ch4_single_modeling.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import pystan\n",
    "from dataclasses import dataclass\n",
    "from typing import OrderedDict\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dummy data generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass(frozen=True)\n",
    "class SingleParameterModel:\n",
    "    a: float\n",
    "    b: float\n",
    "    \n",
    "    def __post_init__(self):\n",
    "        assert 0 < self.a < 1\n",
    "        assert 0 < self.b\n",
    "        \n",
    "    def __call__(self, x: float) -> float:\n",
    "        return self.b * (x ** self.a) - x\n",
    "    \n",
    "    @staticmethod\n",
    "    def of_vertex(x: float, y: float):\n",
    "        a = x / (x + y)\n",
    "        b = 1 / (a * ( x ** ( a - 1 )))\n",
    "        return SingleParameterModel(a, b)\n",
    "        \n",
    "    @staticmethod\n",
    "    def of_two_points(x_1: float, y_1: float, x_2: float, y_2: float):\n",
    "        a = (np.log(x_2 + y_2) - np.log(x_1 + y_1)) / (np.log(x_2) - np.log(x_1))\n",
    "        b = (y_1 + x_1) / (x_1**a)\n",
    "        return SingleParameterModel(a, b)\n",
    "        \n",
    "    @staticmethod\n",
    "    def of_stanfit(stanfit):\n",
    "        extracted = stanfit.extract()\n",
    "        assert \"a\" in extracted\n",
    "        assert \"b\" in extracted\n",
    "        a = np.median(extracted[\"a\"])\n",
    "        b = np.median(extracted[\"b\"])\n",
    "        return SingleParameterModel(a, b)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = SingleParameterModel.of_vertex(2000, 500)\n",
    "g = SingleParameterModel.of_two_points(10, f(10), 1000, f(1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x119de4ad0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame({\"x\": list(range(0, 4000, 1))}).assign(\n",
    "    y_f=lambda df: df.x.map(f),\n",
    "    y_g=lambda df: df.x.map(g)\n",
    ").set_index(\"x\").plot(figsize=(16, 12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_sample = 50\n",
    "dummy_data = pd.DataFrame({}).assign(\n",
    "    x=np.random.uniform(50, 350, n_sample)\n",
    ").assign(\n",
    "    x=lambda df: df.x.map(round).map(lambda x: x*10)\n",
    ").assign(\n",
    "    y=lambda df: df.x.map(f)\n",
    ").assign(\n",
    "    y_obs = lambda df: df.y + np.random.normal(0, 30, n_sample)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>y_obs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2370</td>\n",
       "      <td>493.615398</td>\n",
       "      <td>469.472261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1750</td>\n",
       "      <td>496.707066</td>\n",
       "      <td>472.677412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2860</td>\n",
       "      <td>468.195573</td>\n",
       "      <td>501.218119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1100</td>\n",
       "      <td>449.637653</td>\n",
       "      <td>423.678151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1320</td>\n",
       "      <td>472.978811</td>\n",
       "      <td>488.546257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1910</td>\n",
       "      <td>499.587524</td>\n",
       "      <td>532.552380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2040</td>\n",
       "      <td>499.920633</td>\n",
       "      <td>532.752882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3340</td>\n",
       "      <td>428.019881</td>\n",
       "      <td>454.713571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>880</td>\n",
       "      <td>416.289938</td>\n",
       "      <td>404.677914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3270</td>\n",
       "      <td>434.709971</td>\n",
       "      <td>480.111283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1260</td>\n",
       "      <td>467.477694</td>\n",
       "      <td>406.150486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1560</td>\n",
       "      <td>489.347899</td>\n",
       "      <td>462.583105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1760</td>\n",
       "      <td>496.971871</td>\n",
       "      <td>501.540597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1020</td>\n",
