1{
2 "cells": [
3  {
4   "cell_type": "markdown",
5   "id": "8ae70f4b",
6   "metadata": {},
7   "source": [
8    "<a href=\"http://agrum.org\" target=\"blank\"><img src=\"http://agrum.gitlab.io/theme/img/logoAgrum.png\" align=\"left\" style=\"height:100px\"/></a><a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc/4.0/88x31.png\" /></a><br />This pyAgrum's notebook is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc/4.0/\">Creative Commons Attribution-NonCommercial 4.0 International License</a>."
9   ]
10  },
11  {
12   "cell_type": "code",
13   "execution_count": 1,
14   "id": "c8572d57-0c0b-4869-b39b-07ae4ef58325",
15   "metadata": {
16    "tags": []
17   },
18   "outputs": [],
19   "source": [
20    "import matplotlib.pyplot as plt\n",
21    "import random\n",
22    "\n",
23    "import pandas as pd\n",
24    "import numpy as np\n",
25    "\n",
26    "import pyAgrum as gum\n",
27    "import pyAgrum.lib.notebook as gnb\n",
28    "\n",
29    "import pyAgrum.causal as csl\n",
30    "import pyAgrum.causal.notebook as cslnb"
31   ]
32  },
33  {
34   "cell_type": "markdown",
35   "id": "089f762f",
36   "metadata": {},
37   "source": [
38    "### Building the models\n"
39   ]
40  },
41  {
42   "cell_type": "code",
43   "execution_count": 2,
44   "id": "019ae906-b2bf-4b42-83dd-3b1b682695e8",
45   "metadata": {
46    "tags": []
47   },
48   "outputs": [],
49   "source": [
50    "# building a model including a Simpson's paradox\n",
51    "def fillWithUniform(p,fmin=None,fmax=None):\n",
52    "  if fmin is None:\n",
53    "    vmin=0    \n",
54    "  if fmax is None:\n",
55    "    vmax=p.variable(0).domainSize()-1\n",
56    "    \n",
57    "  mi=int(p.variable(0).numerical(0))\n",
58    "  ma=int(p.variable(0).numerical(p.variable(0).domainSize()-1))\n",
59    "  \n",
60    "  p.fillWith(0)\n",
61    "  \n",
62    "  I=gum.Instantiation(p)\n",
63    "\n",
64    "  I.setFirst()\n",
65    "  while not I.end():\n",
66    "    vars={p.variable(i).name():p.variable(i).numerical(I.val(i)) for i in range(1,p.nbrDim())}\n",
67    "    if fmin is not None:\n",
68    "      vmin=int(eval(fmin,None,vars))\n",
69    "    if fmax is not None:\n",
70    "      vmax=int(eval(fmax,None,vars))\n",
71    "    if vmin<mi:\n",
72    "      vmin=mi\n",
73    "    if vmin>ma:\n",
74    "      vmin=ma\n",
75    "    if vmax<mi:\n",
76    "      vmax=mi\n",
77    "    if vmax>ma:\n",
78    "      vmax=ma\n",
79    "    \n",
80    "    for pos in range(vmin,vmax+1):\n",
81    "      I.chgVal(0,pos)\n",
82    "      p.set(I,1)\n",
83    "    I.incNotVar(p.variable(0))\n",
84    "  p.normalizeAsCPT()\n",
85    "  \n",
86    "size=70\n",
87    "sizeZ=5\n",
88    "bn=gum.fastBN(f\"A[0,{size-1}]->B[0,{size-1}]<-C[0,{sizeZ-1}]->A\")\n",
89    "\n",
90    "bn.cpt(\"C\").fillWith(1).normalize()\n",
91    "fillWithUniform(bn.cpt(\"A\"),fmin=\"C*12\",fmax=\"C*12+30\")\n",
92    "bn.cpt(\"B\").fillWithFunction(\"5+C*4-int(A/8)\",[0.05,0.2,0.5,0.2,0.05]);"
93   ]
94  },
95  {
96   "cell_type": "code",
97   "execution_count": 3,
98   "id": "9b8e4727-adf1-4ae2-9099-78e7cae231c7",
99   "metadata": {
100    "tags": []
101   },
102   "outputs": [],
103   "source": [
104    "#  generating a CSV, taking this model as the causal one.\n",
105    "gum.generateCSV(bn,\"out/sample.csv\",400)\n",
106    "df=pd.read_csv(\"out/sample.csv\")\n",
107    "\n",
108    "cm=csl.CausalModel(bn)\n",
109    "_,p,_=csl.causalImpact(cm,on=\"B\",doing=\"A\")"
110   ]
111  },
112  {
113   "cell_type": "code",
114   "execution_count": 4,
115   "id": "f38fd1c1-cdbf-4105-9664-671c5cd9b23f",
116   "metadata": {
117    "tags": []
118   },
119   "outputs": [],
120   "source": [
121    "# building an Markov-equivalent model, generating a CSV, taking this model as the causal one.\n",
122    "bn2=gum.BayesNet(bn)\n",
123    "bn2.reverseArc(\"C\",\"A\")\n",
124    "\n",
125    "gum.generateCSV(bn2,\"out/sample2.csv\",400)\n",
126    "df2=pd.read_csv(\"out/sample2.csv\")\n",
127    "\n",
128    "cm2=csl.CausalModel(bn2)\n",
129    "_,p2,_=csl.causalImpact(cm2,on=\"B\",doing=\"A\")"
130   ]
131  },
132  {
133   "cell_type": "markdown",
134   "id": "0a88599d-6b73-4636-978e-0ba8283f3d35",
135   "metadata": {
136    "tags": []
137   },
138   "source": [
139    "### The observationnal model and its paradoxal structure (exactly the same with the second Markov-equivalent model)"
140   ]
141  },
142  {
143   "cell_type": "code",
144   "execution_count": 5,
145   "id": "a2c601f0-eb37-432f-9ed3-1c9057168127",
146   "metadata": {
147    "tags": []
148   },
149   "outputs": [
150    {
151     "data": {
