Introduction.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "% matplotlib inline\n",
    "from joblib import Parallel, delayed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_sim(x):\n",
    "    truth = np.random.uniform(size=100) < x\n",
    "    first_random = np.random.randint(2,size=100)\n",
    "    second_random = np.random.randint(2,size=100)\n",
    "    res = np.sum(first_random*truth + (1-first_random)*second_random)/100\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample(data = 0.54):\n",
    "    x = np.random.uniform()\n",
    "    if run_sim(x) == data:\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "98.01% are throwaways\n"
     ]
    }
   ],
   "source": [
    "t = Parallel(n_jobs=-1)(delayed(sample)() for i in range(100000))\n",
    "t = np.array(t,dtype=float)\n",
    "share = np.sum(np.isnan(t))/len(t)*100\n",
    "print(f'{share:.2f}% are throwaways')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_flat = t[~np.isnan(t)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(t_flat, bins=30,density=True)\n",
    "plt.title('Distribution of possible TPPs')\n",
    "plt.xlim(0,1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample(data = 0.54):\n",
    "    x = np.random.uniform(low=0,high=0.5)\n",
    "    if run_sim(x) == data:\n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now you can run the simulations exactly as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = Parallel(n_jobs=-1)(delayed(sample)() for i in range(100000))\n",
    "t = np.array(t,dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "99.10% are throwaways\n"
     ]
    }
   ],
   "source": [
    "# Optional\n",
    "share = np.sum(np.isnan(t))/len(t)*100\n",
