoMeqGXiwYtCbb4wSQA1Vxz0z+9LW6rcf2QyBleNMhLEAQEWfxw9py8leDcCqAANZZKe4pnbRFRa4IC/FBznslN9/S0r0ztfSmJSHlBFjPOMrkZg16aAetx/ZCIfCvY4oea81xzMww9LG7rbf2QfIOVs3SxwAA/nD0nb5cSJjeFaX1xm5tjqSlWzlJTQRY/nDrLaUnSED2tH5J36m0iXl73C6Zp+Cw6kkYw19xIi/Syfkiey911FIPnr8ff1v3c7L+zctbYAi1+OMs1N9IiPawfkmec7XNsSqudd8h7wQrsc2NyI5/R+vohua+lfY7OsHLWeLjPjYg0pbV9js1h5azxKLHPjSM3IvKYO6MwVs4aV5DFMXKTb5mCIzci8pi7ozBWzhpTYIAZACD4W2R7TiY3IvJYa31SHWJZOWtowRb7JKEpoI1sz8lpSSLyWEuHgDrMyuqMmVd35oitFXru6hJ0IbkJTG5EpBXODgFlVxLX6b2rS1AAR25ELtPzla7WcJ+j54xwHmKbAPsKmOAn35obkxtpkt6vdLWI+xzd19p5iALsXV2Gp8Vo+kJBEATHf8j2nCwo0ah6m4i8/cexakcx8vYfN1RLI8eVLvsXktYZ5TxEU0Nyky/lcOSmQUYetRjlSpeMwSjnIZovJDeBIzdyxuijFqNc6ZIxGOU8xIacpvbktmjRIiQmJsJqtSIjIwNbtmxp8f4ffPABunXrBqvVih49emDt2rUeBWt0rY1aAP13XXf1Cvbz3SUSR0Lkvdb2CQqwz8povauLyST/tKTbz/Tee+8hOzsbc+fOxbZt29CrVy+MGDECZWVlzd5/8+bNGD9+PO68805s374dY8eOxdixY7Fr1y6vgzcajlpcv4Jd+s0B3Y9iSfuMch6iSQsjtwULFmDq1KmYMmUK0tLSsHjxYgQGBmLp0qXN3v/ll1/GyJEj8dBDDyE1NRXPPPMM+vbti1deecXr4I3GKPPzLXFc6bbGsfam51Es6YMRzkM0Nay5qbSgpK6uDlu3bsWcOXMabjOZTMjKykJeXl6zj8nLy0N2dnaj20aMGIGVK1c6fZ7a2lrU1tY2/H9lZaU7YbaooKDAZ19LbhVlta3fCUBFySFs21YqcTTKmdjdihc2t5zAHaPYd/6Xj/Qo+fbWEHkiCsDfh7dFQXkdTtbY0M5qQmpkAMx1R7Ftm/ZnIE7V1CPIbIMoyndgqVvJrby8HPX19YiOjm50e3R0NPbs2dPsY0pKSpq9f0mJ8zWRefPm4amnnnIntFZFRkYiMDAQt912m0+/rqwEE+KnvQFzSESzV0CiaEN91XFMvm4MIOMvkRLaXn0nwi6/odX7Tc9+BGcKvpIhIiJqTWBgICIjI2V5LlVuBZgzZ06j0V5lZSUSEhK8+podO3ZEQUEBysvLvQ1PUfm/nsULm081+2+CYMKjIztj4F3fyRuUAnaV1eLJja2vLb66YD5HbkQqERkZiY4dO8ryXG4lt8jISJjNZpSWNp7yKi0tRUxMTLOPiYmJcev+AGCxWGCx+P4NqWPHjrK9sFLp2xdITjbuPjeHXjYRr27fgJKKmmarRx1nh916zUDNL8YTkfvcWt0LCAhAv379sH79+obbbDYb1q9fj8zMzGYfk5mZ2ej+APD55587vT+1bmR6LDbNvhrvTh2Il2/pjXenDsSm2VcbJrEBxqkyIyLPuD0tmZ2djcmTJ6N///4YMGAAFi5ciOrqakyZMgUAMGnSJMTHx2PevHkAgPvvvx/Dhg3DSy+9hFGjRmHFihX4/vvvsWTJEt9+JwbDPn7Ou9HHGGwUS0SXcju5jRs3DseOHcOTTz6JkpIS9O7dG7m5uQ1FI4cOHYLJ9NuAcNCgQVi+fDkef/xxPProo+jcuTNWrlyJ9PR0330XZFjsRk9EzRFEUVT9RqDKykqEhYWhoqICoaGhSodDREQKcCcXsLckERHpDpMbERHpDpMbERHpDpMbERHpDpMbERHpDpMbERHpDpMbERHpDpMbERHpjipPBWjKsc/cl+e6ERGRtjhygCu9RzSR3KqqqgDA62NviIhI+6qqqhAWFtbifTTRfstms+HIkSMICQmBIHjWM9BxJtzhw4fZwqsJvjbN4+viHF+b5vF1cc4Xr40oiqiqqkJcXFyjHsbN0cTIzWQyoUOHDj75WqGhofylc4KvTfP4ujjH16Z5fF2c8/a1aW3E5sCCEiIi0h0mNyIi0h3DJDeLxYK5c+fCYrEoHYrq8LVpHl8X5/jaNI+vi3NyvzaaKCghIiJyh2FGbkREZBxMbkREpDtMbkREpDtMbkREpDtMbkREpDu6Sm6LFi1CYmIirFYrMjIysGXLlhbv/8EHH6Bbt26wWq3o0aMH1q5dK1Ok8nPntcnJycHQoUPRrl07tGvXDllZWa2+llrl7u+Mw4oVKyAIAsaOHSttgApy97U5deoUZsyYgdjYWFgsFnTp0kWXf1Puvi4LFy5E165d0aZNGyQkJGDWrFmoqamRKVp5fPXVVxg9ejTi4uIgCAJWrlzZ6mM2btyIvn37wmKx4LLLLsObb77p26BEnVixYoUYEBAgLl26VPzpp5/EqVOnim3bthVLS0ubvf8333wjms1m8YUXXhB3794tPv7446K/v7+4c+dOmSOXnruvzYQJE8RFixaJ27dvFwsKCsTbb79dDAsLE3/99VeZI5eWu6+LQ1FRkRgfHy8OHTpUvP766+UJVmbuvja1tbVi//79xeuuu07ctGmTWFRUJG7cuFHcsWOHzJFLy93X5Z133hEtFov4zjvviEVFReJnn30mxsbGirNmzZI5cmmtXbtWfOyxx8SPPvpIBCB+/PHHLd6/sLBQDAwMFLOzs8Xdu3eL//jHP0Sz2Szm5ub6LCbdJLcBAwaIM2bMaPj/+vp6MS4uTpw3b16z97/55pvFUaNGNbotIyNDvOeeeySNUwnuvjZNnT9/XgwJCRHfeustqUJUhCevy/nz58VBgwaJr7/+ujh58mTdJjd3X5tXX31VTE5OFuvq6uQKURHuvi4zZswQr7766ka3ZWdni4MHD5Y0TiW5ktwefvhhsXv37o1uGzdunDhixAifxaGLacm6ujps3boVWVlZDbeZTCZkZWUhLy+v2cfk5eU1uj8AjBgxwun9tcqT16apM2fO4Ny5cwgPD5cqTNl5+ro8/fTTiIqKwp133ilHmIrw5LVZvXo1MjMzMWPGDERHRyM9PR3PPfcc6uvr5Qpbcp68LoMGDcLWrVsbpi4LCwuxdu1aXHfddbLErFZyvP9q4lSA1pSXl6O+vh7R0dGNbo+OjsaePXuafUxJSUmz9y8pKZEsTiV48to0NXv2bMTFxV3yy6hlnrwumzZtwhtvvIEdO3bIEKFyPHltCgsLsWHDBtx6661Yu3Yt9u3bh3vvvRfnzp3D3Llz5Qhbcp68LhMmTEB5eTmGDBkCURRx/vx5TJs2DY8++qgcIauWs/ffyspKnD17Fm3atPH6OXQxciPpzJ8/HytWrMDHH38Mq9WqdDiKqaqqwsSJE5GTk4PIyEilw1Edm82GqKgoLFmyBP369cO4cePw2GOPYfHixUqHpqiNGzfiueeewz//+U9s27YNH330EdasWYNnnnlG6dB0Txcjt8jISJjNZpSWlja6vbS0FDExMc0+JiYmxq37a5Unr43Diy++iPnz52PdunXo2bOnlGHKzt3XZf/+/Thw4ABGjx7dcJvNZgMA+Pn5Ye/evUhJSZE2aJl48jsTGxsLf39/mM3mhttSU1NRUlKCuro6BAQESBqzHDx5XZ544glMnDgRd911FwCgR48eqK6uxt13343HHnus1QM39crZ+29oaKhPRm2ATkZuAQEB6NevH9avX99wm81mw/r165GZmdnsYzIzMxvdHwA+//xzp/fXKk9eGwB44YUX8MwzzyA3Nxf9+/eXI1RZufu6dOvWDTt37sSOHTsaPsaMGYOrrroKO3bsQEJCgpzhS8qT35nBgwdj3759DQkfAH7++WfExsbqIrEBnr0uZ86cuSSBOS4ARAP3rJfl/ddnpSkKW7FihWixWMQ333xT3L17t3j33XeLbdu2FUtKSkRRFMWJEyeKjzzySMP9v/nmG9HPz0988cUXxYKCAnHu3Lm63grgzmszf/58MSAgQPzwww/Fo0ePNnxUVVUp9S1Iwt3XpSk9V0u6+9ocOnRIDAkJEWfOnCnu3btX/PTTT8WoqCjx2WefVepbkIS7r8vcuXPFkJAQ8d133xULCwvF//3vf2JKSop48803K/UtSKKqqkrcvn27uH37dhGAuGDBAnH79u3iwYMHRVEUxUceeUScOHFiw/0dWwEeeughsaCgQFy0aBG3ArTkH//4h9ixY0cxICBAHDBggJifn9/wb8OGDRMnT57c6P7vv/++2KVLFzEgIEDs3r27uGbNGpkjlo87r02nTp1EAJd8zJ07V/7AJebu78zF9JzcRNH912bz5s1iRkaGaLFYxOTkZPEvf/mLeP78eZmjlp47r8u5c+fEP//5z2JKSopotVrFhIQE8d577xVPnjwpf+AS+uKLL5p9z3C8FpMnTxaHDRt2yWN69+4tBgQEiMnJyeK//vUvn8bE89yIiEh3dLHmRkREdDEmNyIi0h0mNyIi0h0mNyIi0h0mNyIi0h0mNyIi0h0mNyIi0h0mNyIi0h0mNyIi0h0mNyIi0h0mNyIi0p3/B+iHbbkQVom6AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_mc_estimation_of_pi();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5df3e373-14ca-4d8c-ae3d-1c17c87bf405",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Say I ran an experiment and empirically found $\\bar{X} = \\frac{7980}{10000}$. According to my favorite confidence interval algorithm, I have $p \\in [0.788, 0.808]$ with 95% confidence. Since $\\pi = 4 p$, we have that $\\pi \\in [3.152, 3.224]$ with 95% confidence."