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222       "</svg><br><center><small><em>the observationnal model</em></small></center></div><div class=\"floating-box\"><img 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iyVLluCFF17AxYsX0bNnTwCXPsjx5JNPmo7FKCm6Uhlz94zZeKp5hcZx7MphdHOeYjKJjq9xWaK5hyI6RUm5qoFZiQ2MiCh+OjUw1z9CJCIiEmEDIyIiLbGBERGRltjAiIhIS2xgRESkJTYw0pIx8FUUAOumUFiVWpJZv0qgrsoxlwmflQmxlWEMFlapV/UcyFyfVs11JXNVmC+RDGNg7bxRffFG1bGwANgAELaOk6GwxnplalHZRpUxOPY2bw6qTAJ1RfWZHXNjILAofFYmxHbh2P54Ys6wmPtU9Oy2sGDhPt0z0XihLa56Vc+BzPUpczyvxBDjePF7YKSVhnMtGP/UVjS3Ro9MyspIAxBAS9vlS7trlzRUlE5J+hdjRfWa1aKyjarqurOY9uz2mOsY5xbVZ3bMqw43oPjvlRFjr3lgTPALuDK1dNq8ZGLwy71GWw7U4qerd8fcPivDA8CDljbxMVY9BzLXp8zxdOp6Bfg9MCLbyATWpqd5kO4JX8epUFhRvWa1qGyjSiVQV1Sf2TGPFjIbujyeENtY68YKEO6U7klDelp4rmpovarnQOb6lDmeV2KIsQo2MNKKTGBte0cA7YHwdZwKhRXVa1aLyjaqVAJ1RfWZHfNoIbOhy+MJsY21bqwA4U7tgQ60d4Q/fAqtV/UcyFyfMsfzSgwxVsEGRloRBdYuHNs/7PXy4uFYXjzCFaGwonrNalHZRpVKoK6oPrNjLgoENobPyobYLhzbP+rjQwCYOrQgIli4T/dMQ70jsLw4+jFWPQcy16fM8bwSQ4xV8D0w0pIx8FUUAOumUFiVWpJZv0qgrsoxlwmflQmxlWEMFlapV/UcyFyfVs1lNZ3eA2MDIyKiIJ0aGB8hEhGRltjAiIhIS2xgRESkJdc1sKVLl6KwsBBFRUXBZadPn8aCBQswefJkLFiwAE1NTQ5WSEREbuC6BlZcXIxVq1aFLXvxxRcxbtw4bNu2DePGjcMLL7zgUHWpI9Vy10T7I5O7J7OOWa6dzLFUyfKTYVfGXjKz+5KVEyk618bzYlUmpBX1kjnXZSGOHj0aNTU1YcvKy8vx73//G8ClBnfPPffgkUcecaK8lJBquWui/XmjqsY0d08mmy8i166wL97YfSzqa9GxFOX7mWX5qe63FRl7do2rOpcV24jO9aDc7LDzcmN+djA/Ebj0PbVdCpmQzDlMHtfdgYnU19ejd+/eAIC8vDzU19c7XJG+Gs61oHTtPjS3duBsSxuaWzuwbO0+bf9mKNqf3765L/jLqtOO6oawv3lXHW4wXUc09urKozFfG49ldd3ZsF+SALB659GE78RkzqPKubZrXNW5rNgm2rk2npfQ5tW5TqLHIdX+vLmNFg0slMfjgcfjEf6srKwMPp8PPp+PTS6KVMtdE2fPib/aGJq7J5PNJ5NrZ2Q8ltEy++LJ/ROROY925TBadQ0lKycy2rmOl8pxSLU/b26jRQPLy8vDyZMnAQAnT55Ebq44V62kpAR+vx9+vx95eXnJLFEbqZa7Js6eE/8FJzR3TyabTybXzsh4LKNl9sWT+ycicx7tymG06hpKVk5ktHMdL5XjkGp/3txGiwY2bdo0rFmzBgCwZs0aTJ8+3eGK9JVquWui/Vkxd7hp7p5MNp9Mrp1Zzl20fD/ZOKR49tuKjD27xlWdy4ptop1r43kx5ieqZEIy5zC5XBcltXjxYlRWVqKxsRG5ublYsmQJioqK8OCDD+L48eO4/vrr8fzzz6Nnz54xx2GUVGxuyV2zimh/ZHL3ZNYxy7WTOZYqWX4y7MrYS2Z2X7JyIkXn2nherMqEtKJep+gUJeW6BmYVNjAiovjp1MC0eIRIRERkxAZGRERaYgMjIiItsYEREZGW2MCuAMnKmnNyXFHWoF1ZfTK5hip5icZ1RNl9xmWica3IbpShku+omgnp5ixBmXMgs51deZmpzHVZiGStZGXN2VWLDFHWYOGAXrZk9Y0acG1YLJEo19AsP1EmL69/r27BaKPO7L4AEJbnNyQ/G1+fuhA2bgAIn3tUX7xRFV92owyVfEfVTEg3ZwmKajOeA5nz/YMB12KHyXVFkZLyMfpTp07h2muvjRoBZQd+jP7S3/DGP7UVza2XkwC6dklDRemUmN9XiXcbu2qRUV13FtOe3R6xPCsjDS1tic0lqllk85KJwe92yWxjrEV2HjNZGR4AnrD9NqNyXKId89DjYMU2gH3XjRVEtWVlpAEIoKXt8q9V1fNtdmzsckV/jH7Pnj2YP38+HnjgAezfvx9FRUUoKirCqFGjsG3bNqunoxiSlTVnVy0yomUKGv+qZFVWn1kNMtvI5OWpSPekIT0tvr8kqhwXlXxH1UxIN2cJimpLT/Mg3RN/PqJIonmZVwLLHyH+/ve/x9KlS3H27FmUlJRg5cqVuPXWW1FdXY1f/OIXmDx5stVTUhTJypqzqxYZ0TIFjY8VrMrqM6tBZhuZvDwV7YEOIBBfA1M5Lir5jqqZkG7OEhTV1t4RgPHqUz3fieZlXgksvwNra2vDxIkTcfvttyMvLw+33norAMDr9Vo9FZlIVtacXbXIiJY1uLzYnqw+Y6aeMddQJj9RJi9PlMtnnHtIfnbYNsuLR0Tsd7zZjTJU8h1VMyHdnCUoqm158XAsLx4R9/k2u65IzPL3wG6//Xa88847Ef8vem0nvgd2WbKy5pwcV5Q1aFdWn0yuoUpeonEdUXafcZloXCuyG2Wo5DuqZkK6OUtQ5hzIbGdXXma8dHoPzPIG9r3vfQ9XXXUVAoEAmpub0a3bpVvnQCCAlpYWVFdXWzldVGxgRETx06mBWf4e2KFDh6wekoiIKAK/yExERFpiAyMiIi2xgRERkZa0iZJ6+eWX8frrr8Pj8WDIkCFYvnw5unbt6nRZRETkEC3uwGpra7Fy5Ur4/X5s2rQJHR0d2nxKxg1kQmGNQaKq4alWhNhaNa5KvU5KZtCx2dyiWrYcqEXpmr3YcqA26rhmc6VCSLRd3HQt6kKbO7D29nY0NzcjIyMDFy5cQH5+vtMlaWHBy5VhAbCiUNg+3TNx4szF4Da3eXNQ9XVj3OGpVoTYyqxjVSCtm0Jikxl0rBI+/Lf3DwbDhV+vOoYeXdPR1NweNi4CiDlXKoRE2xWw66ZrUSdJCfO1wiuvvIIVK1aga9eumDBhAp577rmY6/N7YJfusor/XpnwODLhqVaF2KoEn1oV1OtUSGyyg47jDR/ukuZBa4far4nOuVIlJNqOgF03XYuAXt8D0+IRYlNTE8rLy7Fjxw58/PHH+Pbbb/HWW29FrFdWVgafzwefz4f6+noHKnWX7Qe/sWQcmfBUq0JsVYJPrQrqdSokNtlBx/GGDwcikiXjryFVQqLtCNh107WoGy0a2Icffoh+/fohJycHXbp0wcyZM7F79+6I9UpKSuD3++H3+5GXl+dApe4ycXCuJePIhKdaFWKrEnxqVVCvUyGxyQ46jjd82BOR7R9/DakSEm1HwK6brkXdaNHArrvuOnz66ae4cOECAoEAKioqGA4sYdSgyABYUShsn+6ZEevEG55qVYitzDpWBNK6KSQ22UHH8YYPPz1vRES4cI+u6RHjxporVUKi7cgodNO1qBtt3gN75plnsH79emRkZOD73/8+/vSnPyErK/oJ5ntgl8mEwhqDRFXDU60IsbVqXJV6nZTMoGOzuUW1bDlQi00H6lA0NB9ThxYIxzWbKxVCou3ilmtRp/fAtGlg8WIDIyKKn04NTItHiEREREZsYEREpCU2MCIi0hIbGBERaYkNzEHJyj4T5bmpZAvK5CWajSOqRZTVaGQ2rjGnT1Yq5s+ZnVur8illyGQJypx/s3FkxtBNKl6bVtMmCzHVJCv7TJTnVjigV9zZgsZxJnhzsMuQlxgAYu6TqJZD9ecjshpfvW9M2Nxmx6ro2W1hOX1D8rPx3pLJpscmFfPnzHIN543qizeqEs+nlCGTJSjK6jSef7NxZMbQTSpem3bgx+gdkKzss2h5bpnpwMV2wQZRaok2TqisjDQAAbS0Xb6cQseRGaPTmgfGBL+vZnasthyoxU9XR6ay/GNhIaYOLYg6h9vy56wgk2topJJPKUMmSzBaVmfo+TcbR2YM3Th9bfJj9BRTsrLPouW2eUxOu7EWmfy39DQP0j3R9ymeDLnQDEezY7XpQJ1wjGjLZcfVkUyuoZFKPqUMmSzBaFmdocvNxpEZQzepeG3ahQ3MAcnKPouW2xZAfNmCMvlv7R0BtAei71M8GXKhGY5mx6poqPif1Ym2XHZcHcnkGhqp5FPKkMkSjJbVGbrcbByZMXSTitemXdjAHJCs7LNoeW4r5o6MK1tQNI4xL3F58XAsLx4RdZxotYiyGkMf/Zgdq6lDCyJy+obkZ8d8fCgzro5kcg2tyKeUIZMlGC2rM/T8m40jM4ZuUvHatAvfA3NQsrLPRHluKtmCMnmJZuOIahFlNRqZjWvM6ZPllvw5K5mdW6vyKWXIZAnKnH+zcWTG0I1T16ZO74GxgRERUZBODYyPEImISEtsYEREpCU2MCIi0pI2DaypqQmLFi3ClClTMHXqVOzeHfnlVSIiunJo08Aef/xxTJo0CVu3bsXGjRvh9Xptmceu/DHVcVW2U8m+czuzfZLJe5QZVya7T6VelfpEP7ci808lw1J1bON+yxxflezOVLjGKX5aZCGeOXMGn3zyCZ5++mkAQGZmJjIzMy2fx678MdVxVbYzy8LTMVMtYp8MeX6jBlwbzMIDxHmPMpl/onGM2X0q9arUJzr3b1TVJJz5JxrXLMPSqv0ekp+NL7/LrOw8DsbjK5XdaTj/qXCNkxotPkb/n//8B7/73e/g9XrxxRdfYNiwYfj973+Pq666Kuo28X6M3q78MdVxVbaTycLTLe9PJd8PiMx7lMn8EwnN7rOy3qyMNLS0ic+taIzM9DRcbI8cM57MP9G4WRkeAJ6otchSPU+hxzd6dqcHF9vlf03pdo27DT9Gb7H29nbs378fCxYswIYNG9CtWze8+OKLEeuVlZXB5/PB5/Ohvr4+rjnsyh9THVdlO5ksPN0y1VTy/YDIvEeZzD+ReDIc4xnXY3gdWp94DPEv8Hgy/0TjpnvSkJ4WXo3KNaJ6nkKPb9TsTo/xaMWm2zVO6rRoYAUFBSgoKMAtt9wCAJg9ezb2798fsV5JSQn8fj/8fj/y8vLimsOu/DHVcVW2k8nC0y1TTSXfD4jMe5TJ/BOJJ8MxnnGN7Si0PvEY4l/i8WT+icZtD3SgvSO8GpVrRPU8hR7fqNmdgfgeEul2jZM6LRpY7969cd111+Grr74CAFRUVGDw4MGWzmFX/pjquCrbyWTh6ZapJrNPxiw8Ud6jTOafaJx4Hh/GM+7y4ujnVjTGirnDE878E427vHhEzFqs3G9jZqXx+EbP7hwR8/zrfo2TOi3eAwMuvQ/28MMPo7W1Ff369cOKFSvQo0ePqOurRknZlT+mOq7KdirZd25ntk8yeY8y48pk96nUq1Kf6OdWZP6pZFiqjm3cb5njq5LdmQrXuFvo9B6YNg0sXsxCJCKKn04NTItHiEREREZsYEREpCU2MCIi0hIbGBERaYkNjIiItMQGZmBVKKgxkHTLgVqUrtmLLQdqo86lGkhrRiXU1q7jYBWVfRIF4dp1fI37LbOOSlCvynEgShVahPkmi1VhvsZA0h5d09HUfCmY7/WqYxiSn43/88PBCQe+WrVPZmG5Vh0H1XBcK/apf69u+O93QbKdQbjFo/rZcnyrjpwK2+8J3hzs+rox5joF3TNRe+ZiWH1mQb0qx4FBt5RK+D2w71gV5hstkNQowwO0mRx5s0BaMzL7ZFcAcLTjEG84rpFV+wQAXdKA0FWsOL7GcyYisw4QO6hX9Tgw6JbM8HtgGrIqzFc2/FXmbw1mgbRmZPbJrgDgaMch3nBcI6v26ZLEQmxF8xjPmXhWuT92sYJ6VY8Dg24plbCBfceqMF/Z8FeZfG2zQFozMvtkVwBwtOMQbziukVX7dEliIbaieYznTDyrXOhtrKBe1ePAoFtKJWxg37EqzFcUSNqja3rY6yH52Xhm/kjTwFezQFor9smuAOBowayJPD5MZJ+MQbITvDl4ep71x3fF3JER+z3Bm2O6Tp/umRHbxMo6VD0ODLqlVML3wAysCgU1BpJuOVCLTQfqUDQ0H1OHFgjnUg2ktWKf7ApHtSoc16xemXVEQbh2HV/jfsusoxLUq3IciGLR6T0wNjAiIgrSqYHxESIREWmJDYyIiLTEBkZERFrSqoG1t7dj9uzZuPfee50uhYiIHKZVA/vnP/8Jr9dr6xx25cap5uWZ1WNVFp7KfifzWCWLVdmNKtmSMuvI1Gdcx648SiKnaZOFeOLECWzduhUPPfQQXn75ZVvmsCs3TiYv7zZvDqoMeXkBIGY9VmXhqex3Mo9VsrL7rMpuVMmWlNlvmfqM69yYnx3MgExkn4jcSJs7sCeeeAKPPPIIPB6ZDIv4NZxrQenafWhu7cDZljY0t3Zg2dp9Cd8FiMZdumZf2C8ZAPiwusGwzl4sWxO9Hpl6rVrHyWNlxbgyquvORpyT1TuPxn3XItqH1TuPJnwOZOoTrRPavFT3icittGhgW7ZsQU5ODoYNi/03x7KyMvh8Pvh8PtTX18c1h125cfK5fOHSPWlIT4ue1WdVFp7KfifzWCUru8+q7EaVbEmZ/ZapT7bWRPMoidxCi0eIVVVV2Lx5M95//320tLTg3Llz+NWvfoU///nPYeuVlJSgpKQEwKUvMsfDrtw4+Vy+cO2BDiAQ3sBC67EqC09lv5N5rJKV3WdVdqNKtqTMfsvUJ1tronmURG6hxR1YaWkpKisrUVFRgb/+9a8YN25cRPNKlF25caJxlxcPN83LW148AsuLo9djVRaeyn4n81glK7vPquxGlWxJmf2WqU+0jjED0oo8SiK30C5KaufOnXjppZfwyiuvxFzP6SxEmXFl8vLM6rEqC09lv5N5rJLFquxGlWxJmXVk6jOuY1ceJaUmnaKktGtgspiFSEQUP50amBaPEImIiIzYwIiISEtsYEREpCU2MCIi0hIbmGZUMvZkxpFRdbgBz2z6ElWHG2yvz+jtPTW4b9UuvL2nRnobq+ZmliCRO2nxRWa6RCVjT2Ycme0WvFyJD6svNa6/bK3GBG8OXr1vTOz6Cvvijd3x12c05sly1J65CADY/MVJPPXu/8XO3023fB9FrMpHJCLr8Q5MEyoZe7LjmG1Xdbgh2Lw67ahuCLsTE9ZXGX99Rm/vqQk2r04nzlyMeSdmVaaiVfmIRGQPNjBNqGTsyY5jtt32g9+YLreqPqP1n9fGtTxaLSpzW5WPSET2YAPThErGnuw4ZttNHJxrutyq+ozuGFYQ1/JotajMbVU+IhHZgw1MEyoZe7LjmG03alAOJnhzwpZN8OZg1KDLy6yqz+iuW/uhT/fMsGV9umfirlv7WbqPIlblIxKRPRglpRmVjD2ZcWRUHW7A9oPfYOLg3LDmZUd9Rm/vqcH6z2txx7CCmM0rVi2qmCVIVxKdoqTYwIiIKEinBsZHiEREpCU2MCIi0hIbGBERaYkNjIiItKRFlNTx48fx61//Gt988w08Hg9+/OMf495773W6LCIicpAWd2AZGRl49NFHsXnzZrz11lt49dVXcfDgQafLSgqzQFqrAmtlxpWZy4p6ZMYwBuyKAndVxhFtwzBfInfS4g6sd+/e6N27NwDg6quvxg033IDa2loMHjzY4crsZRZIa1Vgrcy8AcB0LivqkRnDGLA7JD8bX9adD75eOLY/Cgf0inucCd4c7Pq6MWybqiOnGOZL5FLafQ+spqYG8+fPx3vvvYdrron+pVLdvwfWcK4F45/aiubWy5FIXbukoaJ0SvALwrF+buW8WRlpAAJoabt8qRjnsqIemTGq685i2rPbTcfKTAcutl9+rTKOcYxOm5dM5BeaKWXxe2A2OX/+PBYtWoTHHntM2LzKysrg8/ng8/lQX1/vQIXWMQuktSqwVmbe9DQP0j2x57KiHpkxZIN0PUh8HOMY8dZARPbS4hEiALS2tuLnP/857rrrLsycOVO4TklJCUpKSgBcugPTmVkgrVWBtTLztncEAITfqBvnsqIemTFkg3QDSHwc4xjx1kBE9tLiDiwQCKC0tBRerxf33Xef0+UkhVkgrVWBtTLzLi8ejuXFI2LOZUU9MmOIAnaH5GeHvV44tj9WzB0Z9zgTvDlh26yYO5JhvkQupsV7YLt27cLcuXNx0003wePxAACWLVuGH/7wh1G30f09sE5mgbRWBdbKjCszlxX1yIxhDNgVBe6qjCPahmG+dCXR6T0wLRqYilRpYEREyaRTA9PiESIREZERGxgREWmJDYyIiLTEBkZERFpiAyMtqWQu2pUbSUTO0OaLzESdVDIX7cqNJCLn8A6MtNJwrgWla/ehubUDZ1va0NzagWVr95km5Me7DRG5HxsYaUUlc9Gu3EgichYbGGlFJXPRrtxIInIWGxhpRSVz0a7cSCJyFj/EQdq5c+T1GO/NjStzUWUbInI3NjDSUs7VWXE3IZVtiMi9+AiRiIi0xAZGRERaYgMjIiItsYEREZGW2MCIiEhLKfspxEOHDmH48OFK2546dQq9evWyuCL7sF776VYz67VXKtd77Ngxm6uxjufIkSMBp4twG5/Pp80/qQ2w3mTQrWbWay/W6w58hEhERFpiAyMiIi2xgQn8+Mc/drqEuLBe++lWM+u1F+t1B74HRkREWuIdGBERaYkNzGDbtm2YMmUKJk2ahBdeeMHpciIsXboUhYWFKCoqCi47ffo0FixYgMmTJ2PBggVoampysMJwx48fxz333INp06Zh+vTpeOWVVwC4t+bm5mbMmTMHM2fOxPTp0/HMM88AAGpqajBnzhxMmjQJDz74IC5evOhwpeHa29sxe/Zs3HvvvQDcXe/48eMxY8YMzJo1Cz6fD4B7rwcAaGpqwqJFizBlyhRMnToVu3fvdm29X331FWbNmhX87+abb8Y//vEP19abKDawEO3t7XjsscewcuVKlJeXY926dTh48KDTZYUpLi7GqlWrwpa9+OKLGDduHLZt24Zx48a5qvFmZGTg0UcfxebNm/HWW2/h1VdfxcGDB11bc1ZWFsrKyvDuu+9iw4YN+OCDD7Bnzx786U9/wk9/+lN88MEH6NGjB15//XWnSw3zz3/+E16vN/ja7fW+9tpr2LhxY/Cj3W69HgDg8ccfx6RJk7B161Zs3LgRXq/XtfXecMMN2LhxIzZu3Ij169eja9eumDFjhmvrTRQbWIjPPvsMAwYMQP/+/ZGZmQmfz4dNmzY5XVaY0aNHo0ePHmHLysvLUVxcDOBSgysvL3eiNKHevXvj5ptvBgBcffXVuOGGG1BbW+vamj0eD7KzswEAbW1taGtrg8fjwUcffYTZs2cDAO6++25XXRcnTpzA1q1bcc899wAAAoGAq+sVcev1cObMGXzyySeYP38+ACAzMxM9evRwbb2hKioqMGDAAPTt21eLelWwgYWoq6vDddddF3zdp08f1NXVOViRnPr6evTu3RsAkJeXh/r6eocrEqupqcGBAwcwcuRIV9fc3t6OWbNmobCwELfddhsGDBiA7t27IyPjUnCN266LJ554Ao888gg8Hg8AoLGx0dX1ejwe/OQnP8Edd9yBsrIyAO69hmtqapCTk4Pf/va3mD17NkpLS/Htt9+6tt5Qfr8fd955JwD3Ht9EsYGlGI/HE/xF5ibnz5/HokWL8Nhjj+Gaa64J+5nbak5PT8fGjRuxc+dO7N27F1999ZXTJUW1ZcsW5OTkYNiwYU6XIm3NmjV45513sHLlSqxevRoff/xx2M/ddD20t7dj//79WLBgATZs2IBu3brhxRdfDFvHTfV2unjxIjZv3hy8Cw/lxnpVsYGFyM/Px/Hjx4OvT5w4gfz8fAcrkpOXl4eTJ08CAE6ePInc3FyHKwrX2tqKn//857jrrrswc+ZMAO6vGQB69OiBsWPHYs+ePThz5gza2toAuOu6qKqqwubNmzF+/HgsXrwYH330ER5//HHX1gsABQUFAIDc3FzMmDEDe/fude31UFBQgIKCAtxyyy0AgNmzZ2P//v2urbfTtm3bcPPNNyMvLw+AHn/eVLCBhRgxYgSOHDmCmpoaXLx4EX6/H9OnT3e6LFPTpk3DmjVrAFz6262bag4EAigtLYXX68V9990XXO7WmhsaGoKf0GpubsaHH34Ir9eLsWPHYsOGDQCAtWvXhn0K1EmlpaWorKxERUUF/vrXv2LcuHF47rnnXFvvt99+i3PnzgX/f8eOHbjxxhtdez307t0b1113XfAuvKKiAoMHD3ZtvZ3WrVsX/IQn4N4/b4niF5kN3n//fTzxxBNob2/HvHnz8NBDDzldUpjFixejsrISjY2NyM3NxZIlS1BUVIQHH3wQx48fx/XXX4/nn38ePXv2dLpUAMCuXbswd+5c3HTTTcHHFsuWLcPIkSNdWfMXX3yB3/zmN+jo6EBHRwduv/12/PKXv8TRo0exePFinD59Gt///vfx7LPPIisry+lyw+zcuRMvvfQSXnnlFdfWe/ToUfzsZz8DcOnx3Jw5c/DQQw+hsbHRldcDAPznP//Bww8/jNbWVvTr1w8rVqxAR0eHa+v99ttvMW7cOGzfvh3du3cHAFcf30SwgRERkZb4CJGIiLTEBkZERFpiAyMiIi2xgRERkZbYwIiISEtsYERJ9N5772HgwIGorq52uhQi7bGBESXRunXr8IMf/ADr1q1zuhQi7bGBESXJ+fPnUVVVhaeeegrr1693uhwi7bGBESVJeXk5Jk2ahO9973vo2bMnPv/8c6dLItIaGxhRkoTm0/l8Pj5GJEoQo6SIkuD06dMYM2YMcnJyAAAdHR3weDyoqKhImX/agijZeAdGlAQbNmzAj370I1RUVKCiogI7d+5E37598cknnzhdGpG22MCIkmDdunWYMWNG2LJZs2bxMSJRAvgIkYiItMQ7MCIi0hIbGBERaYkNjIiItMQGRkREWmIDIyIiLbGBERGRlv4/v4N1Ar0Mna4AAAAASUVORK5CYII=\n",
223       "\"><br><center><small><em>the trend is increasing</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
224       "\"><br><center><small><em>the trend is decreasing for any value for C !</em></small></center></div>"
225      ],
226      "text/plain": [
227       "<IPython.core.display.HTML object>"
228      ]
229     },
230     "metadata": {},
231     "output_type": "display_data"
232    },
233    {
234     "data": {
235      "text/html": [
236       "\n",
237       "      <style>\n",
238       "      .floating-box {\n",
239       "      display: inline-block;\n",
240       "      margin: 7px;\n",
241       "      padding : 3px;\n",
242       "      border: 2px solid #FFFFFF;  \n",
243       "      valign:middle;\n",
244       "      background-color: #FDFDFD;\n",
245       "      }\n",
246       "      </style>\n",
247       "      <div class=\"floating-box\"><svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"89pt\" height=\"188pt\" viewBox=\"0.00 0.00 89.00 188.00\">\n",
248       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 184)\">\n",
249       "<title>G</title>\n",
250       "<!-- C -->\n",
251       "<g id=\"node1\" class=\"node\">\n",
252       "<title>C</title>\n",
253       "<g id=\"a_node1\"><a xlink:title=\"(2) C\">\n",
254       "<ellipse fill=\"#404040\" stroke=\"black\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
255       "<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"white\">C</text>\n",
256       "</a>\n",
257       "</g>\n",
258       "</g>\n",
259       "<!-- B -->\n",
260       "<g id=\"node2\" class=\"node\">\n",
261       "<title>B</title>\n",
262       "<g id=\"a_node2\"><a xlink:title=\"(1) B\">\n",
263       "<ellipse fill=\"#404040\" stroke=\"black\" cx=\"54\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
264       "<text text-anchor=\"middle\" x=\"54\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"white\">B</text>\n",
265       "</a>\n",
266       "</g>\n",
267       "</g>\n",
268       "<!-- C&#45;&gt;B -->\n",
269       "<g id=\"edge3\" class=\"edge\">\n",
270       "<title>C-&gt;B</title>\n",
271       "<g id=\"a_edge3\"><a xlink:title=\"(2, 1) : \">\n",
272       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M33.4,-72.41C36.51,-64.34 40.33,-54.43 43.83,-45.35\"/>\n",
273       "<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"47.13,-46.55 47.46,-35.96 40.6,-44.03 47.13,-46.55\"/>\n",
274       "</a>\n",
275       "</g>\n",
276       "</g>\n",
277       "<!-- A -->\n",
278       "<g id=\"node3\" class=\"node\">\n",
279       "<title>A</title>\n",
280       "<g id=\"a_node3\"><a xlink:title=\"(0) A\">\n",