       "      <td>438.801327</td>\n",
       "      <td>465.408402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2980</td>\n",
       "      <td>459.450182</td>\n",
       "      <td>439.740182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>600</td>\n",
       "      <td>354.194727</td>\n",
       "      <td>354.975428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1180</td>\n",
       "      <td>459.161021</td>\n",
       "      <td>459.430249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2580</td>\n",
       "      <td>484.868015</td>\n",
       "      <td>493.318102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>3360</td>\n",
       "      <td>426.059493</td>\n",
       "      <td>390.712735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2840</td>\n",
       "      <td>469.563240</td>\n",
       "      <td>499.113523</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1950</td>\n",
       "      <td>499.873733</td>\n",
       "      <td>459.333025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>660</td>\n",
       "      <td>369.795905</td>\n",
       "      <td>373.080283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1410</td>\n",
       "      <td>480.128377</td>\n",
       "      <td>503.346575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2750</td>\n",
       "      <td>475.389496</td>\n",
       "      <td>460.458622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2140</td>\n",
       "      <td>499.046429</td>\n",
       "      <td>498.786399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>980</td>\n",
       "      <td>432.852657</td>\n",
       "      <td>408.989470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>2500</td>\n",
       "      <td>488.601562</td>\n",
       "      <td>531.563623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>690</td>\n",
       "      <td>377.075834</td>\n",
       "      <td>379.608062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2420</td>\n",
       "      <td>491.845346</td>\n",
       "      <td>468.229427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1980</td>\n",
       "      <td>499.979920</td>\n",
       "      <td>497.325911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>3490</td>\n",
       "      <td>412.800516</td>\n",
       "      <td>438.517620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>2410</td>\n",
       "      <td>492.215426</td>\n",
       "      <td>540.863164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>1770</td>\n",
       "      <td>497.225018</td>\n",
       "      <td>501.549954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>3290</td>\n",
       "      <td>432.825933</td>\n",
       "      <td>397.157462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>2080</td>\n",
       "      <td>499.685010</td>\n",
       "      <td>538.390337</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>2290</td>\n",
       "      <td>496.021079</td>\n",
       "      <td>481.831736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>3380</td>\n",
       "      <td>424.077642</td>\n",
       "      <td>441.033248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>3110</td>\n",
       "      <td>448.969969</td>\n",
       "      <td>449.607036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>2060</td>\n",
       "      <td>499.822125</td>\n",
       "      <td>533.414407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>2230</td>\n",
       "      <td>497.469499</td>\n",
       "      <td>520.397735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>2130</td>\n",
       "      <td>499.176216</td>\n",
       "      <td>518.639850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>2540</td>\n",
       "      <td>486.794844</td>\n",
       "      <td>516.282730</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>2350</td>\n",
       "      <td>494.266603</td>\n",
       "      <td>468.535186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>3120</td>\n",
       "      <td>448.121936</td>\n",
       "      <td>457.869249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>3430</td>\n",
       "      <td>419.030107</td>\n",
       "      <td>394.257469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>2750</td>\n",