    "print(f'{share:.2f}% are throwaways')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_cut = t[~np.isnan(t)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEICAYAAABVv+9nAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAEy1JREFUeJzt3X2UbXVdx/H3R65ICPh0x5QHGUkljWVLG0srH9EiJOgPU1xiqCRZKzPFDFOXlj2YmpVl2U0IfCKNLK+SJamElmCDqPGgRYhwBWQQIQVFwG9/7H25wzBz58w5ex7uj/drrVlzzt77/Pb3/GbmM7/zO3vvk6pCktSeu613AZKk1WHAS1KjDHhJapQBL0mNMuAlqVEGvCQ1yoBvWJK3J3nNQG09KMm3kuzW3z8ryS8O0Xbf3keSHDtUeyvY7+8muTbJ1Wu970Vquf3nleRJSbbtZNtTkvzu2lWnXZEBv4tKclmSbyf5ZpLrk/xHkhcluf1nWlUvqqrXj9jWU3e2TVVdXlV7VdVtA9T+uiTvXtD+z1TVqZO2vcI6DgBOAB5RVQ9Yy30vZtSf17jm/ZPe/lVJbpx3//H9P47v9vevS3Jmkh/sH/+6JLf067b/zj1uterV5Az4XdvPVtXewIHAG4DfBE4aeidJNg3d5gZxIPD1qrpmvQtZC/P+Se9VVXv1i3943rJP9sve2K/fH7gGOGVeM+/r100BnwI+kCRr9Ry0MgZ8A6rqhqraCjwLODbJIXDHl/FJNif5cD/yui7JJ5PcLcm7gAcBH+pHZq9IMt2P7o5Lcjnw8XnL5of9DyT5TJIbknwwyX37fd1pemH7q4QkhwG/BTyr39/n+/W3T/n0db06yVeSXJPknUnu1a/bXsexSS7vp1detVTfJLlX//i5vr1X9+0/FTgT2Lev45RFHvukJNuS/Fa/n8uSPGe5tvt1D0nyb33fXJvkff3yJPnj/nndkOQLi/285u1j0X0vUusRST43b2T9yKW2HVVV3QS8FzhkkXW3AKcCDwDut9Tz1fpqdWR2l1RVn+mD9fHABQtWnwBsoxt5ATy2e0g9N8njgV+sqn+FLkT7bZ4IPBz4HvD9i+zyF4CfBr4MvBN4K3DMMjX+c5LfBx5SVUtt+7z+68l0I8h3An8OPHfeNj8JHAw8DPhMkg9U1cWLtPVnwL2Ag4D7AR8Frqqqk5L8DPDuqtp/JyU/ANgM7EfXZ/+UZLaqvrRU23Svol7f338ysDsw07f3U8AT+rpvAH4QuH6Mfd8uyaOBk4GfBWbpfgZbkxxcVTfv5LntVJK9gOcA5y+y7h50P6NtVXVtkj9b4vlqHTmCb8+VwH0XWX4L8EDgwKq6pao+WctfiOh1VXVjVX17ifXvqqoLqupG4DXAM9O/CTuh5wBvqapLq+pbwCuBoxe8evjtqvp2VX0e+Dzwwwsb6Wt5FvDKqvpmVV0G/BF3/EcxitdU1c1V9W/AGex4njtr+xa6KaB9q+o7VfWpecv3pgv2VNXFVXXVSva9yDYvBP6qqs6tqtv69zJupvunMI6XJ7keuATYiy7It3tmv+4K4EeAn5v3vBZ7vlpHBnx79gOuW2T5m+j+YD+a5NIkJ47Q1hUrWP8V4O50I85J7du3N7/tTdzxVcT8o15uoguihTbTjSYXtrXfCmr5Rv8PbP7j9x2h7VcAoXt1cWGSFwBU1cfpXo28Dfhaki1J9lnhvhc6EDihn565vg/gA5bYdhRvrqp7V9UDqurIqvrfeeve36+7f1U9parO29nz1foy4BuS5DF0AXOn0VM/yjyhqg6ieyn/siSHbl+9RJPLjfAPmHf7QXSjuGuBG4E959W1GzumhkZp90q60Jrf9q3A15Z53ELXsmNkOb+tr66gjfskueeCx1+5XNtVdXVVvbCq9gV+CfiLJA/p1721qn4E+CG6qZrfWOG+F7oC+L0+eLd/7VlVp63geU5kZ89X68eAb0CSfZIcAfwt3Zzyfy2yzRH9G2EB/g+4rf+CLjgPGmPXxyR5RJI9gd8BTu8Po/xvYI8kT09yd+DVwD3mPe5rwHTmHdK5wGnAS5M8uJ8H/n26ozduXUlxfS3vB34vyd5JDgReBrx754+8k99Osnv/XsURwN8t13aSn0+yfW7/G3T/1G5L8pgkP9b3y43Ad9jxcxhp34ts89fAi/p2k+Sefd/vvcLnObalnu9a7V+LM+B3bR9K8k26EdyrgLcAz19i24cC/wp8C/g08BdVdVa/7g+AV/cv71++gv2/i+4QuquBPYBfg+6oHuBXgHfQjWhvpHuDd7vtIfX1JJ9dpN2T+7bPpnsD9zvAi1dQ13wv7vd/Kd0rm/f27Y/qarrAuhJ4D/CiqvriCG0/Bjg3ybeArcBLqurLwD50gfwNuimXrwNvHmPft6uqWbp5+D/vt7+EO86br4Wlnq/WUfzAD2lxSZ7E8kfZSBuWI3hJapQBL0mNcopGkhrlCF6SGrWmlyrYvHlzTU9Pr+UuJWmXd955511bVVPLb3lHaxrw09PTzM7OruUuJWmXl+Qry291Z07RSFKjDHhJapQBL0mNMuAlqVHLBnySk/tPn7lg3rI3Jfli/2k0/5Dk3qtbpiRppUYZwZ8CHLZg2ZnAIVX1SLorB75y4LokSRNaNuCr6mwWfIBEVX103qVbz6H7cF5J0gYyxBz8C4CPLLUyyfFJZpPMzs3NDbA7SdIoJgr4dJ9mfyvdtaoXVVVbqmqmqmamplZ8IpYkaUxjn8ma5Fi6T5g5dIQPb5Y2jOkTz7jTssve8PR1qERaXWMFfJLDgN8EnlhVNw1bkiRpCKMcJnka3Ue8HZxkW5Lj6D4abG/gzCSfS/L2Va5TkrRCy47gq+rZiyw+aRVqkSQNyDNZJalRBrwkNcqAl6RGGfCS1CgDXpIaZcBLUqMMeElqlAEvSY0y4CWpUQa8JDXKgJekRhnwktQoA16SGmXAS1KjDHhJapQBL0mNMuAlqVEGvCQ1yoCXpEYZ8JLUKANekhplwEtSowx4SWqUAS9JjTLgJalRBrwkNWrZgE9ycpJrklwwb9l9k5yZ5H/67/dZ3TIlSSs1ygj+FOCwBctOBD5WVQ8FPtbflyRtIMsGfFWdDVy3YPFRwKn97VOBnxu4LknShMadg//+qroKoP9+/6U2THJ8ktkks3Nzc2PuTpK0Uqv+JmtVbamqmaqamZqaWu3dSZJ64wb815I8EKD/fs1wJUmShrBpzMdtBY4F3tB//+BgFUkDmT7xjPUuQVpXoxwmeRrwaeDgJNuSHEcX7E9L8j/A0/r7kqQNZNkRfFU9e4lVhw5ciyRpQJ7JKkmNMuAlqVEGvCQ1yoCXpEYZ8JLUKANekhplwEtSowx4SWqUAS9JjTLgJalRBrwkNWrcq0lKG4ZXjZQW5whekhplwEtSowx4SWqUAS9JjTLgJalRBrwkNcqAl6RGGfCS1CgDXpIaZcBLUqMMeElqlAEvSY0y4CWpUQa8JDVqooBP8tIkFya5IMlpSfYYqjBJ0mTGDvgk+wG/BsxU1SHAbsDRQxUmSZrMpFM0m4DvS7IJ2BO4cvKSJElDGDvgq+qrwJuBy4GrgBuq6qMLt0tyfJLZJLNzc3PjVypJWpFJpmjuAxwFPBjYF7hnkmMWbldVW6pqpqpmpqamxq9UkrQik0zRPBX4clXNVdUtwAeAHx+mLEnSpCYJ+MuBxybZM0mAQ4GLhylLkjSpSebgzwVOBz4L/Fff1paB6pIkTWjTJA+uqtcCrx2oFknSgDyTVZIaZcBLUqMMeElqlAEvSY0y4CWpUQa8JDXKgJekRhnwktQoA16SGjXRmazSWpo+8Yz1LkHapTiCl6RGGfCS1CgDXpIaZcBLUqMMeElqlAEvSY0y4CWpUQa8JDXKgJekRnkmqzYcz1iVhuEIXpIaZcBLUqMMeElqlAEvSY0y4CWpURMFfJJ7Jzk9yReTXJzkcUMVJkmazKSHSf4p8M9V9YwkuwN7DlCTJGkAYwd8kn2AJwDPA6iq7wLfHaYsSdKkJpmiOQiYA/4myflJ3pHkngPVJUma0CQBvwl4NPCXVfUo4EbgxIUbJTk+yWyS2bm5uQl2J0laiUkCfhuwrarO7e+fThf4d1BVW6pqpqpmpqamJtidJGklxg74qroauCLJwf2iQ4GLBqlKkjSxSY+ieTHwnv4ImkuB509ekiRpCBMFfFV9DpgZqBZJ0oA8k1WSGmXAS1KjDHhJapQBL0mNMuAlqVEGvCQ1yoCXpEYZ8JLUKANekhplwEtSowx4SWqUAS9JjTLgJalRBrwkNcqAl6RGGfCS1CgDXpIaZcBLUqMMeElqlAEvSY0y4CWpUQa8JDXKgJekRhnwktQoA16SGmXAS1KjJg74JLslOT/Jh4coSJI0jCFG8C8BLh6gHUnSgCYK+CT7A08H3jFMOZKkoUw6gv8T4BXA95baIMnxSWaTzM7NzU24O0nSqMYO+CRHANdU1Xk7266qtlTVTFXNTE1Njbs7SdIKbZrgsT8BHJnkcGAPYJ8k766qY4YpTXcF0yeesd4lSM0aewRfVa+sqv2raho4Gvi44S5JG4fHwUtSoyaZorldVZ0FnDVEW5KkYTiCl6RGGfCS1CgDXpIaZcBLUqMMeElqlAEvSY0y4CWpUQa8JDXKgJekRhnwktSoQS5VIC3Hq0ZKa88RvCQ1yoCXpEYZ8JLUKANekhplwEtSowx4SWqUAS9JjTLgJalRnuikQXlCk7RxOIKXpEYZ8JLUKANekhplwEtSowx4SWqUAS9JjRo74JMckOQTSS5OcmGSlwxZmCRpMpMcB38rcEJVfTbJ3sB5Sc6sqosGqk2SNIGxR/BVdVVVfba//U3gYmC/oQqTJE1mkDn4JNPAo4BzF1l3fJLZJLNzc3ND7E6SNIKJAz7JXsDfA79eVf+3cH1VbamqmaqamZqamnR3kqQRTRTwSe5OF+7vqaoPDFOSJGkIkxxFE+Ak4OKqestwJUmShjDJCP4ngOcCT0nyuf7r8IHqkiRNaOzDJKvqU0AGrEWSNCDPZJWkRhnwktQoA16SGmXAS1Kj/ExWjcXPXpU2PgNeO2WQS7sup2gkqVEGvCQ1yoCXpEYZ8JLUKANekhplwEtSowx4SWqUAS9JjTLgJalRBrwkNcqAl6RGGfCS1CgDXpIaZcBLUqMMeElqlAEvSY3yAz/ugvwQD+muwRG8JDXKgJekRjlF0zCnYqS7tolG8EkOS/KlJJckOXGooiRJkxt7BJ9kN+BtwNOAbcB/JtlaVRcNVZzuaKkR+WVvePoaVyJpVzDJCP5HgUuq6tKq+i7wt8BRw5QlSZrUJHPw+wFXzLu/DfixhRslOR44vr97c5ILJthnSzYD1w7RUP5wiFbW1WB9Ma4N1Ifr3hcbiH2xw8HjPGiSgM8iy+pOC6q2AFsAksxW1cwE+2yGfbGDfbGDfbGDfbFDktlxHjfJFM024IB59/cHrpygPUnSgCYJ+P8EHprkwUl2B44Gtg5TliRpUmNP0VTVrUl+FfgXYDfg5Kq6cJmHbRl3fw2yL3awL3awL3awL3YYqy9Sdadpc0lSA7xUgSQ1yoCXpEatSsAvdwmDJPdI8r5+/blJplejjo1ghL54WZKLknwhyceSHLgeda6FUS9tkeQZSSpJs4fIjdIXSZ7Z/25cmOS9a13jWhnhb+RBST6R5Pz+7+Tw9ahztSU5Ock1S50rlM5b+376QpJHL9toVQ36RfeG6/8CBwG7A58HHrFgm18B3t7fPhp439B1bISvEfviycCe/e1fviv3Rb/d3sDZwDnAzHrXvY6/Fw8Fzgfu09+//3rXvY59sQX45f72I4DL1rvuVeqLJwCPBi5YYv3hwEfozkF6LHDucm2uxgh+lEsYHAWc2t8+HTg0yWInTu3qlu2LqvpEVd3U3z2H7nyCFo16aYvXA28EvrOWxa2xUfrihcDbquobAFV1zRrXuFZG6YsC9ulv34tGz7epqrOB63ayyVHAO6tzDnDvJA/cWZurEfCLXcJgv6W2qapbgRuA+61CLettlL6Y7zi6/9AtWrYvkjwKOKCqPryWha2DUX4vHgY8LMm/JzknyWFrVt3aGqUvXgcck2Qb8E/Ai9emtA1npXmyKteDH+USBiNd5qABIz/PJMcAM8ATV7Wi9bPTvkhyN+CPgeetVUHraJTfi0100zRPontV98kkh1TV9atc21