281       "<ellipse fill=\"#404040\" stroke=\"black\" cx=\"54\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n",
282       "<text text-anchor=\"middle\" x=\"54\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"white\">A</text>\n",
283       "</a>\n",
284       "</g>\n",
285       "</g>\n",
286       "<!-- A&#45;&gt;C -->\n",
287       "<g id=\"edge2\" class=\"edge\">\n",
288       "<title>A-&gt;C</title>\n",
289       "<g id=\"a_edge2\"><a xlink:title=\"(0, 2) : \">\n",
290       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M47.6,-144.41C44.49,-136.34 40.67,-126.43 37.17,-117.35\"/>\n",
291       "<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"40.4,-116.03 33.54,-107.96 33.87,-118.55 40.4,-116.03\"/>\n",
292       "</a>\n",
293       "</g>\n",
294       "</g>\n",
295       "<!-- A&#45;&gt;B -->\n",
296       "<g id=\"edge1\" class=\"edge\">\n",
297       "<title>A-&gt;B</title>\n",
298       "<g id=\"a_edge1\"><a xlink:title=\"(0, 1) : \">\n",
299       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M57.65,-143.91C59.68,-133.57 61.98,-120.09 63,-108 64.34,-92.06 64.34,-87.94 63,-72 62.28,-63.5 60.93,-54.31 59.49,-46.01\"/>\n",
300       "<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"62.91,-45.29 57.65,-36.09 56.03,-46.56 62.91,-45.29\"/>\n",
301       "</a>\n",
302       "</g>\n",
303       "</g>\n",
304       "</g>\n",
305       "</svg><br><center><small><em>the Markov-equivalent model</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
306       "\"><br><center><small><em>the trend is increasing</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
307       "\"><br><center><small><em>the trend is decreasing for any value for C !</em></small></center></div>"
308      ],
309      "text/plain": [
310       "<IPython.core.display.HTML object>"
311      ]
312     },
313     "metadata": {},
314     "output_type": "display_data"
315    }
316   ],
317   "source": [
318    "gnb.flow.row(gnb.getBN(bn),\n",
319    "             df.plot.scatter(x='A', y='B'),\n",
320    "             df.plot.scatter(x='A', y='B', c='C',colormap=\"tab20\"),\n",
321    "             captions=[\"the observationnal model\",\"the trend is increasing\",\"the trend is decreasing for any value for C !\"])\n",
322    "gnb.flow.row(gnb.getBN(bn2),\n",
323    "             df2.plot.scatter(x='A', y='B'),\n",
324    "             df2.plot.scatter(x='A', y='B', c='C',colormap=\"tab20\"),\n",
325    "             captions=[\"the Markov-equivalent model\",\"the trend is increasing\",\"the trend is decreasing for any value for C !\"])"
326   ]
327  },
328  {
329   "cell_type": "markdown",
330   "id": "e1eda35b-4d37-466e-937b-f4ebc2359825",
331   "metadata": {},
332   "source": [
333    "### The paradox is revealed in the trend of the inferred means : the means are increasing with the value of $A$ **except for any value of $C$** ..."
334   ]
335  },
336  {
337   "cell_type": "code",
338   "execution_count": 6,
339   "id": "cb69929e-5978-4a43-a4d5-f38c59ce801d",
340   "metadata": {
341    "tags": []
342   },
343   "outputs": [
344    {
345     "data": {
346      "text/html": [
347       "\n",
348       "      <style>\n",
349       "      .floating-box {\n",
350       "      display: inline-block;\n",
351       "      margin: 7px;\n",
352       "      padding : 3px;\n",
353       "      border: 2px solid #FFFFFF;  \n",
354       "      valign:middle;\n",
355       "      background-color: #FDFDFD;\n",
356       "      }\n",
357       "      </style>\n",
358       "      <div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
359       "\"><br><center><small><em>$P(B|A=10)$</em></small></center></div><div class=\"floating-box\"><img 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\n",
360       "\"><br><center><small><em>$P(B|A=20)$</em></small></center></div><div class=\"floating-box\"><img 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\n",
361       "\"><br><center><small><em>$P(B|A=30)$</em></small></center></div><br/><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
362       "\"><br><center><small><em>P(B | $A=10,C=0)$</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
363       "\"><br><center><small><em>P(B | $A=20,C=0)$</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
364       "\"><br><center><small><em>P(B | $A=30,C=0)$</em></small></center></div><div class=\"floating-box\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
365       "\"><br><center><small><em>P(B | $A=10,C=2$)</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
366       "\"><br><center><small><em>P(B | $A=20,C=2$)</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