       "      <td>475.389496</td>\n",
       "      <td>511.350266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>2320</td>\n",
       "      <td>495.181501</td>\n",
       "      <td>441.482460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>2660</td>\n",
       "      <td>480.662879</td>\n",
       "      <td>491.901143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>1490</td>\n",
       "      <td>485.445383</td>\n",
       "      <td>491.636504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>1420</td>\n",
       "      <td>480.844925</td>\n",
       "      <td>476.151238</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       x           y       y_obs\n",
       "0   2370  493.615398  469.472261\n",
       "1   1750  496.707066  472.677412\n",
       "2   2860  468.195573  501.218119\n",
       "3   1100  449.637653  423.678151\n",
       "4   1320  472.978811  488.546257\n",
       "5   1910  499.587524  532.552380\n",
       "6   2040  499.920633  532.752882\n",
       "7   3340  428.019881  454.713571\n",
       "8    880  416.289938  404.677914\n",
       "9   3270  434.709971  480.111283\n",
       "10  1260  467.477694  406.150486\n",
       "11  1560  489.347899  462.583105\n",
       "12  1760  496.971871  501.540597\n",
       "13  1020  438.801327  465.408402\n",
       "14  2980  459.450182  439.740182\n",
       "15   600  354.194727  354.975428\n",
       "16  1180  459.161021  459.430249\n",
       "17  2580  484.868015  493.318102\n",
       "18  3360  426.059493  390.712735\n",
       "19  2840  469.563240  499.113523\n",
       "20  1950  499.873733  459.333025\n",
       "21   660  369.795905  373.080283\n",
       "22  1410  480.128377  503.346575\n",
       "23  2750  475.389496  460.458622\n",
       "24  2140  499.046429  498.786399\n",
       "25   980  432.852657  408.989470\n",
       "26  2500  488.601562  531.563623\n",
       "27   690  377.075834  379.608062\n",
       "28  2420  491.845346  468.229427\n",
       "29  1980  499.979920  497.325911\n",
       "30  3490  412.800516  438.517620\n",
       "31  2410  492.215426  540.863164\n",
       "32  1770  497.225018  501.549954\n",
       "33  3290  432.825933  397.157462\n",
       "34  2080  499.685010  538.390337\n",
       "35  2290  496.021079  481.831736\n",
       "36  3380  424.077642  441.033248\n",
       "37  3110  448.969969  449.607036\n",
       "38  2060  499.822125  533.414407\n",
       "39  2230  497.469499  520.397735\n",
       "40  2130  499.176216  518.639850\n",
       "41  2540  486.794844  516.282730\n",
       "42  2350  494.266603  468.535186\n",
       "43  3120  448.121936  457.869249\n",
       "44  3430  419.030107  394.257469\n",
       "45  2750  475.389496  511.350266\n",
       "46  2320  495.181501  441.482460\n",
       "47  2660  480.662879  491.901143\n",
       "48  1490  485.445383  491.636504\n",
       "49  1420  480.844925  476.151238"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dummy_data.plot.scatter(x=\"x\", y=\"y_obs\", figsize=(16, 12))\n",
    "plt.savefig('profit_scatter.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# modeling with generated data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = {\n",
    "    \"x\": dummy_data.x.to_list(),\n",
    "    \"y\": dummy_data.y_obs.to_list(),\n",
    "    \"n\": dummy_data.shape[0]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_code = \"\"\"\n",
    "data {\n",
    "    int n;\n",
    "    vector[n] x;\n",
    "    vector[n] y;\n",
    "}\n",
    "parameters {\n",
    "    real<lower=0, upper=1> a;\n",
    "    real<lower=0> b;\n",
    "    real<lower=0> sigma;\n",
    "}\n",
    "transformed parameters {\n",
    "    vector<lower=0>[n] y_p;\n",
    "    for(i in 1:n)\n",
    "        y_p[i] = b*(x[i]^a) - x[i]; \n",
    "}\n",
    "model {\n",
    "    a ~ uniform(0, 1);\n",
    "    b ~ uniform(0, 100);\n",
    "    sigma ~ normal(0, 100);\n",
    "    y ~ normal(y_p, sigma);\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_22a19322936018b8c8eaec3e5754494d NOW.\n"
     ]
    }
   ],
   "source": [
    "model = pystan.StanModel(model_code=model_code)\n",