obpS+eDZxSVX+U5HHAu/q++N7ql7ehrDg3V2MEP8olDG7fJskmupddO3tpsqsa6XIOSZ4KvAo4sqpuXqPa1tpyfbE3cAhwVpLL6OYYtzb6RuuofyMfrKpbqurLwJfoAr81o/TFccD7Aarq08AedBciu6tZ8eVhViPgR7mEwVbg2P72M4CPV/8uQmOW7Yt+WuKv6MK91XlWWKYvquqGqtpcVdNVNU33fsSRVTXWRZY2uFH+Rv6R7g14kmymm7K5dE2rXBuj9MXlwKEASR5OF/Bza1rlxrAV+IX+aJrHAjdU1VU7e8DgUzS1xCUMkvwOMFtVW4GT6F5mXUI3cj966Do2ghH74k3AXsDf9e8zX15VR65b0atkxL64SxixL/4F+KkkFwG3Ab9RVV9fv6pXx4h9cQLw10leSjcl8bwWB4RJTqObktvcv9/wWuDuAFX1drr3Hw4HLgFuAp6/bJsN9pMkCc9klaRmGfCS1CgDXpIaZcBLUqMMeElqlAEvSY0y4CWpUf8PjZe3PDkWbBkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(t_cut, bins=15,density=True)\n",
    "plt.title('Distribution of possible TPPs')\n",
    "plt.xlim(0,1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Eu+nTlvQRZc3OBhal0/cCJ0tSblWamVmfZbo8cnoD85XA4cBNEbGirMkYYB1ARGyTtAkYAWzIsVaz/PV0mWGzQSbTl7YRsT0ipgBjgaMlTSprUmlvvvxTAJJmS+qQ1NHd3d37as3MrG69OksnIt4CHgdmlM3qAsYBSNoLGA68UWH5hRHRHhHto0aNqqtgMzOrT5azdEZJOiid3hc4Bfh1WbMlwEXp9DnAoxGx2x6+mZk1T5Zj+KOBRelx/CHAjyLix5LmAh0RsQS4BbhT0lqSPfuZDavYzMzqUjPwI+I5YGqF1+eUTG8Bzs23NDMzy5N/aWtmVhAOfDOzgnDgm5kVhAPfzKwgHPhmZgXhwDczKwgHvplZQTjwzcwKwoFvZlYQDnwzs4Jw4JuZFYQD38ysIBz4ZmYF4cA3MyuITPe0NbMBpNZ9eq/d1D912B7He/hmZgXhwDczK4gs97QdJ+kxSWskvSDpqxXanChpk6RV6WNOpb7MzKx5shzD3wZ8PSKeljQMWCnpXyNidVm7ZRFxZv4lmplZHrLc0/Y14LV0+h1Ja4AxQHngm9lA5y98B7VeHcOX1EZyQ/MVFWYfI+lZSQ9K+liV5WdL6pDU0d3d3etizcysfpkDX9IBwD8BV0TE22WznwYOi4ijgO8B91fqIyIWRkR7RLSPGjWq3prNzKwOmQJfUgtJ2P9jRPxz+fyIeDsi3k2nlwItkkbmWqmZmfVJlrN0BNwCrImIeVXafChth6Sj03435lmomZn1TZazdI4F/hz4laRV6WvfAg4FiIgFwDnAFyVtA94HZkZENKBeMzOrU5azdJ4EVKPNjcCNeRVlZmb58y9tzcwKwoFvZlYQDnwzs4Jw4JuZFYQD38ysIBz4ZmYF4TtemRVNrQuk2aDlPXwzs4Jw4JuZFYQD38ysIBz4ZmYF4cA3MysIB76ZWUE48M3MCsKBb2ZWEA58M7OCcOCbmRVEzUsrSBoH3AF8CPgAWBgR3y1rI+C7wOnAZmBWRDydf7lmFfhSAWaZZLmWzjbg6xHxtKRhwEpJ/xoRq0vanAYckT4+Cdyc/mtmZnuImod0IuK1HXvrEfEOsAYYU9bsbOCOSCwHDpI0Ovdqzcysbr06hi+pDZgKrCibNQZYV/K8i93/U0DSbEkdkjq6u7t7V6mZmfVJ5sCXdADwT8AVEfF2+ewKi8RuL0QsjIj2iGgfNWpU7yo1M7M+yRT4klpIwv4fI+KfKzTpAsaVPB8LrO97eWZmlpeagZ+egXMLsCYi5lVptgS4UInpwKaIeC3HOs3MrI+ynKVzLPDnwK8krUpf+xZwKEBELACWkpySuZbktMyL8y/VzMz6ombgR8STVD5GX9omgC/nVZSZmeXPv7Q1MysIB76ZWUE48M3MCsKBb2ZWEA58M7OCcOCbmRWEA9/MrCAc+GZmBeHANzMrCAe+mVlBOPDNzArCgW9mVhAOfDOzgnDgm5kVhAPfzKwgHPhmZgWR5RaHt0p6XdLzVeafKGmTpFXpY07+ZZqZWV9lucXh7cCNwB09tFkWEWfmUpGZmTVEzT38iHgCeKMfajEzswbK6xj+MZKelfSgpI9VayRptqQOSR3d3d05vbWZmWWRR+A/DRwWEUcB3wPur9YwIhZGRHtEtI8aNSqHtzYzs6z6HPgR8XZEvJtOLwVaJI3sc2VmZparPge+pA9JUjp9dNrnxr72a2Zm+ap5lo6ku4ETgZGSuoBvAy0AEbEAOAf4oqRtwPvAzIiIhlVsZmZ1qRn4EXF+jfk3kpy2aWZmezD/0tbMrCAc+GZmBeHANzMriCyXVjAzS1w7vId5m/qvDquL9/DNzArCgW9mVhAOfDOzgnDgm5kVhAPfzKwgHPhmZgXhwDczKwgHvplZQTjwzcwKwoFvZlYQDnwzs4LwtXRsYOjpGi5mlon38M3MCiLLLQ5vBc4EXo+ISRXmC/gucDqwGZgVEU/nXaiZ7eFqfQrz1TSbLsse/u3AjB7mnwYckT5mAzf3vSwzM8tblnvaPiGprYcmZwN3pDcuXy7pIEmjI+K1nGo0s0Gg7eqf1L1s53fOyLGS4srjS9sxwLqS513pa7sFvqTZJJ8CGHrgqD5tAFYsna3NrsCayVmRjzy+tFWF16JSw4hYGBHtEdE+dD+fdWFm1p/yCPwuYFzJ87HA+hz6NTOzHOUR+EuAC5WYDmzy8Xszsz1PltMy7wZOBEZK6gK+DbQARMQCYCnJKZlrSU7LvLhRxZqZWf2ynKVzfo35AXw5t4rMzKwh/EtbM7OCcOCbmRWEA9/MrCAc+GZmBeHANzMrCAe+mVlBOPDNzArCd7yyPUJn6581uwSzQc+Bb2b9otZ/6m1b7uqnSorLh3TMzArCgW9mVhAOfDOzgnDgm5kVhAPfzKwgHPhmZgXh0zKtX/g8e7Pmy7SHL2mGpBclrZV0dYX5syR1S1qVPi7Nv1QzM+uLLLc4HArcBJxKcsPyX0paEhGry5oujojLG1CjmZnlIMse/tHA2oh4OSJ+B/wQOLuxZZmZWd6yBP4YYF3J8670tXJ/Iuk5SfdKGlepI0mzJXVI6ti+eVMd5ZqZWb2yBL4qvBZlzx8A2iLij4CHgUWVOoqIhRHRHhHtQ/cb3rtKzcysT7IEfhdQusc+Flhf2iAiNkbE1vTpD4CP51OemZnlJUvg/xI4QtJ4SXsDM4ElpQ0kjS55ehawJr8SzcwsDzXP0omIbZIuBx4ChgK3RsQLkuYCHRGxBPiKpLOAbcAbwKwG1mxmZnXI9MOriFgKLC17bU7J9DXANfmWZgONf1xltmfzpRXMzArCgW9mVhAOfDOzgnDgm5kVhAPfzKwgHPhmZgXhwDczKwgHvplZQfiOV2a2R+jLD/fattyVYyWDl/fwzcwKwoFvZlYQDnwzs4LwMXz7D3o6jurjpGYDmwPfMvPVMM0GNge+mQ1qtXZUivTJ1YFvZgOeP31m4y9tzcwKIlPgS5oh6UVJayVdXWH+PpIWp/NXSGrLu1AzM+ubmod0JA0FbgJOBbqAX0paEhGrS5pdArwZEYdLmglcD5zXiIKtNn+8NcuuSGemZTmGfzSwNiJeBpD0Q+BsoDTwzwauTafvBW6UpIiIHGstlCJthGbWP7IE/hhgXcnzLuCT1dpExDZJm4ARwIbSRpJmA7PTp1tfuf7M5+spehAaSflY9dj8zB7n9rzsHm+3sSgwj8UuTRqLnv/WmuTIehfMEviV8qN8zz1LGyJiIbAQQFJHRLRneP9Bz