367       "\"><br><center><small><em>P(B | $A=30,C=2$)</em></small></center></div><div class=\"floating-box\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
368       "\"><br><center><small><em>P(B | $A=10,C=4$)</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI8AAACsCAYAAABCW/8LAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAVd0lEQVR4nO2de1BU5f/H38ACKhp4A7G+hmgEfjUxNRsqUQcUUkZLa8xSC83xUs2kk44advNrNl6mRjQ1BvUr5jeTzGySZFQ0ASHKK4sg95XrAsvCAns5l98fxP6ABXbPYc+es7vP67895+F83nt47znPec7n+TwupaWlLAgEHriKLYBgvxDzEHhDzEPgDTEPgTfEPATeEPMQeEPMQ+CNTGwB9oZarcbkyZMxaNAgAICbmxtefPFF7N+/HwMHDhRZnW0hVx6O5ObmYujQoZDL5ZDL5bh8+TJycnLw008/iS3N5hDzcEQul+Opp54yfvb19cXo0aNBUZSIqsSB3LY4IpfLERQUBACgKAoXL15EZWUl5s+fL7Iy20PMwxG5XI7S0lKcP38eWq0Wnp6eOHr0KEaMGCG2NJtDblsc0Ol0KCwsxJkzZ3Dv3j08ePAA69atw6ZNm8SWJgrEPBwoKCiAq6srgoODAbQ/ac2YMQN1dXUwGAwiq7M9xDwcyM3NxdNPPw0PDw8AQE1NDeLj4xEREQF3d3eR1dke0ufhQMfj+YQJE+Dm5gYfHx9ER0fjgw8+EFuaKLiQZDACX8hti8AbYh4Cb4h5CLwh5iHwhpiHwBtiHgJv7NY8J06cQExMDIKCgnp8PVBYWIg33ngDkyZNQnh4OFJSUno9VmNjI9asWYOQkBC88MILOH/+PKf9YsFFl0KhwNtvv41nnnkG06ZNw44dO4yZAFzOVWfsdpDQz88P7733Hq5fvw6tVttlH0VRePfdd/Hmm28iKSkJWVlZWLVqFYKCghAYGGhyrLi4OLi7uyMnJwdyuRyxsbEICQkxvj03t18suOiKi4vD8OHDkZ2djaamJixfvhwnT57E8uXLOZ2rzgh+5YmPj8e2bduMn9VqNcaPH2/yD+dKVFQU5s2bh6FDh5rsKyoqQk1NDVatWgU3NzeEhYVh2rRpOHfunEnb1tZWpKSkYNOmTfDy8sL06dMRERFhTO4yt//jjz/Gxx9/3KtOg8GAPXv24IUXXsD48eMREBCAgIAAREVF9ev7m9PVHYVCgQULFmDAgAHw9fVFeHg4CgoKOJ2r7gh+5Xnw4AGef/554+fc3FwEBgZiwIABXdrFxsbizz//7PEY06dPR2JiYr90sCyL/Px8k+3FxcVwc3Pr8isLCQlBVlaWRft37tzZZ9y9e/ciKysLP/74I3x8fPDuu+9i8ODB2L59e5d2XL+/OV3diY2NxYULF/D8889DrVYjLS0NGzdu7LFtb+eqO4KbJz8/H7GxscbPcrkcISEhJu36a47OBAYGYvjw4Thy5AhWrVqFzMxMZGVldTFxB62trRg8eHCXbUOGDIFGo7Fof19oNBocP34cKSkpGD16NID2K+avv/6KMWPGdGnL9ftz1TVjxgycPn0aEydOBE3TWLx4MebNmweKoiw+V90R9Lal1+tRVlbWxSx5eXmYMGGCkGHh7u6Oo0eP4sqVK5g+fTq+++47zJ8/H/7+/iZtBw0aZHLCNRqN8R9jbn9fZGdnY8yYMRg7dqxxW1NTE0aOHMnna3HS3RmGYbBy5UpERUVBLpfj1q1bUKvV2L17N6dz1R1BrzyFhYUYNWqUcVYBy7K4efMmFi5caNJ25cqVfV62T5w4wSl2SEgIzpw5Y/z86quvYvHixSbtAgMDQdM0SkpKjP/kvLw8Y56yuf19UV9fD29vb+NnlmXx+++/45133jFpy/X7c9HV2NiIiooKrFixAp6envD09MRrr72Gffv2YevWrRafq+4Iap4HDx6gvr4eZWVl8PPzQ3x8PCoqKvDEE0+YtOVqDoqiQFEUaJoGwzDQarWQyWSQydq/Ul5eHsaOHQuWZXHy5EnU1tZiyZIlJscZNGgQ5s2bh/379+Orr76CXC5HamoqkpOTLdrfMUywb98+k2M//fTTuH//PnJzczFu3Dh8/fXXcHFxwYIFC/r9/c3p6sywYcPwr3/9C0lJSVizZg1aWlqQnJxsTGqz9Fx1R9DbVn5+PmbOnImlS5ciPDwcXl5e8Pf3R3x8fL+PfeDAAQQHB+Pbb7/FuXPnEBwcjAMHDhj3nzt3Ds899xymTp2K9PR0JCUlwdPTE0D7r/zgwYPGtjt37oRWq8XUqVPxwQcfYOfOnV0ed/vaX1VVhWnTpvWo8ZlnnsF7772Hd955By+99BKUSiWOHTtmtcSxvnR1/46HDx/GtWvX8Oyzz2LWrFlwd3dHXFyc2XPVF4Lm86xcuRJLly5FdHS0UCFERa/XIzo6GikpKSST0Nrk5+dj/PjxQoYQFQ8PD1y+fFlsGaIh2G1LrVajvr4eAQEBQoUgiAxJQyXwxm5fjBLEh5iHwBvR3qpPnjxZ9M50S0sLvLy8nDY+0P6O7NatW7z+VjTz+Pn5IScnR6zwAIC0tDTMmjXLaeMD7WNRfCG3LQJviHkIvCHmIfCGmIcnOkqHqw+uii1DVIh5eKJQKXCn4g6atc1iSxENYh6elNaVAmg3kbNCzMOTkvoSAECRskhkJeJBzMMDjVYDrb599odCpQDLOufrQWIeHihUCri6tp86hmGgalWJrEgciHl4UFxXDAPdXoOQBYvyhnKRFYkDMQ9HWLarWWiGdtp+DzEPRxrbGkEzdJdtVeoqMCwjkiLxIObhSHm96S3KxcUFtc21IqgRF2IejhTVFYFiuq4zQTN0j6ZydIh5OMCyLCobK022MyzjlP0eYh4OKJuVcHFx6XmfRgmKdq6Vb4h5OFDWUGbSWe5A5ipDlbrKxorEhZiHA0XKol6fqgy0AWX1ZTZWJC7EPBZCMzSUzcpe97NgUVxXbENF4kPMYyFV6iq4ubr12aaxrRE6SmcjReJjkXnS0tIwZ84chIeH49ChQ722u3jxIgICAnD37l2rCZQKZfVlxlcSvSFzlaFCVWEjReJj1jw0TWPHjh04fvw4UlNT8csvv+Dhw4cm7TQaDY4dO4bQ0FAhdIpOcV0xWPT99lxP653q1mXWPLdv38aTTz6JMWPGwMPDAzExMbh06ZJJu3379mHt2rUWleawN/SU3uI3587UaTZrnpqaGmM9PQDw9/dHTU1Nlzb3799HVVUV5syZY32FEqCisQIyV8umuLXqW9GiaxFYkTTo96Q/hmHwxRdfYO/evWbbfv/99zh9+jQAQKVSIS0trb/h+4VGo7FIQ7O2GSMMli1A6+Ligj/++AMDZAPMtrU0vlQxax4/Pz9UVv7/kHxVVRX8/PyMnzUaDQoKCrB06VIAgFKpxOrVq5GQkGAyG3HZsmVYtmwZAGDu3Lmiz5a0dMZmYnoimrRNFh83yC8IsyaaP64UZoz2B7O3rcmTJ6O0tBQKhQJ6vR4XLlxAZGSkcf9jjz2GW7duIT09Henp6ZgyZUqPxrFXWvWt0OjMl83tTHlDuVOkppo1j0wmw+eff44VK1YgIiICCxYsQFBQEPbv34/U1FRbaBQVhUphdnynOxRNQd2mFkiRdLCozzN79mzMnj27y7beqof/8MMP/VclIUqUJWbHd3qivKEcPoN8rC9IQpARZjOUNXB/9KYYyinGe4h5+kDdpuZ11QHaH+8dvd9DzNMH/Z0NWqeps5ISaULM0wfFymKTlFNLYVjG4afkEPP0AsuyeKR6xPvvnWFKDjFPL9S31Pe7z1LTXNNr5qEjQMzTC+UN5f2ei+Xm4obqpmorKZIexDy9UKQsAs3276rh6KmpxDw9wDCMVa4Yjp6aSszTA9XN1XB1sc6paWhp4D1WJHWIeXqgvL7cah1dmasMFY2OmZpKzNMDfU2x4YqBNhhL0DkaxDzdMNAG1LfUW+14LFhjCTpHg5inG5WNlRannFpKs7YZbYY2qx5TChDzdKOsvgx6Wm/VY7q5uuFRA//RaqlCzNMNIR6tDbTBIR/ZiXk6oTVoOeUqc4FPXpDUIebpxCPVI6v3dzrQUTqHqxZPzNOJkvoSq/d3OnB1cXW4FA1ink6U1pcKdmxH7PcQ8/xD56ruQuFo1eKJef6hXFVurOouFAzDoKGlQdAYtoSY5x+KlcWCv8B0tGrxxDxoTzm1xdJHNEOjqM5xUlOJeQCoWlU2SxetVleDYRyjWjwxD2DTW4kjVYsn5kH7Kwm+U2y4QjO0w4w2O715GJbpsaq7kPGKlY4x3uP05umrqrtgMR2kWrzTm6e8wXopp5biKNXind481kw5tRQDbRD0VYitcHrz9FXVXSgcZUqOU5vHQBs4V/2yFuo2tdm6zlLHKhXgExISEBERgaioKCxbtgyPHtlHyqWe0os2p0rmKoOeEib9w1ZYpQL8hAkTcOHCBaSkpCA6OhpffvmlYIKtiY7Sifbr19N6xzePJRXgw8LCMHDgQADAlClTUF0t/cn9Okpns4HBvjTYM2ZzLnuqAH/79u1e2585c6bX2sJSKuKto3RwZ9wxunW0+cYC4ca44crVK1ab2mxrrJqwe+7cOdy9e7fXiqhSKeLNsixOZZ+CR5sHKgfZbnS5O6NbR4P1ZzEreJZoGvqDWcubqwDfwY0bNxAfH4+EhATJL15SWl8qmTrJ8iq5YDM2hKbfFeCB9oVLtm3bhoSEBIwYYdkaDWLBsizSCtIkU7mCYRikF6aLLYMXZm9bnSvA0zSN119/3VgBftKkSYiMjMSXX36J1tZWrF+/HgDw+OOPIyEhQXDxfCioKUCrvlVsGUZYsChUFqKhpQHDvIaJLYcTVqkAf+rUKeuqEgiGYXC98LpkrjodMAyDPx7+gYWhC8WWwgn77ObzJLcqV5JjKyza02DtLUnMacxD0RTSi9Ild9XpgGIoXCu4JrYMTjiNee48uiP5HJqaphq7qiLmFObRU3pklWSJPqJsDoqhkJafZjcTA53CPH+X/23znB2+NLY12k2Os8ObR2vQIqcsR/JXnQ4MtMFurj4Ob56skiy7+Ed0pkXXgoe1pmvXSw2HNk+LrgX3Ku71u5K7rTEwBlx/eF3ykwMd2jwZxRl209fpjo7SIa86T2wZfeKw5lG3qfGg+oHdmsdAG3Cj8Iak+2oOa54bhTckf9k3h4E24N6je2LL6BWHNE+9ph7FdcV2n2BOMRQyizMlOyrukOaxh86mpTAsg7/L/xZbRo84nHk6hvjt/arTAcVQyCnLgdYgbMk7PjicedIK0iTdyeQDwzDILs0WW4YJDmUehUohygxQoaFZGncf3UWLrkVsKV1wGPOwLItrBdcc7qrTAcMyyCzOFFtGFxzGPFJKahcChmWQV52HpjbpJMs7hHmkltQuFAzD4EbRDbFlGHEI80gtqV0oWLAoUhZJppaz3ZuHYRhcfyi9pHah6EiWlwJ2b57cqlzBFhuRIlJKlrdr80g9qV0opJIsb9fmsYekdqGoaapBhUrcZHm7NY+9JLULBcVQSCsQN13VLs3DsO3zu+01V8daqFpVkFfJRYsvzJqIAlKnqcNv939DU1uT0151OqAYClfzr+Jh7UNEhkTCy9PLpvHtxjwUTSGjKAN3Ku7YvG6ylKEYCuUN5TieeRwvPfUSJo2eZLOi5HZhHkWDAim5KdBROmKcHmBYBgzN4HrBddyvuI+of0fZpOKGpM2jNWhxJf8KipW2W1jEnqEYCspmJb7P/h5Tx0zFc2OfE7RUsCTNw7IsCmoKcDn/MiiacvqOMRdYsKAYCn+V/4W86jxET4yGv7e/ILEkZ54mbRMu5V5CdVM1udr0A4qh0KRtQvLfyQgeFYyZT82Eh8zDqjGsUsRbp9Nhw4YNCA8Px8KFC6FQcF9ykWEZ/FX2F/6b+V9UqCuIcawExVDIq8pDYkYiipTWXaLSKkW8z5w5A29vb1y7dg2rVq3C7t27OYlQNiuRlJWEzOJMUAxld9ODpQ7N0tAatLh4/yJ+vv2z1TISrVLE+9KlS1i8eDEA4OWXX0ZGRoZFBqBoCtcLruN/Of9DQ0sDudoITOfH+rsVd/v9I7VKEe/ObWQyGYYMGQKVSoVhw3p/XGTB4ljGMbQZ2kiH2IZ0PNZfzb+K+xX3+zWP36Yd5s4V4EtKSvCf1f+xZXgTmtXNGOI9xGnjA0CNoob335o1jyVFvDva+Pv7g6IoNDc3Y+jQoSbH6lwBPiYmBhcuXOAt3BqIrUHs+B0a+GKVIt6RkZFITk4GAPz2228ICwuz+bqdBNtjlSLer7/+OjZu3Ijw8HD4+PjgwIEDttBOEBmrFPEeMGBAj+M/ffHGG29wai8EYmsQO35/NbiUlpaSQRUCL+wyGYwgDWxino8++ghTp07F3Llzu2w/fvw45syZY1z8xJbxc3NzsWjRIkRHRyMmJqbPBeisQWVlJZYuXYqIiAhERkYiMTERANDY2Ii33noLs2bNwltvvQW1WphZr73F37VrF+bMmYOoqCisWbOGU3yb3LaysrLg5eWFjRs3GkenMzIycPDgQSQmJsLT0xN1dXWCLbfUU/zly5cjNjYWs2fPxtWrV3H48OFeF5mzBrW1taitrcXEiROh0WgQExODo0eP4uzZs/D29sb69etx6NAhqNVqbN261Wbxq6qqEBYWBplMZvwBWxrfJleeGTNmwNvbu8u2U6dOYd26dcaF3YRcp6un+ACg0WgAAE1NTT0uQGdNfH19MXHiRADA4MGDMW7cOFRXVyM1NRVLliwBACxZsgSpqak2jT9z5kzIZO3PTVzXhxUtJaO4uBjZ2dnYs2cPPD09sX37dkyePNlm8T/55BOsWLECu3btAsMwxnEqW6BQKCCXyxEaGgqlUglfX18AwMiRI6FUCl8ipnP8zvz4449YsGCBxccRrcNM0zTUajV+/vlnbNu2DRs2bLDp2/SkpCTExcUhMzMTcXFx2LJli03itrS0YN26ddixYweGDOn6asLFxUXwwdXe4sfHx8PNzQ2LFi2y+FiimWfUqFGYN28eXFxcEBoaCldXVzQ02G4Cf3JyMqKiogAA8+fPx507dwSPaTAYsHbtWixatMgYe+TIkaitbZ86XFtbK+jtu6f4QPsV5/Lly/jmm284mVc088ydOxc3b94E0H4LMxgMfb6Ftza+vr7G+BkZGQgICBA0Hsuy2LJlC8aPH4/Vq1cbt0dERODs2bMAgLNnz5q8+hE6flpaGo4cOYKEhAQMHDiQ0zFt8rT1/vvv4+bNm1CpVBgxYgQ+/PBDvPLKK9i8eTPkcjnc3d2xfft2hIWF2Sx+YGAgPvvsM1AUBU9PT+zcuROTJk0SJD4A/Pnnn3jttdcQHBxs/HVv3rwZoaGh2LBhAyorK/H444/j4MGD8PHxsVn8Tz/9FHq93hhzypQp2LVrl0XHJCPMBN6QEWYCb4h5CLwh5iHwhpiHwBtiHgJviHkIvCHmIfCGmIfAm/8DUkTrN7V6uCgAAAAASUVORK5CYII=\n",
369       "\"><br><center><small><em>P(B | $A=20,C=4$)</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
370       "\"><br><center><small><em>P(B | $A=30,C=4$)</em></small></center></div>"
371      ],
372      "text/plain": [
373       "<IPython.core.display.HTML object>"
374      ]
375     },
376     "metadata": {},
377     "output_type": "display_data"
378    }
379   ],
380   "source": [
381    "for v in [10,20,30]:\n",
382    "  gnb.flow.add_html(gnb.getPosterior(bn,target=\"B\",evs={\"A\":v}),f\"$P(B|A={v})$\")\n",
383    "gnb.flow.new_line()\n",
384    "for v in [10,20,30]:\n",
385    "  gnb.flow.add_html(gnb.getPosterior(bn,target=\"B\",evs={\"A\":v,\"C\":0}),f\"P(B | $A={v},C=0)$\")\n",
386    "gnb.flow.add_separator(10)\n",
387    "for v in [10,20,30]:\n",
388    "  gnb.flow.add_html(gnb.getPosterior(bn,target=\"B\",evs={\"A\":v,\"C\":2}),f\"P(B | $A={v},C=2$)\")\n",
389    "gnb.flow.add_separator(10)\n",
390    "for v in [10,20,30]:\n",
391    "  gnb.flow.add_html(gnb.getPosterior(bn,target=\"B\",evs={\"A\":v,\"C\":4}),f\"P(B | $A={v},C=4$)\")\n",
392    "gnb.flow.display()"
393   ]
394  },
395  {
396   "cell_type": "markdown",
397   "id": "43487e02-8e96-4776-8b8a-2ae457c7cf4c",
398   "metadata": {
399    "tags": []
400   },
401   "source": [
402    "### Now that the paradoxal structure is understood and the paradox is revealed, will we choose to observe $C$ (or not) before deciding to increase or decrease $A$ (with the goal to maximize $B$) ?\n",
403    "\n",
404    "Of course, it depends on the causal structure of the problem !"