    "stanfit = model.sampling(data=data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_22a19322936018b8c8eaec3e5754494d.\n",
       "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
       "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
       "\n",
       "          mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "a          0.8  1.3e-4 4.6e-3   0.79    0.8    0.8   0.81   0.81   1180   1.01\n",
       "b         5.59  5.8e-3    0.2    5.2   5.46   5.59   5.72   5.98   1188   1.01\n",
       "sigma    27.94    0.08   2.96   22.8  25.81  27.73  29.77  34.62   1517    1.0\n",
       "y_p[1]   497.0    0.07   4.15 488.58 494.22 497.06 499.79 505.04   4029    1.0\n",
       "y_p[2]  497.22    0.12   4.86 487.61 493.93 497.24 500.44 506.75   1747    1.0\n",
       "y_p[3]   474.1     0.1   5.23 463.83 470.55 474.08 477.58 484.47   2862    1.0\n",
       "y_p[4]  447.73    0.17   6.23 435.18 443.54 447.82 451.94 460.18   1308    1.0\n",
       "y_p[5]   471.8    0.16   5.83 460.06 467.87  471.9 475.71 483.33   1384    1.0\n",
       "y_p[6]   500.8     0.1   4.54 491.84 497.77 500.88  503.8 509.71   2057    1.0\n",
       "y_p[7]  501.72    0.09   4.32 493.22 498.84 501.78 504.64 510.23   2455    1.0\n",
       "y_p[8]  436.56    0.17   7.44 422.03 431.54 436.53 441.48 451.35   1873    1.0\n",
       "y_p[9]  413.79    0.18   6.47  400.8 409.48 413.81 418.17 426.69   1262    1.0\n",
       "y_p[10] 442.85    0.16   7.07 429.14 438.09 442.87 447.57 456.81   1956    1.0\n",
       "y_p[11] 466.09    0.16   5.95 454.07 462.08 466.19 470.07 477.88   1359    1.0\n",
       "y_p[12] 489.07    0.14    5.3 478.49 485.49 489.13  492.6 499.61   1532    1.0\n",
       "y_p[13] 497.52    0.12   4.84  488.0 494.27 497.56 500.73 507.01   1762    1.0\n",
       "y_p[14] 436.66    0.18   6.34 423.88  432.4  436.7 440.94 449.27   1289    1.0\n",
       "y_p[15]  466.0    0.11    5.7 454.95 462.17 465.98  469.8  477.3   2510    1.0\n",
       "y_p[16] 351.22    0.18   6.38 338.49  347.0 351.26  355.5 363.84   1226    1.0\n",
       "y_p[17]  457.5    0.17    6.1 445.13 453.37 457.57 461.59 469.62   1331    1.0\n",
       "y_p[18] 489.31    0.07   4.42 480.43 486.33 489.35 492.21 497.95   4112    1.0\n",
       "y_p[19] 434.71    0.18   7.55 419.94 429.62 434.67 439.72 449.79   1851    1.0\n",
       "y_p[20] 475.36     0.1   5.15 465.17 471.89 475.34 478.79 485.65   2930    1.0\n",
       "y_p[21] 501.26     0.1   4.46 492.44 498.28 501.32 504.25 510.01   2163    1.0\n",
       "y_p[22] 366.89    0.18   6.45 353.98 362.59 366.95 371.18 379.71   1232    1.0\n",
       "y_p[23] 479.27    0.15   5.64 468.02 475.45 479.36 483.03 490.53   1428    1.0\n",
       "y_p[24] 480.71    0.08   4.86  471.0 477.47 480.73 483.92 490.36   3273    1.0\n",
       "y_p[25] 501.31    0.08    4.2 493.14 498.45 501.37 504.22 509.57   2877    1.0\n",
       "y_p[26]  430.6    0.18   6.39 417.79 426.34 430.65 434.93 443.31   1280    1.0\n",
       "y_p[27] 492.64    0.07   4.28 484.08 489.74 492.67 495.49 500.99   4166    1.0\n",
       "y_p[28] 374.21    0.18   6.47 361.35  369.9 374.28 378.53  387.1   1236    1.0\n",
       "y_p[29] 495.48    0.07   4.19 486.97 492.66 495.51 498.25 503.58   4115    1.0\n",
       "y_p[30]  501.5    0.09   4.41 492.81 498.58 501.56 504.46 510.17   2251    1.0\n",
       "y_p[31] 422.19     0.2   8.27 405.97 416.59 422.09 427.67 438.71   1735    1.0\n",
       "y_p[32]  495.8    0.07   4.18 487.34 492.98 495.83 498.57 503.87   4100    1.0\n",
       "y_p[33] 497.82    0.11   4.82 488.33 494.57 497.87  501.0 507.28   1777    1.0\n",
       "y_p[34] 441.08    0.16   7.18 427.19 436.24 441.08 445.87 455.24   1930    1.0\n",
       "y_p[35] 501.67    0.08   4.27 493.25 498.78 501.73 504.54 510.06   2611    1.0\n",
       "y_p[36] 499.01    0.07   4.13 490.72 496.24  499.1 501.86  507.1   3651    1.0\n",
       "y_p[37] 432.84    0.18   7.66 417.83 427.68 432.82  437.9 448.14   1831    1.0\n",
       "y_p[38] 456.23    0.13   6.28  444.0 452.06 456.25 460.43 468.55   2211    1.0\n",
       "y_p[39] 501.72    0.09   4.29 493.23 498.81 501.77 504.59 510.13   2531    1.0\n",
       "y_p[40] 500.17    0.07   4.15 492.05 497.39 500.23 503.01 508.25   3335    1.0\n",
