Gilles86/test_red.ipynb

## test_red.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc as pm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "Metropolis: [n_red]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "      <progress value='600000' class='' max='600000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [600000/600000 00:22&lt;00:00 Sampling 4 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 50_000 tune and 100_000 draw iterations (200_000 + 400_000 draws total) took 23 seconds.\n"
     ]
    }
   ],
   "source": [
    "model = pm.Model()\n",
    "\n",
    "with model:\n",
    "    n = 100\n",
    "    n_red = pm.DiscreteUniform('n_red', lower=1, upper=100)\n",
    "\n",
    "    p1 = pm.Deterministic('p1', n_red/n)\n",
    "\n",
    "    vase1 = pm.Binomial('vase1', n=1, p=p1, observed=1)\n",
    "    p_seeing_red1 = pm.Deterministic('seeing_red1', (n_red)/(n))\n",
    "\n",
    "    n_red2 = pm.Deterministic('n_red2', n_red - 1)\n",
    "    p_seeing_red2 = pm.Deterministic('seeing_red2', (n_red2)/(n-1))\n",
    "\n",
    "    trace = pm.sample(100000, tune=50000, cores=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: ylabel='Count'>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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k1fHExESFhIR4oEVdRyACAABdUlJSonUvFCk6boR5rLLiXT0o9ch4oJ5EIAIAAF0WHTfCHBztyxhDBAAA/B6BCAAA+D1umQEAgG7TcOG8ysrK3I75wiBrAhEAAOg21Scq9KLDofI6qyTfGWRNIAIAAK1cyZT6yMFxPjfQmkAEAABa6UtT6juCQAQAANrUV6bUdwSBCAAA9Ji2BlmXlZWpsfFqD7WobQQiAADQY1oOspaksuJDsn1pvIZ7sF0tEYgAAOjj2hog3ZtT4VsOsq6seLdXvrczCEQAAPRxLQdI9+XB0V1FIAIAwA/40wDprmDrDgAA4PcIRAAAwO9xywwAAHRIyyn03jh9vqsIRAAAoNVMtLbCTssp9N44fb6rCEQAAPiZ9hZL3FVeqeuGjWp63k7YuXgKvTdOn+8qAhEAAH7mUosl9sWw0xEEIgAA/JAvLJbYm5hlBgAA/B6BCAAA+D0CEQAA8HsEIgAA4PcIRAAAwO8RiAAAgN/zaCC6/vrrZbFYWj1+9KMfSZIMw1BWVpZiYmLUr18/TZ06VeXl5W6f4XK5tHjxYkVGRio8PFxpaWk6efKkW43D4VBGRoasVqusVqsyMjJ09uzZ3jpNAADg5Ty6DtGhQ4fU0NBgPj98+LBmzJihb33rW5KkNWvWaO3atdqyZYtGjBihJ554QjNmzNCxY8fUv39/SVJmZqb++Mc/Kj8/X4MGDdKyZcuUmpqqkpISBQQESJLS09N18uRJFRQUSJIWLFigjIwM/fGPf+zlMwYAoEnLrTIkKTExUSEhIZ2qQffwaCC69tpr3Z7/9Kc/1fDhwzVlyhQZhqH169dr1apVmj17tiRp69atstls2rFjhxYuXCin06lNmzZp27Ztmj59uiQpLy9PsbGxKioq0syZM3X06FEVFBRo//79SkpKkiRt3LhRycnJOnbsmEaOHNm7Jw0AgKSSkhKte6FI0XEjJDUtjPigpEmTJnWqBt3Da8YQ1dfXKy8vTz/4wQ9ksVhUUVGhqqoqpaSkmDUhISGaMmWKiouLJTX9oZw/f96tJiYmRuPGjTNr9u3bJ6vVaoYhSZo4caKsVqtZAwCAJ0THjVDc2JsUN/YmM/R0pQZXzmu27nj55Zd19uxZ3XPPPZKkqqoqSZLNZnOrs9ls+uijj8ya4OBgDRw4sFVN8/urqqoUFRXV6vuioqLMmra4XC65XC7zeU1NTedPCgAA+ASvCUSbNm3S7bffrpiYGLfjFovF7blhGK2OtdSypq36y33O6tWr9dhjj3Wk6QAAeAzjjLqHV9wy++ijj1RUVKR7773XPGa32yWpVS9OdXW12Wtkt9tVX18vh8NxyZpTp061+s7Tp0+36n262MqVK+V0Os3HiRMnunZyAAD0oOZxRvkHjyv/4HGte6GoVUDC5XlFINq8ebOioqL09a9/3TwWFxcnu92uwsJC81h9fb327NljDiZLTExUUFCQW01lZaUOHz5s1iQnJ8vpdOrgwYNmzYEDB+R0Oi85KC0kJEQDBgxwewAA4EkNF86rrKxMxcXF5qOsrEy2ocMZZ3SFPH7LrLGxUZs3b9bcuXMVGPhFcywWizIzM5Wdna34+HjFx8crOztbYWFhSk9PlyRZrVbNmzdPy5Yt06BBgxQREaHly5crISHBnHU2evRozZo1S/Pnz9eGDRskNU27T01NZYYZAMBrNIedi5WVlamx8WrzefWJCr3ocKi8zvpFTfEh2b40XsN7raV9k8cDUVFRkY4fP64f/OAHrV5bsWKF6urqtGjRIjkcDiUlJWnXrl3mGkSStG7dOgUGBmrOnDmqq6vTtGnTtGXLFnMNIknavn27lixZYs5GS0tLU25ubs+fHACgz2trDI/U+XE8HQ07kYPjFDf2JvN5ZcW7XWo33Hk8EKWkpMgwjDZfs1gsysrKUlZWVrvvDw0NVU5OjnJyctqtiYiIUF5e3pU2FQCAVlquFSR1fb0gwo7neDwQAQDg65rXCoLv8opB1QAAAJ5EDxEAAH1IRwZnozUCEQAAfQgz0bqGQAQAQB/D4OzOYwwRAADwe/QQAQDQCS3XHWJ8Tt9AIAIAoBNarjvE+Jy+gUAEAEAnXbzuUEfG57S1mjU9S96FQAQAQA9razVrepa8C4EIAIBe0HI1a2Z+eRcCEQAA3azl4ojcHvN+BCIAALpZy8URuT3m/QhEAAD0gIsXR+T2mPdjYUYAAOD3CEQAAMDvEYgAAIDfIxABAAC/RyACAAB+j0AEAAD8HoEIAAD4PQIRAADwewQiAADg9whEAADA7xGIAACA32MvMwBAn+NyuVRSUtLqeGJiokJCQjzQIng7AhEAwKd0JOyUlJRo3QtFio4bYb5eWfGuHpQ0adKk3moqfAiBCADgUzoadqLjRpi7zXdVW+GrrKxMjY1XX9HnwvsQiAAAXqu9QGIbOvyKw05HtBW+yooPyfal8Rre49+O3kQgAgB4rZ4MJB0dZ9Syp6my4t0r/GZ4IwIRAMBrtAwpbfUGdVcgYZwRLubxafcff/yxvve972nQoEEKCwvTl7/8Zbd/GQzDUFZWlmJiYtSvXz9NnTpV5eXlbp/hcrm0ePFiRUZGKjw8XGlpaTp58qRbjcPhUEZGhqxWq6xWqzIyMnT27NneOEUAQAc1h5T8g8ebHrsP6cyZT3rs+5p7f5ofF4cj+BePBiKHw6HJkycrKChIf/7zn3XkyBE988wzuuaaa8yaNWvWaO3atcrNzdWhQ4dkt9s1Y8YM1dbWmjWZmZnauXOn8vPztXfvXp07d06pqalqaGgwa9LT01VaWqqCggIVFBSotLRUGRkZvXm6AIAOuDikREYP6dXvbrhwXmVlZSouLlZxcfH/DaBuuPwb4fM8esvsqaeeUmxsrDZv3mweu/76681/NgxD69ev16pVqzR79mxJ0tatW2Wz2bRjxw4tXLhQTqdTmzZt0rZt2zR9+nRJUl5enmJjY1VUVKSZM2fq6NGjKigo0P79+5WUlCRJ2rhxo5KTk3Xs2DGNHDmy904aAOC1qk9U6EWHQ+V1VkkMoPYnHu0h+sMf/qAJEyboW9/6lqKionTjjTdq48aN5usVFRWqqqpSSkqKeSwkJERTpkxRcXGxpKbu1fPnz7vVxMTEaNy4cWbNvn37ZLVazTAkSRMnTpTVajVrWnK5XKqpqXF7AAD6vsjBcR7roYLneDQQffDBB3ruuecUHx+vV155Rffdd5+WLFmi//7v/5YkVVVVSZJsNpvb+2w2m/laVVWVgoODNXDgwEvWREVFtfr+qKgos6al1atXm+ONrFarYmNjr+xkAQAexe0wXIpHb5k1NjZqwoQJys7OliTdeOONKi8v13PPPafvf//7Zp3FYnF7n2EYrY611LKmrfpLfc7KlSu1dOlS83lNTQ2hCAC8VHPYadbW4oncDsOleDQQRUdHa8yYMW7HRo8erd/97neSJLvdLqmphyc6Otqsqa6uNnuN7Ha76uvr5XA43HqJqqurzWmTdrtdp06davX9p0+fbtX71CwkJIT9bgDAR3Q07DTfDpNYTwjuPHrLbPLkyTp27JjbsXfffVdDhw6VJMXFxclut6uwsNB8vb6+Xnv27DHDTmJiooKCgtxqKisrdfjwYbMmOTlZTqdTBw8eNGsOHDggp9PJWhMA0Ecw9gdXwqM9RA8++KAmTZqk7OxszZkzRwcPHtTzzz+v559/XlLTba7MzExlZ2crPj5e8fHxys7OVlhYmNLT0yVJVqtV8+bN07JlyzRo0CBFRERo+fLlSkhIMGedjR49WrNmzdL8+fO1YcMGSdKCBQuUmprKDDMAAODZQHTzzTdr586dWrlypR5//HHFxcVp/fr1uvvuu82aFStWqK6uTosWLZLD4VBSUpJ27dql/v37mzXr1q1TYGCg5syZo7q6Ok2bNk1btmxRQECAWbN9+3YtWbLEnI2Wlpam3Nzc3jtZAADgtTy+dUdqaqpSU1Pbfd1isSgrK0tZWVnt1oSGhionJ0c5OTnt1kRERCgvL+9KmgoAAPooj2/dAQAA4Gke7yECAPiHtnaXb7mzPOApBCIAQK9oubs8O8vDmxCIAAC9pnnjVsDbMIYIAAD4PQIRAADwewQiAADg9whEAADA7xGIAACA3yMQAQAAv0cgAgAAfo9ABAAA/B6BCAAA+D0CEQAA8HsEIgAA4PcIRAAAwO+xuSsAwCMaLpxXWVmZ27GysjI1Nl7toRbBnxGIAAAeUX2iQi86HCqvs5rHyooPyfal8RruwXbBPxGIAAAeEzk4TnFjbzKfV1a868HWwJ8RiAAAneJyuVRSUuJ2rL6+XpIUHBxsHktMTFRISEivtg3oKgIRAKBTSkpKtO6FIkXHjTCPlRUXKSC0v8bclCSpqafnQUmTJk3yUCuBziEQAQA6LTpuRKtbXQHh17gdA3wJgQgA+qi2bm311m0sZpDB1xCIAKCPanlrqzdvYzGDDL6GQAQAfdjFt7ba6rWR3HuN2upValnTUcwggy8hEAGAn2ir16Zlr1FbA6ZP/v2IZpaVKSEhQRK3vtA3EYgAwI+07LVpS1sDpl984x0zSHHrC30RgQgAcFkXBylufaEvYnNXAADg9whEAADA73k0EGVlZclisbg97Ha7+bphGMrKylJMTIz69eunqVOnqry83O0zXC6XFi9erMjISIWHhystLU0nT550q3E4HMrIyJDVapXValVGRobOnj3bG6cIAF6teeZZcXGxiouL/2/AdIOnmwX0Oo/3EI0dO1aVlZXm4+IpoWvWrNHatWuVm5urQ4cOyW63a8aMGaqtrTVrMjMztXPnTuXn52vv3r06d+6cUlNT1dDwxb/Q6enpKi0tVUFBgQoKClRaWqqMjIxePU8A8EbVJyr04hvvKP/g8abH7kM6c+YTTzcL6HUeH1QdGBjo1ivUzDAMrV+/XqtWrdLs2bMlSVu3bpXNZtOOHTu0cOFCOZ1Obdq0Sdu2bdP06dMlSXl5eYqNjVVRUZFmzpypo0ePqqCgQPv371dSUtMeOxs3blRycrKOHTumkSNH9t7JAoAXYsA04AU9RH//+98VExOjuLg4fec739EHH3wgSaqoqFBVVZVSUlLM2pCQEE2ZMkXFxcWSmtbLOH/+vFtNTEyMxo0bZ9bs27dPVqvVDEOSNHHiRFmtVrOmLS6XSzU1NW4PAADQN3k0ECUlJem///u/9corr2jjxo2qqqrSpEmT9Mknn6iqqkqSZLPZ3N5js9nM16qqqhQcHKyBAwdesiYqKqrVd0dFRZk1bVm9erU55shqtSo2NvaKzhUAAHgvjwai22+/Xd/4xjeUkJCg6dOn63/+538kNd0aa2axWNzeYxhGq2Mttaxpq/5yn7Ny5Uo5nU7zceLEiQ6dEwAA8D1dCkTDhg3TJ5+0HnR39uxZDRs2rMuNCQ8PV0JCgv7+97+b44pa9uJUV1ebvUZ2u1319fVyOByXrDl16lSr7zp9+nSr3qeLhYSEaMCAAW4PAADQN3UpEH344Ydus7iauVwuffzxx11ujMvl0tGjRxUdHa24uDjZ7XYVFhaar9fX12vPnj3mnjuJiYkKCgpyq6msrNThw4fNmuTkZDmdTh08eNCsOXDggJxOZ6/s+AwAALxfp2aZ/eEPfzD/+ZVXXpHV+sUGgQ0NDdq9e7euv/76Dn/e8uXLdccdd2jIkCGqrq7WE088oZqaGs2dO1cWi0WZmZnKzs5WfHy84uPjlZ2drbCwMKWnp0uSrFar5s2bp2XLlmnQoEGKiIjQ8uXLzVtwkjR69GjNmjVL8+fP14YNGyRJCxYsUGpqKjPMAACApE4GorvuuktS05icuXPnur0WFBSk66+/Xs8880yHP+/kyZP67ne/qzNnzujaa6/VxIkTtX//fg0dOlSStGLFCtXV1WnRokVyOBxKSkrSrl271L9/f/Mz1q1bp8DAQM2ZM0d1dXWaNm2atmzZooCAALNm+/btWrJkiTkbLS0tTbm5uZ05dQAA0Id1KhA1NjZKkuLi4nTo0CFFRkZe0Zfn5+df8nWLxaKsrCxlZWW1WxMaGqqcnBzl5OS0WxMREaG8vLyuNhMAAPRxXVqYsaKiorvbAQBoh8vlUklJSavjiYmJCgkJabemaRuOq3uljYCv6/JK1bt379bu3btVXV1t9hw1+9WvfnXFDQMANCkpKdG6F4oUHTfCPFZZ8a4elMzJIW3VlBUfku1L4zW8txsM+KAuBaLHHntMjz/+uCZMmKDo6OjLrgsEALgy0XEjzO01OlrDNhxAx3UpEP3yl7/Uli1b2CAVAAD0CV0KRPX19azhAwA9pOV4IMYCAT2vSwsz3nvvvdqxY0d3twUAoC/GA+UfPN702H1IZ8603h0AQPfpUg/R559/rueff15FRUUaP368goKC3F5fu3ZttzQOAPzVxeOBGAsE9LwuBaK//e1v+vKXvyxJOnz4sNtrDLAGgJ7XcOG8ysrKzOfcVgOuTJcC0f/+7/92dzsAAJ1QfaJCLzocKq9r2kKJKfbAlenyOkQAAM+KHBzHbTWgm3QpEN16662XvDX2l7/8pcsNAgAA6G1dCkTN44eanT9/XqWlpTp8+HCrTV8BAAC8XZcC0bp169o8npWVpXPnzl1RgwAAAHpbl9Yhas/3vvc99jEDAAA+p1sHVe/bt0+hoaHd+ZEA0Ke0tSv9xbvWA/CMLgWi2bNnuz03DEOVlZV688039e///u/d0jAA6Ita7krfctd6AJ7RpUBktVrdnl911VUaOXKkHn/8caWkpHRLwwDA17XVG1RWVibb0OGX3bkeQO/qUiDavHlzd7cDAHxeW5uy7iqv1HXDRn1xjAUUAa90RWOISkpKdPToUVksFo0ZM0Y33nhjd7ULAHxOy9thzeHn4t6glgsottyCQ2IbDsATuhSIqqur9Z3vfEevvvqqrrnmGhmGIafTqVtvvVX5+fm69tpru7udAOATOrspa8stOCR6kQBP6NK0+8WLF6umpkbl5eX65z//KYfDocOHD6umpkZLlizp7jYCQJ/WvAVH8yMyeoinmwT4nS71EBUUFKioqEijR482j40ZM0a/+MUvGFQNwOcwFR5AlwJRY2OjgoKCWh0PCgpSY2PjFTcKAHoTU+EBdCkQ3XbbbXrggQf061//WjExMZKkjz/+WA8++KCmTZvWrQ0EgN5w8difjmhvSj2DoQHf1KVAlJubqzvvvFPXX3+9YmNjZbFYdPz4cSUkJCgvL6+72wgAXqdlr5LEYGjAl3UpEMXGxuqtt95SYWGh3nnnHRmGoTFjxmj69Ond3T4A8Fote5U6MqsMgHfq1Cyzv/zlLxozZoxqamokSTNmzNDixYu1ZMkS3XzzzRo7dqxef/31HmkoAABAT+lUD9H69es1f/58DRgwoNVrVqtVCxcu1Nq1a/XVr3612xoIAN6grVWoGS8E9B2d6iH661//qlmzZrX7ekpKSqtBhgDQFzSPGco/eLzpsfuQzpz5xNPNAtBNOtVDdOrUqTan25sfFhio06dPX3GjAMAbdXYVagC+o1M9RNddd12rPXcu9re//U3R0dFdasjq1atlsViUmZlpHjMMQ1lZWYqJiVG/fv00depUlZeXu73P5XJp8eLFioyMVHh4uNLS0nTy5Em3GofDoYyMDFmtVlmtVmVkZOjs2bNdaicAAOh7OhWIvva1r+mRRx7R559/3uq1uro6Pfroo0pNTe10Iw4dOqTnn39e48ePdzu+Zs0arV27Vrm5uTp06JDsdrtmzJih2tpasyYzM1M7d+5Ufn6+9u7dq3Pnzik1NVUNDQ1mTXp6ukpLS1VQUKCCggKVlpYqIyOj0+0E4PtcLpeKi4vdHk3jgRou/2YAfVanbpk9/PDDeumllzRixAjdf//9GjlypCwWi44ePapf/OIXamho0KpVqzrVgHPnzunuu+/Wxo0b9cQTT5jHDcPQ+vXrtWrVKs2ePVuStHXrVtlsNu3YsUMLFy6U0+nUpk2btG3bNnPKf15enmJjY1VUVKSZM2fq6NGjKigo0P79+5WUlCRJ2rhxo5KTk3Xs2DGNHDmyU+0F4NtYPwhAWzoViGw2m4qLi/XDH/5QK1eulGEYkiSLxaKZM2fq2Weflc1m61QDfvSjH+nrX/+6pk+f7haIKioqVFVV5bY3WkhIiKZMmaLi4mItXLhQJSUlOn/+vFtNTEyMxo0bp+LiYs2cOVP79u2T1Wo1w5AkTZw4UVarVcXFxe0GIpfLJZfLZT5vXmoAgO+73PpBDRfOtxoewKwyoG/r9MKMQ4cO1Z/+9Cc5HA699957MgxD8fHxGjhwYKe/PD8/X2+99ZYOHTrU6rWqqipJahWwbDabPvroI7MmODi41XfbbDbz/VVVVYqKimr1+VFRUWZNW1avXq3HHnuscycEoE+oPlGhFx0OlddZzWP0IgF9W5dWqpakgQMH6uabb+7yF584cUIPPPCAdu3apdDQ0HbrLBaL23PDMFoda6llTVv1l/uclStXaunSpebzmpoaxcbGXvJ7AXifrq4fFDk4jlWoAT/S5UB0pUpKSlRdXa3ExETzWENDg1577TXl5ubq2LFjkpp6eC6euVZdXW32GtntdtXX18vhcLj1ElVXV5u7VNvtdp06darV958+ffqSt/dCQkIUEhJyZScJwONajhmipwdAWzo1y6w7TZs2TWVlZSotLTUfEyZM0N13363S0lINGzZMdrtdhYWF5nvq6+u1Z88eM+wkJiYqKCjIraayslKHDx82a5KTk+V0OnXw4EGz5sCBA3I6nWYNgL6tecxQ3NibFBk9xNPNAeCFPNZD1L9/f40bN87tWHh4uAYNGmQez8zMVHZ2tuLj4xUfH6/s7GyFhYUpPT1dUtN2IfPmzdOyZcs0aNAgRUREaPny5UpISDBnnY0ePVqzZs3S/PnztWHDBknSggULlJqaygwzAAAgyYOBqCNWrFihuro6LVq0SA6HQ0lJSdq1a5f69+9v1qxbt06BgYGaM2eO6urqNG3aNG3ZskUBAQFmzfbt27VkyRJzNlpaWppyc3N7/XwAAIB38qpA9Oqrr7o9t1gsysrKUlZWVrvvCQ0NVU5OjnJyctqtiYiIUF5eXje1EoC3ajmAWmK6PICO8apABABXgkUXAXQVgQiAz2prSr1t6HCmywPoNAIRAJ/FlHoA3YVABMCnXbwNB71BALqKQATA49oaDC01rTXGAqkAegOBCECva2vsz67ySl03bJR5rLLiXT0osYAqgF5BIALQ69ob+3PxYGgA6E0EIgAewdgfAN7EY3uZAQAAeAsCEQAA8HsEIgAA4PcYQwTAKzVcOK+ysjK3Y0zDB9BTCEQAvFL1iQq96HCovM4qSTr59yOaWVamhIQEs4aNWwF0FwIRAK8VOTjObSbai2+8YwYkia06AHQfAhEAn3FxQJKYrg+g+zCoGgAA+D0CEQAA8HsEIgAA4PcIRAAAwO8RiAAAgN9jlhmAHuVyuVRSUuJ2jPWDAHgbAhGAHlVSUqJ1LxQpOm6EeYz1gwB4GwIRgB4XHTeC9YMAeDXGEAEAAL9HIAIAAH6PW2YAOqytAdItd6BvWcMAagC+gEAEoMNaDpCurHhXD0qaNGlSuzUMoAbgCwhEADql5QDpy9UwgBqAL2AMEQAA8Hv0EAFoU0cWVGy4cF5lZWWXrAEAX+DRHqLnnntO48eP14ABAzRgwAAlJyfrz3/+s/m6YRjKyspSTEyM+vXrp6lTp6q8vNztM1wulxYvXqzIyEiFh4crLS1NJ0+edKtxOBzKyMiQ1WqV1WpVRkaGzp492xunCPis5rFA+QePf/HYfUhnznxi1lSfqNCLb7xzyRoA8AUeDUSDBw/WT3/6U7355pt68803ddttt+nOO+80Q8+aNWu0du1a5ebm6tChQ7Lb7ZoxY4Zqa2vNz8jMzNTOnTuVn5+vvXv36ty5c0pNTVVDQ4NZk56ertLSUhUUFKigoEClpaXKyMjo9fMFfE3zWKDmR2T0kFY1kYPjLlsDAN7Oo7fM7rjjDrfnTz75pJ577jnt379fY8aM0fr167Vq1SrNnj1bkrR161bZbDbt2LFDCxculNPp1KZNm7Rt2zZNnz5dkpSXl6fY2FgVFRVp5syZOnr0qAoKCrR//34lJSVJkjZu3Kjk5GQdO3ZMI0eO7N2TBgAAXsdrBlU3NDQoPz9fn376qZKTk1VRUaGqqiqlpKSYNSEhIZoyZYqKi4slNXXpnz9/3q0mJiZG48aNM2v27dsnq9VqhiFJmjhxoqxWq1nTFpfLpZqaGrcHAADomzweiMrKynT11VcrJCRE9913n3bu3KkxY8aoqqpKkmSz2dzqbTab+VpVVZWCg4M1cODAS9ZERUW1+t6oqCizpi2rV682xxxZrVbFxsZe0XkCAADv5fFANHLkSJWWlmr//v364Q9/qLlz5+rIkSPm6xaLxa3eMIxWx1pqWdNW/eU+Z+XKlXI6nebjxIkTHT0lAADgYzweiIKDg/WlL31JEyZM0OrVq3XDDTfoZz/7mex2uyS16sWprq42e43sdrvq6+vlcDguWXPq1KlW33v69OlWvU8XCwkJMWe/NT8AAEDf5PFA1JJhGHK5XIqLi5PdbldhYaH5Wn19vfbs2WNuE5CYmKigoCC3msrKSh0+fNisSU5OltPp1MGDB82aAwcOyOl0um03AAAA/JdHZ5n927/9m26//XbFxsaqtrZW+fn5evXVV1VQUCCLxaLMzExlZ2crPj5e8fHxys7OVlhYmNLT0yVJVqtV8+bN07JlyzRo0CBFRERo+fLlSkhIMGedjR49WrNmzdL8+fO1YcMGSdKCBQuUmprKDDP4rbYWXZRab9QKAP7Co4Ho1KlTysjIUGVlpaxWq8aPH6+CggLNmDFDkrRixQrV1dVp0aJFcjgcSkpK0q5du9S/f3/zM9atW6fAwEDNmTNHdXV1mjZtmrZs2aKAgACzZvv27VqyZIk5Gy0tLU25ubm9e7KAF2m5Aasknfz7Ec0sK1NCQoIkVpwG4F88Gog2bdp0ydctFouysrKUlZXVbk1oaKhycnKUk5PTbk1ERITy8vK62kzA57XsESorK5Nt6HC3TVorK97Vi2+8o/I6a1MNu9QD8CPsZQb0Me3tQbarvFLXDRvV9LydsNO86rTELvUA/AuBCOhj2rod1hyACDsA0DYCEdAHNe9B1owABACX5nXT7gEAAHobgQgAAPg9AhEAAPB7BCIAAOD3CEQAAMDvMcsM8CFtrTFUX18vqWmjZIkVpgGgKwhEgA9pe42hIgWE9teYm5L+7zkrTANAZxGIAB/T1hpDAeHXsOgiAFwBxhABAAC/RyACAAB+j0AEAAD8HoEIAAD4PQIRAADwe8wyA7wEawwBgOcQiAAvwRpDAOA5BCLAi7DGEAB4BmOIAACA36OHCPCQlmOGGB8EAJ5DIAI8pOWYIcYHAYDnEIgAD7p4zBDjgwDAcxhDBAAA/B6BCAAA+D0CEQAA8HuMIQJ6QVurUDOrDAC8B4EI6AFtTanfVV6p64aN+uIYs8oAwGsQiIAr1F7vz8UBqDn8tFyFGgDgHQhEQCd1pveHKfUA4Bs8Oqh69erVuvnmm9W/f39FRUXprrvu0rFjx9xqDMNQVlaWYmJi1K9fP02dOlXl5eVuNS6XS4sXL1ZkZKTCw8OVlpamkydPutU4HA5lZGTIarXKarUqIyNDZ8+e7elTRB/UvKBi/sHjTY/dhxR0dYTixt5kPiKjh3i6mQCATvBoINqzZ49+9KMfaf/+/SosLNSFCxeUkpKiTz/91KxZs2aN1q5dq9zcXB06dEh2u10zZsxQbW2tWZOZmamdO3cqPz9fe/fu1blz55SamqqGhgazJj09XaWlpSooKFBBQYFKS0uVkZHRq+eLvqN5QUXCDwD0DR69ZVZQUOD2fPPmzYqKilJJSYn+3//7fzIMQ+vXr9eqVas0e/ZsSdLWrVtls9m0Y8cOLVy4UE6nU5s2bdK2bds0ffp0SVJeXp5iY2NVVFSkmTNn6ujRoyooKND+/fuVlJQkSdq4caOSk5N17NgxjRw5sndPHAAAeBWvWofI6XRKkiIiIiRJFRUVqqqqUkpKilkTEhKiKVOmqLi4WFLT7Yvz58+71cTExGjcuHFmzb59+2S1Ws0wJEkTJ06U1Wo1a1pyuVyqqalxewAAgL7JawZVG4ahpUuX6itf+YrGjRsnSaqqqpIk2Ww2t1qbzaaPPvrIrAkODtbAgQNb1TS/v6qqSlFRUa2+MyoqyqxpafXq1Xrssceu7KTg81g/CAD8g9cEovvvv19/+9vftHfv3lavWSwWt+eGYbQ61lLLmrbqL/U5K1eu1NKlS83nNTU1io2NveR3ou9puSO9xPpBANAXeUUgWrx4sf7whz/otdde0+DBg83jdrtdUlMPT3R0tHm8urra7DWy2+2qr6+Xw+Fw6yWqrq7WpEmTzJpTp061+t7Tp0+36n1qFhISopCQkCs/Ofi8i3ekl5hCDwB9kUfHEBmGofvvv18vvfSS/vKXvyguLs7t9bi4ONntdhUWFprH6uvrtWfPHjPsJCYmKigoyK2msrJShw8fNmuSk5PldDp18OBBs+bAgQNyOp1mDQAA8F8e7SH60Y9+pB07duj3v/+9+vfvb47nsVqt6tevnywWizIzM5Wdna34+HjFx8crOztbYWFhSk9PN2vnzZunZcuWadCgQYqIiNDy5cuVkJBgzjobPXq0Zs2apfnz52vDhg2SpAULFig1NZUZZgAAwLOB6LnnnpMkTZ061e345s2bdc8990iSVqxYobq6Oi1atEgOh0NJSUnatWuX+vfvb9avW7dOgYGBmjNnjurq6jRt2jRt2bJFAQEBZs327du1ZMkSczZaWlqacnNze/YEAQCAT/BoIDIM47I1FotFWVlZysrKarcmNDRUOTk5ysnJabcmIiJCeXl5XWkm/Ehb23IwowwA+j6vGFQNeIuWs8qYUQYA/oFABLRw8awyZpQBgH/wqpWqAQAAPIFABAAA/B6BCAAA+D0CEQAA8HsMqobfaGuj1sTERLZoAQAQiOA/Wk6pr6x4Vw9KbN8CACAQwb+03KgVAACJQIQ+qq3bYy1XnW64cF5lZWWXrAEA+AcCEfqklrfHpNarTlefqNCLDofK66zt1gAA/AOBCH1Wy9tjba06HTk47rI1AIC+j2n3AADA79FDBJ/XkfFCAABcCoEIPq8j44UAALgUAhH6hI6MFwIAoD2MIQIAAH6PQAQAAPwet8zgc1oOomYANQDgShGI4NXam0G2q7xS1w0b1fScAdQAgCtEIIJXu9QMsuZB1AygBgBcKQIRvB4zyAAAPY1B1QAAwO8RiAAAgN/jlhm8CjPIAACeQCCCxzCDDADgLQhE8BhmkAEAvAWBCB7FDDIAgDdgUDUAAPB7BCIAAOD3PBqIXnvtNd1xxx2KiYmRxWLRyy+/7Pa6YRjKyspSTEyM+vXrp6lTp6q8vNytxuVyafHixYqMjFR4eLjS0tJ08uRJtxqHw6GMjAxZrVZZrVZlZGTo7NmzPXx2aMnlcqm4uNh8NM0ga/B0swAA8Gwg+vTTT3XDDTcoNze3zdfXrFmjtWvXKjc3V4cOHZLdbteMGTNUW1tr1mRmZmrnzp3Kz8/X3r17de7cOaWmpqqh4Ysf2vT0dJWWlqqgoEAFBQUqLS1VRkZGj58f3DUPos4/eLzpsfuQzpz5xNPNAgDAs4Oqb7/9dt1+++1tvmYYhtavX69Vq1Zp9uzZkqStW7fKZrNpx44dWrhwoZxOpzZt2qRt27Zp+vTpkqS8vDzFxsaqqKhIM2fO1NGjR1VQUKD9+/crKSlJkrRx40YlJyfr2LFjGjlyZO+crJ9pb0q9behwZpABALyO144hqqioUFVVlVJSUsxjISEhmjJlioqLiyU19TicP3/erSYmJkbjxo0za/bt2yer1WqGIUmaOHGirFarWdMWl8ulmpoatwc6rlVvED1CAAAv5rXT7quqqiRJNpvN7bjNZtNHH31k1gQHB2vgwIGtaprfX1VVpaioqFafHxUVZda0ZfXq1Xrssceu6Bz8HVPqAQC+wmt7iJpZLBa354ZhtDrWUsuatuov9zkrV66U0+k0HydOnOhkywEAgK/w2h4iu90uqamHJzo62jxeXV1t9hrZ7XbV19fL4XC49RJVV1dr0qRJZs2pU6daff7p06db9