405   ]
406  },
407  {
408   "cell_type": "code",
409   "execution_count": 7,
410   "id": "c418598d-17b6-4377-8d4a-02486538ae10",
411   "metadata": {
412    "tags": []
413   },
414   "outputs": [
415    {
416     "data": {
417      "text/html": [
418       "\n",
419       "      <style>\n",
420       "      .floating-box {\n",
421       "      display: inline-block;\n",
422       "      margin: 7px;\n",
423       "      padding : 3px;\n",
424       "      border: 2px solid #FFFFFF;  \n",
425       "      valign:middle;\n",
426       "      background-color: #FDFDFD;\n",
427       "      }\n",
428       "      </style>\n",
429       "      <div class=\"floating-box\"><svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"89pt\" height=\"188pt\" viewBox=\"0.00 0.00 89.00 188.00\">\n",
430       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 184)\">\n",
431       "<title>G</title>\n",
432       "<!-- A -->\n",
433       "<g id=\"node1\" class=\"node\">\n",
434       "<title>A</title>\n",
435       "<ellipse fill=\"#404040\" stroke=\"#4a4a4a\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
436       "<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"white\">A</text>\n",
437       "</g>\n",
438       "<!-- B -->\n",
439       "<g id=\"node2\" class=\"node\">\n",
440       "<title>B</title>\n",
441       "<ellipse fill=\"#404040\" stroke=\"#4a4a4a\" cx=\"54\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
442       "<text text-anchor=\"middle\" x=\"54\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"white\">B</text>\n",
443       "</g>\n",
444       "<!-- A&#45;&gt;B -->\n",
445       "<g id=\"edge1\" class=\"edge\">\n",
446       "<title>A-&gt;B</title>\n",
447       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M32.47,-72.05C35.58,-63.98 39.4,-54.07 42.9,-44.99\"/>\n",
448       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M34.33,-72.77C37.45,-64.7 41.27,-54.79 44.77,-45.71\"/>\n",
449       "<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"47.13,-46.55 47.46,-35.96 40.6,-44.03 47.13,-46.55\"/>\n",
450       "</g>\n",
451       "<!-- C -->\n",
452       "<g id=\"node3\" class=\"node\">\n",
453       "<title>C</title>\n",
454       "<ellipse fill=\"#404040\" stroke=\"#4a4a4a\" cx=\"54\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n",
455       "<text text-anchor=\"middle\" x=\"54\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"white\">C</text>\n",
456       "</g>\n",
457       "<!-- C&#45;&gt;A -->\n",
458       "<g id=\"edge2\" class=\"edge\">\n",
459       "<title>C-&gt;A</title>\n",
460       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M46.67,-144.77C43.55,-136.7 39.73,-126.79 36.23,-117.71\"/>\n",
461       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M48.53,-144.05C45.42,-135.98 41.6,-126.07 38.1,-116.99\"/>\n",
462       "<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"40.4,-116.03 33.54,-107.96 33.87,-118.55 40.4,-116.03\"/>\n",
463       "</g>\n",
464       "<!-- C&#45;&gt;B -->\n",
465       "<g id=\"edge3\" class=\"edge\">\n",
466       "<title>C-&gt;B</title>\n",
467       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M56.67,-143.72C58.69,-133.4 61,-119.92 62,-107.92 63.34,-92.06 63.34,-87.94 62,-72.08 61.29,-63.64 59.94,-54.46 58.5,-46.18\"/>\n",
468       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M58.64,-144.1C60.66,-133.74 62.97,-120.26 64,-108.08 65.34,-92.06 65.34,-87.94 64,-71.92 63.27,-63.35 61.92,-54.17 60.47,-45.84\"/>\n",
469       "<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"62.91,-45.29 57.65,-36.09 56.03,-46.56 62.91,-45.29\"/>\n",
470       "</g>\n",
471       "</g>\n",
472       "</svg><br><center><small><em>the first causal model</em></small></center></div><div class=\"floating-box\"><img 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\n",
473       "\"><br><center><small><em>Doing $A=10$</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
474       "\"><br><center><small><em>Doing $A=20$</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
475       "\"><br><center><small><em>Doing $A=30$</em></small></center></div>"
476      ],
477      "text/plain": [
478       "<IPython.core.display.HTML object>"
479      ]
480     },
481     "metadata": {},
482     "output_type": "display_data"
483    }
484   ],
485   "source": [
486    "gnb.flow.add_html(cslnb.getCausalModel(cm),\"the first causal model\")\n",
487    "for v in [10,20,30]:\n",
488    "  gnb.flow.add_html(gnb.getProba(p.extract({'A':v})),f\"Doing $A={v}$\")\n",
489    "gnb.flow.display()"
490   ]
491  },
492  {
493   "cell_type": "markdown",
494   "id": "4dd09a4c-ef6b-4056-becf-3618b723ecc7",
495   "metadata": {},
496   "source": [
497    "### If $C$ is cause for $A$, observing $C$ really gives a new information about $B$."
498   ]
499  },
500  {
501   "cell_type": "code",
502   "execution_count": 8,
503   "id": "bd32a5b4-60a9-42ba-b487-8d5d6897c547",
504   "metadata": {
505    "tags": []
506   },
507   "outputs": [
508    {
509     "data": {
510      "text/html": [
511       "\n",
512       "      <style>\n",
513       "      .floating-box {\n",
514       "      display: inline-block;\n",
515       "      margin: 7px;\n",
516       "      padding : 3px;\n",
517       "      border: 2px solid #FFFFFF;  \n",
518       "      valign:middle;\n",
519       "      background-color: #FDFDFD;\n",
520       "      }\n",
521       "      </style>\n",
522       "      <div class=\"floating-box\"><svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"90pt\" height=\"188pt\" viewBox=\"0.00 0.00 90.00 188.00\">\n",
523       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 184)\">\n",
524       "<title>G</title>\n",
525       "<!-- A -->\n",
526       "<g id=\"node1\" class=\"node\">\n",
527       "<title>A</title>\n",
528       "<ellipse fill=\"#404040\" stroke=\"#4a4a4a\" cx=\"27\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n",
529       "<text text-anchor=\"middle\" x=\"27\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"white\">A</text>\n",
530       "</g>\n",
531       "<!-- B -->\n",
532       "<g id=\"node2\" class=\"node\">\n",
533       "<title>B</title>\n",
534       "<ellipse fill=\"#404040\" stroke=\"#4a4a4a\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
535       "<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"white\">B</text>\n",
536       "</g>\n",
537       "<!-- A&#45;&gt;B -->\n",
538       "<g id=\"edge1\" class=\"edge\">\n",
539       "<title>A-&gt;B</title>\n",
540       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M22.77,-144.06C20.97,-133.69 18.92,-120.21 18,-108.07 16.8,-92.04 16.8,-87.96 18,-71.93 18.65,-63.39 19.85,-54.21 21.13,-45.88\"/>\n",
541       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M24.74,-143.72C22.94,-133.39 20.89,-119.91 20,-107.93 18.8,-92.04 18.8,-87.96 20,-72.07 20.63,-63.65 21.83,-54.47 23.11,-46.19\"/>\n",
542       "<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"25.58,-46.55 23.75,-36.11 18.68,-45.41 25.58,-46.55\"/>\n",
543       "</g>\n",
544       "<!-- C -->\n",
545       "<g id=\"node3\" class=\"node\">\n",
546       "<title>C</title>\n",
547       "<ellipse fill=\"#404040\" stroke=\"#4a4a4a\" cx=\"55\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
548       "<text text-anchor=\"middle\" x=\"55\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"white\">C</text>\n",
549       "</g>\n",
550       "<!-- A&#45;&gt;C -->\n",
551       "<g id=\"edge2\" class=\"edge\">\n",
552       "<title>A-&gt;C</title>\n",
553       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M32.71,-144.04C35.98,-135.85 40.02,-125.77 43.69,-116.58\"/>\n",
554       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M34.56,-144.78C37.84,-136.59 41.87,-126.51 45.55,-117.33\"/>\n",
555       "<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"47.95,-118.05 48.41,-107.47 41.45,-115.45 47.95,-118.05\"/>\n",
556       "</g>\n",
557       "<!-- C&#45;&gt;B -->\n",
558       "<g id=\"edge3\" class=\"edge\">\n",
559       "<title>C-&gt;B</title>\n",
560       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M47.44,-72.78C44.16,-64.59 40.13,-54.51 36.45,-45.33\"/>\n",
561       "<path fill=\"none\" stroke=\"#4a4a4a\" d=\"M49.29,-72.04C46.02,-63.85 41.98,-53.77 38.31,-44.58\"/>\n",
562       "<polygon fill=\"#4a4a4a\" stroke=\"#4a4a4a\" points=\"40.55,-43.45 33.59,-35.47 34.05,-46.05 40.55,-43.45\"/>\n",
563       "</g>\n",
564       "</g>\n",
565       "</svg><br><center><small><em>the second causal model</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
566       "\"><br><center><small><em>Doing $A=10$</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
567       "\"><br><center><small><em>Doing $A=20$</em></small></center></div><div class=\"floating-box\"><img src=\"data:image/png;base64,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\n",
568       "\"><br><center><small><em>Doing $A=30$</em></small></center></div>"
569      ],
570      "text/plain": [
571       "<IPython.core.display.HTML object>"
572      ]
573     },
574     "metadata": {},
575     "output_type": "display_data"
576    }
577   ],
578   "source": [
579    "gnb.flow.add_html(cslnb.getCausalModel(cm2),\"the second causal model\")\n",
580    "for v in [10,20,30]:\n",
581    "  gnb.flow.add_html(gnb.getProba(p2.extract({'A':v})),f\"Doing $A={v}$\")\n",
582    "gnb.flow.display()"
583   ]
584  },
585  {
586   "cell_type": "markdown",
587   "id": "f5ab0cb8-2fd7-4332-9f7b-2f9037ed719d",
588   "metadata": {
589    "tags": []
590   },
591   "source": [
592    "### if $A$ is cause for $C$, observing $C$ may lead to misinterpretations about the causal role of $A$."
593   ]
594  },
595  {
596   "cell_type": "code",
597   "execution_count": null,
598   "id": "e72aa3e7-7f55-42a7-8849-279cde7b6e6b",
599   "metadata": {},
600   "outputs": [],
601   "source": []
602  }
603 ],
604 "metadata": {
605  "kernelspec": {
606   "display_name": "Python 3 (ipykernel)",
607   "language": "python",
608   "name": "python3"
609  },
610  "language_info": {
611   "codemirror_mode": {
612    "name": "ipython",
613    "version": 3
614   },
615   "file_extension": ".py",
616   "mimetype": "text/x-python",
617   "name": "python",
618   "nbconvert_exporter": "python",
619   "pygments_lexer": "ipython3",
620   "version": "3.9.6"
621  }
622 },
623 "nbformat": 4,
624 "nbformat_minor": 5
625}
626