       "y_p[41]  501.4    0.08   4.21 493.17 498.52 501.45  504.3 509.69   2830    1.0\n",
       "y_p[42] 491.03    0.07   4.35 482.39 488.11 491.07 493.92 499.44   4151    1.0\n",
       "y_p[43] 497.55    0.07   4.15 489.15 494.78 497.61 500.36 505.62   3984    1.0\n",
       "y_p[44] 455.44    0.14   6.33 443.12 451.23 455.46 459.67 467.83   2192    1.0\n",
       "y_p[45] 428.07    0.19   7.94  412.5 422.76 428.01 433.29 443.92   1784    1.0\n",
       "y_p[46] 480.71    0.08   4.86  471.0 477.47 480.73 483.92 490.36   3273    1.0\n",
       "y_p[47] 498.32    0.07   4.14 489.97 495.57 498.39 501.16 506.44   3809    1.0\n",
       "y_p[48] 485.52    0.08    4.6 476.36 482.44 485.56 488.52 494.63   3644    1.0\n",
       "y_p[49] 484.89    0.14   5.46 473.96 481.21 484.95 488.53 495.77   1478    1.0\n",
       "y_p[50] 480.03    0.15   5.62 468.81 476.21  480.1 483.77 491.26   1434    1.0\n",
       "lp__    -187.3    0.04   1.28 -190.7 -187.9 -187.0 -186.4 -185.9   1131    1.0\n",
       "\n",
       "Samples were drawn using NUTS at Mon Nov 25 17:01:33 2019.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stanfit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = SingleParameterModel.of_stanfit(stanfit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "modeled_data= pd.DataFrame({\"x\": list(range(0, 4000, 1))}).assign(\n",
    "    y_modeled=lambda df: df.x.map(h)\n",
    ")\n",
    "modeled_data.set_index(\"x\").plot(figsize=(16, 12))\n",
    "plt.savefig('profit_modeled.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11de05590>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(16,12))\n",
    "ax.scatter(x=dummy_data[\"x\"], y=dummy_data[\"y_obs\"])\n",
    "ax.plot(modeled_data[\"x\"], modeled_data[\"y_modeled\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig.savefig('profit_modeled_observed.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot for articles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame({\"x\": list(range(0, 4000, 1))}).assign(\n",
    "    y=lambda df: df.x.map(lambda x: (x**0.5))\n",
    ").set_index(\"x\").plot(figsize=(16, 12))\n",
    "plt.savefig('decay.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame({\"x\": list(range(0, 4000, 1))}).assign(\n",
    "    y=lambda df: df.x.map(SingleParameterModel(0.8, 6.0))\n",
    ").set_index(\"x\").plot(figsize=(16, 12))\n",
    "plt.savefig('profit_example.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "dummy_data.to_csv(\"dummy_data.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2370</td>\n",
       "      <td>494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1750</td>\n",
       "      <td>497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2860</td>\n",
       "      <td>468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1100</td>\n",
       "      <td>450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1320</td>\n",
       "      <td>473</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1910</td>\n",
       "      <td>500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2040</td>\n",
       "      <td>500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3340</td>\n",
       "      <td>428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>880</td>\n",
       "      <td>416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3270</td>\n",
       "      <td>435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1260</td>\n",
       "      <td>467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1560</td>\n",
       "      <td>489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1760</td>\n",
       "      <td>497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1020</td>\n",
       "      <td>439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2980</td>\n",
       "      <td>459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>600</td>\n",
       "      <td>354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1180</td>\n",
       "      <td>459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2580</td>\n",
       "      <td>485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>3360</td>\n",
       "      <td>426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2840</td>\n",
       "      <td>470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1950</td>\n",