T5dLCQkRCEhId1yLn1NW+OD6uvrJUnBwcGS2IMMAOBbvDYQxcXFyW63q7CwUDfeeKOkph/dPXv26KmnnpIkJSYmKigoSIWFhZozZ44kqbKyUocPH9aaNWskScnJyXI6nTp48KBuueUWSdKBAwfkdDrN0ITOaXvLjSIFhPbXmJuS/u85e5ABAHyHRwPRuXPn9N5775nPKyoqVFpaqoiICA0ZMkSZmZnKzs5WfHy84uPjlZ2drbCwMKWnp0uSrFar5s2bp2XLlmnQoEGKiIjQ8uXLlZCQYM46Gz16tGbNmqX58+drw4YNkqQFCxYoNTWVGWZXoK3xQQHh1zCDDADgkzwaiN58803deuut5vOlS5dKkubOnastW7ZoxYoVqqur06JFi+RwOJSUlKRdu3apf//+5nvWrVunwMBAzZkzR3V1dZo2bZq2bNmigIAAs2b79u1asmSJORstLS2t3bWPAACA//FoIJo6daoMw2j3dYvFoqysLGVlZbVbExoaqpycHOXk5LRbExERoby8vCtpKgAA6MO8fpYZAABATyMQAQAAv0cgAgAAfs9rp93De7Rcd4g1hgAAfQ2BCG7a25R1V3mlrhs2quk5awwBAPoYAhHctL3oYlMAYo0hAEBfRSBCK2zKCgDwNwyqBgAAfo8eIj/HgGkAAAhEfoUB0wAAtI1A5EcYMA0AQNsIRH6GAdMAALTGoGoAAOD3CEQAAMDvEYgAAIDfYwxRH8aUegAAOoZA1EcwpR4AgK4jEPURTKkHAKDrCER9CFPqAQDoGgZVAwAAv0cgAgAAfo9bZj6KGWQAAHQfApGPajmImhlkAAB0HYHIB7Q3pd42dDgzyAAA6AYEIh9wqSn19AgBAHDlCEQ+gin1AAD0HAKRF2LANAAAvYtA5IUYMA0AQO8iEHmpi2+RcXsMAICexcKMAADA7/lVIHr22WcVFxen0NBQJSYm6vXXX/d0kwAAgBfwm1tmL7zwgjIzM/Xss89q8uTJ2rBhg26//XYdOXJEQ4YM8Vi72ltjiEHUAAD0Hr8JRGvXrtW8efN07733SpLWr1+vV155Rc8995xWr17tsXaxxhAAAJ7nF4Govr5eJSUleuihh9yOp6SkqLi4uM33uFwuuVwu87nT6ZQk1dTUdGvbPv30U513fa76zz8zj104X6+qD97RsQFNvURVx99TQMjV5vO2jlFz6RpPfz811FDDv9/UXKLmw/f06dhB3f4bK33xu20YxqULDT/w8ccfG5KMN954w+34k08+aYwYMaLN9zz66KOGJB48ePDgwYNHH3icOHHiklnBL3qImlksFrfnhmG0OtZs5cqVWrp0qfm8sbFR//znPzVo0KB239MVNTU1io2N1YkTJzRgwIBu+1y0xrXuHVzn3sF17h1c597Rk9fZMAzV1tYqJibmknV+EYgiIyMVEBCgqqoqt+PV1dWy2WxtvickJEQhISFux6655pqeaqIGDBjAv2y9hGvdO7jOvYPr3Du4zr2jp66z1Wq9bI1fTLsPDg5WYmKiCgsL3Y4XFhZq0qRJHmoVAADwFn7RQyRJS5cuVUZGhiZMmKDk5GQ9//zzOn78uO677z5PNw0AAHiY3wSib3/72/rkk0/0+OOPq7KyUuPGjdOf/vQnDR061KPtCgkJ0aOPPtrq9hy6H9e6d3CdewfXuXdwnXuHN1xni2Fcbh4aAABA3+YXY4gAAAAuhUAEAAD8HoEIAAD4PQIRAADwewSiXvDss88qLi5OoaGhSkxM1Ouvv37J+j179igxMVGhoaEaNmyYfvnLX/ZSS31bZ67zSy+9pBkzZujaa6/VgAEDlJycrFdeeaUXW+u7Ovv33OyNN95QYGCgvvzlL/dsA/uQzl5rl8ulVatWaejQoQoJCdHw4cP1q1/9qpda67s6e523b9+uG264QWFhYYqOjta//uu/6pNPPuml1vqm1157TXfccYdiYmJksVj08ssvX/Y9vf5b2C2bhaFd+fn5RlBQkLFx40bjyJEjxgMPPGCEh4cbH330UZv1H3zwgREWFmY88MADxpEjR4yNGzcaQUFBxm9/+9tebrlv6ex1fuCBB4ynnnrKOHjwoPHuu+8aK1euNIKCgoy33nqrl1vuWzp7nZudPXvWGDZsmJGSkmLccMMNvdNYH9eVa52WlmYkJSUZhYWFRkVFhXHgwIFWezjCXWev8+uvv25cddVVxs9+9jPjgw8+MF5//XVj7Nixxl133dXLLfctf/rTn4xVq1YZv/vd7wxJxs6dOy9Z74nfQgJRD7vllluM++67z+3YqFGjjIceeqjN+hUrVhijRo1yO7Zw4UJj4sSJPdbGvqCz17ktY8aMMR577LHublqf0tXr/O1vf9t4+OGHjUcffZRA1EGdvdZ//vOfDavVanzyySe90bw+o7PX+emnnzaGDRvmduznP/+5MXjw4B5rY1/TkUDkid9Cbpn1oPr6epWUlCglJcXteEpKioqLi9t8z759+1rVz5w5U2+++abOnz/fY231ZV25zi01NjaqtrZWERERPdHEPqGr13nz5s16//339eijj/Z0E/uMrlzrP/zhD5owYYLWrFmj6667TiNGjNDy5ctVV1fXG032SV25zpMmTdLJkyf1pz/9SYZh6NSpU/rtb3+rr3/9673RZL/hid9Cv1mp2hPOnDmjhoaGVhvI2my2VhvNNquqqmqz/sKFCzpz5oyio6N7rL2+qivXuaVnnnlGn376qebMmdMTTewTunKd//73v+uhhx7S66+/rsBA/nPTUV251h988IH27t2r0NBQ7dy5U2fOnNGiRYv0z3/+k3FE7ejKdZ40aZK2b9+ub3/72/r888914cIFpaWlKScnpzea7Dc88VtID1EvsFgsbs8Nw2h17HL1bR2Hu85e52a//vWvlZWVpRdeeEFRUVE91bw+o6PXuaGhQenp6Xrsscc0YsSI3mpen9KZv+nGxkZZLBZt375dt9xyi772ta9p7dq12rJlC71El9GZ63zkyBEtWbJEjzzyiEpKSlRQUKCKigr2xewBvf1byP+y9aDIyEgFBAS0+j+N6urqVsm3md1ub7M+MDBQgwYN6rG2+rKuXOdmL7zwgubNm6cXX3xR06dP78lm+rzOXufa2lq9+eabevvtt3X//fdLavrRNgxDgYGB2rVrl2677bZeabuv6crfdHR0tK677jpZrVbz2OjRo2UYhk6ePKn4+PgebbMv6sp1Xr16tSZPnqwf//jHkqTx48crPDxcX/3qV/XEE0/Qi99NPPFbSA9RDwoODlZiYqIKCwvdjhcWFmrSpEltvic5OblV/a5duzRhwgQFBQX1WFt9WVeus9TUM3TPPfdox44d3P/vgM5e5wEDBqisrEylpaXm47777tPIkSNVWlqqpKSk3mq6z+nK3/TkyZP1j3/8Q+fOnTOPvfvuu7rqqqs0ePDgHm2vr+rKdf7ss8901VXuP50BAQGSvujBwJXzyG9hjw3XhmEYX0zp3LRpk3HkyBEjMzPTCA8PNz788EPDMAzjoYceMjIyMsz65qmGDz74oHHkyBFj06ZNTLvvgM5e5x07dhiBgYHGL37xC6OystJ8nD171lOn4BM6e51bYpZZx3X2WtfW1hqDBw82vvnNbxrl5eXGnj17jPj4eOPee+/11Cn4hM5e582bNxuBgYHGs88+a7z//vvG3r17jQkTJhi33HKLp07BJ9TW1hpvv/228fbbbxuSjLVr1xpvv/22ubyBN/wWEoh6wS9+8Qtj6NChRnBwsHHTTTcZe/bsMV+bO3euMWXKFLf6V1991bjxxhuN4OBg4/rrrzeee+65Xm6xb+rMdZ4yZYohqdVj7ty5vd9wH9PZv+eLEYg6p7PX+ujRo8b06dONfv36GYMHDzaWLl1qfPbZZ73cat/T2ev885//3BgzZozRr18/Izo62rj77ruNkydP9nKrfcv//u//XvK/ud7wW2gxDPr4AACAf2MMEQAA8HsEIgAA4PcIRAAAwO8RiAAAgN8jEAEAAL9HIAIAAH6PQAQAAPwegQgAAPg9AhEAAPB7BCIAAOD3CEQAAMDvEYgAAIDf+/+WxT7OC+fCKgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import numpy as np\n",
    "sns.histplot(trace.posterior['seeing_red2'].to_dataframe(), bins=np.arange(0, 1.01, .01))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "seeing_red2    0.745633\n",
       "dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(trace.posterior['seeing_red2'].to_dataframe() > .5).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7401235173022255"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as ss\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "possible_original_n = np.arange(101)\n",
    "p_draw_red_given_par = possible_original_n/100.\n",
    "p_draw_red = (np.arange(101) / 100.).sum()\n",
    "p_par = 1./101.\n",
    "\n",
    "p_par_given_draw_red = p_draw_red_given_par * p_par / p_draw_red\n",
    "\n",
    "p_par_given_draw_red = pd.Series(p_par_given_draw_red, index=possible_original_n)\n",
    "\n",
    "\n",
    "p_par_given_draw_red.plot()\n",
    "\n",
    "p_par_given_draw_red.loc[51:].sum() *100\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}