2Oxi8diF4/FLh6LXSR11Ltsli9tu4BxJc/HAuurtZG0FzAceKPeoszMLH9ZAv+XwBGSxkvaG5gJLClrswS4KJ0+B3jUx+/NzPYsNQ/ppMfkLwceAoYCt0bEC5LmAh0RsQS4BbhT0lqSPfuZGd57YR/qHmw8Frt4LHbxWOzisdil7rGQd8TNzIrBv7Q1MysIB76ZWUE0PPB9WYZdMozF1yStlvScpEckHdaMOvtDrbEoaXeOpJA0aE/JyzIWkv403TZekDRof3mX4W/kUEmPSXom/Ts5vRl1NpqkWyW9Lqnib5WUuCEdp+ckTcvUcUQ07EHyJe9vgA8DewPPAh8ta/MlYEE6PRNY3MiamvXIOBYnAful018s8lik7YYBTwDLgfZm193E7eII4Bng4PT5Hza77iaOxULgi+n0R4HOZtfdoLE4HpgGPF9l/unAgyS/gZoOrMjSb6P38HdeliEifgfsuCxDqbOBRen0vcDJkgb4j0UrqjkWEfFYRGxOny4n+c3DYJRluwD478DfAFv6s7h+lmUs/gtwU0S8CRARr/dzjf0ly1gEcGA6PZzdfxM0KETEE/T8W6azgTsisRw4SNLoWv02OvArXZZhTLU2EbEN2HFZhsEmy1iUuoTkf/DBqOZYSJoKjIuIH/dnYU2QZbuYAEyQ9JSk5ZJm9Ft1/SvLWFwLXCCpC1gK/Nf+KW2P09s8ARp/A5TcLsswCGReT0kXAO3ACQ2tqHl6HAtJQ4C/B2b1V0FNlGW72IvksM6JJJ/6lkmaFBFvNbi2/pZlLM4Hbo+Iv5N0DMnvfyZFxAeNL2+PUlduNnoP35dl2CXLWCDpFOAvgbMiYms/1dbfao3FMGAS8LikTpJjlEsG6Re3Wf9G/iUifh8R/xd4keQ/gMEmy1hcAvwIICL+DWglubBa0WTKk3KNDnxflmGXmmORHsb4nyRhP1iP00KNsYiITRExMiLaIqKN5PuMsyKi7otG7cGy/I3cT/KFPpJGkhzieblfq+wfWcbit8DJAJImkgR+d79WuWdYAlyYnq0zHdgUEa/VWqihh3SicZdlGHAyjsXfAgcA96TfW/82Is5qWtENknEsCiHjWDwEfEbSamA78I2I2Ni8qhsj41h8HfiBpL8gOYQxazDuIEq6m+QQ3sj0+4pvAy0AEbGA5PuL04G1wGbg4kz9DsKxMjOzCvxLWzOzgnDgm5kVhAPfzKwgHPhmZgXhwDczKwgHvplZQTjwzcwK4v8D7H/7Q1hQCI0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "flat_prior = np.random.uniform(size=1000000)\n",
    "plt.hist(flat_prior,bins=10,density=True, label='Prior')\n",
    "plt.hist(t_flat, bins=30,density=True, label='Posterior')\n",
    "plt.title('Distribution of $x$ with no assumptions')\n",
    "plt.legend()\n",
    "plt.xlim(0,1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cut_prior = np.random.uniform(low=0,high=0.5,size=1000000)\n",
    "plt.hist(cut_prior,bins=10,density=True, label='Prior')\n",
    "plt.hist(t_cut, bins=15,density=True, label='Posterior')\n",
    "plt.title('Distribution of $x$ assuming TPP <50%')\n",
    "plt.legend()\n",
    "plt.xlim(0,1);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}