       "      <td>500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>660</td>\n",
       "      <td>370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1410</td>\n",
       "      <td>480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2750</td>\n",
       "      <td>475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2140</td>\n",
       "      <td>499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>980</td>\n",
       "      <td>433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>2500</td>\n",
       "      <td>489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>690</td>\n",
       "      <td>377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2420</td>\n",
       "      <td>492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1980</td>\n",
       "      <td>500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>3490</td>\n",
       "      <td>413</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>2410</td>\n",
       "      <td>492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>1770</td>\n",
       "      <td>497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>3290</td>\n",
       "      <td>433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>2080</td>\n",
       "      <td>500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>2290</td>\n",
       "      <td>496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>3380</td>\n",
       "      <td>424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>3110</td>\n",
       "      <td>449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>2060</td>\n",
       "      <td>500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>2230</td>\n",
       "      <td>497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>2130</td>\n",
       "      <td>499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>2540</td>\n",
       "      <td>487</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>2350</td>\n",
       "      <td>494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>3120</td>\n",
       "      <td>448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>3430</td>\n",
       "      <td>419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>2750</td>\n",
       "      <td>475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>2320</td>\n",
       "      <td>495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>2660</td>\n",
       "      <td>481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>1490</td>\n",
       "      <td>485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>1420</td>\n",
       "      <td>481</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       x    y\n",
       "0   2370  494\n",
       "1   1750  497\n",
       "2   2860  468\n",
       "3   1100  450\n",
       "4   1320  473\n",
       "5   1910  500\n",
       "6   2040  500\n",
       "7   3340  428\n",
       "8    880  416\n",
       "9   3270  435\n",
       "10  1260  467\n",
       "11  1560  489\n",
       "12  1760  497\n",
       "13  1020  439\n",
       "14  2980  459\n",
       "15   600  354\n",
       "16  1180  459\n",
       "17  2580  485\n",
       "18  3360  426\n",
       "19  2840  470\n",
       "20  1950  500\n",
       "21   660  370\n",
       "22  1410  480\n",
       "23  2750  475\n",
       "24  2140  499\n",
       "25   980  433\n",
       "26  2500  489\n",
       "27   690  377\n",
       "28  2420  492\n",
       "29  1980  500\n",
       "30  3490  413\n",
       "31  2410  492\n",
       "32  1770  497\n",
       "33  3290  433\n",
       "34  2080  500\n",
       "35  2290  496\n",
       "36  3380  424\n",
       "37  3110  449\n",
       "38  2060  500\n",
       "39  2230  497\n",
       "40  2130  499\n",
       "41  2540  487\n",
       "42  2350  494\n",
       "43  3120  448\n",
       "44  3430  419\n",
       "45  2750  475\n",
       "46  2320  495\n",
       "47  2660  481\n",
       "48  1490  485\n",
       "49  1420  481"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy_data.assign(\n",
    "    y=lambda df: df.y.map(round)\n",
    ")[[\"x\", \"y\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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