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c55a1f22-5f1a-4bcc-82ab-6267722609bf",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "What is the probability that $\\pi$ is in this confidence interval?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2bdd899-03aa-4471-97f5-a614ce1212ba",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Main take-away"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15c56591-3677-4f1f-9110-eddc8efcdb2d",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "Do not interpret confidence levels as probabilities *a posteriori*!\n",
    "\n",
    "(I hope you understand this sentence now!)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0379da5-a38a-49d7-b481-a963d82fb838",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### References"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be3a9ae3-5e8c-43d1-bde3-682267e850c3",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "General articles:\n",
    "\n",
    "* https://en.wikipedia.org/wiki/Confidence_interval,\n",
    "* https://en.wikipedia.org/wiki/Credible_interval.\n",
    "\n",
    "To better understand the difference between frequentism and Bayesianism, here is another fascinating read with another illuminating example: https://jakevdp.github.io/blog/2014/06/12/frequentism-and-bayesianism-3-confidence-credibility/.\n",
    "\n",
    "About the example studied in this presentation:\n",
    "\n",
    "* Simplified version of the argument: https://en.wikipedia.org/wiki/Confidence_interval.\n",
    "* Original version of the argument: Welch, B. L. (1939). \"On Confidence Limits and Sufficiency, with Particular Reference to Parameters of Location\". The Annals of Mathematical Statistics. 10 (1): 58–69.\n",
    "* See also Pratt, J. W. (1961). \"Book Review: Testing Statistical Hypotheses. by E. L. Lehmann\". Journal of the American Statistical Association. 56 (293): 163–167."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f048e673-349a-488c-888c-417146b4bf41",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Thanks for your attention!"
   ]
  }
 ],
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