Safety in AVs.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "##importing data into Jupyter Notebook\n",
    "import pandas as pd\n",
    "df_dis = pd.read_csv(\"mp1_av_disengagements.csv\")\n",
    "df_mil = pd.read_csv(\"mp1_av_totalmiles.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of AV disengagements over the entire duration of available data : 1024\n"
     ]
    }
   ],
   "source": [
    "print(\"Total number of AV disengagements over the entire duration of available data :\",len(df_dis))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of unique months that have recorded AV disengagements : 15\n"
     ]
    }
   ],
   "source": [
    "# Counting the number of unique months that have recorded AV disengagements\n",
    "m = len(df_dis.groupby('Month').count())\n",
    "print(\"Number of unique months that have recorded AV disengagements :\",m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Splitting the month and year and then counting unique months - This will be later used to set the right index\n",
    "df_dis['month']=df_dis['Month'].apply(lambda x:x.split('-')[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "List of unique locations of AV disengagements : ['urban-street' 'highway']\n"
     ]
    }
   ],
   "source": [
    "print(\"List of unique locations of AV disengagements :\",df_dis['Location'].unique())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of unique causes of AV disengagements : 10\n"
     ]
    }
   ],
   "source": [
    "print(\"Number of unique causes of AV disengagements :\",len(df_dis['Cause'].unique()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of missing values : 532\n"
     ]
    }
   ],
   "source": [
    "print(\"Number of missing values :\",df_dis.isnull().sum().sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Causes of disengagement')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "Cause=df_dis['Cause'].value_counts()\n",
    "\n",
    "#pie chart\n",
    "patches,texts,_=plt.pie(Cause,labels=Cause.keys(),autopct='%1.1f%%')\n",
    "plt.legend(loc=(2,0))\n",
    "plt.title(\"Causes of disengagement\", fontsize=18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Based on pie chart, top two leading causes are :\n",
      "1) Unwanted Driver Discomfort\n",
      "2) Recklessly behaving agent\n"
     ]
    }
   ],
   "source": [
    "print(\"Based on pie chart, top two leading causes are :\\n1) Unwanted Driver Discomfort\\n2) Recklessly behaving agent\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#Creating timestamp from Month column\n",
    "date_list = []\n",
    "for i in df_mil['Month']:\n",
    "    date_list.append(pd.to_datetime(\"20\" + str(i.split(\"-\")[0]) + \" \" + str(i.split(\"-\")[1])))\n",
    "df_mil['Timestamp']= date_list\n",
    "df_milg = df_mil.groupby('Timestamp').sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Disengagement/Mile over time with monthly granularity\n",
    "df_milg['Dis/Mile']=df_milg['total number of disengagements']/df_milg['miles driven in autonomous mode']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_mil = df_milg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Trend of AV Disengagement/Mile over time')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_mil.groupby('Timestamp').sum()['Dis/Mile'].plot(figsize=(12,8))\n",
    "plt.xlabel(\"Month\",size=15)\n",
    "plt.ylabel(\"Disengagements/Mile\",size=15)\n",
    "plt.title(\"Trend of AV Disengagement/Mile over time\", size=20)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yes, the AVs are maturing over time as the number of Disengagements per mile is decreasing over time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The following distributions signify about the samples drawn from it:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### a. Gaussian distribution:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To answer this, we referenced: https://en.wikipedia.org/wiki/Normal_distribution\n",
    "\n",
    "This distribution signify that the samples drawn from it is symmetry by the mean of the distribution and it is unimodal. The distribution is the highest at the mean and descend towards two opposite directions from the mean until it reach near zero but never actually touch that. \n",
    "\n",
    "The normal density is given by:\n",
    "$$f(x) = \\frac{1}{\\sqrt{2\\pi \\sigma^2}}\\exp{\\left[-\\frac{(x-\\mu)^2}{2\\sigma^2}\\right]}, \\quad -\\infty<x<\\infty$$\n",
    "where $\\mu$ is the mean of the distribution and $\\sigma$ is the variance of the distributions.\n",
    "\n",
    "The distribution function $F(x)$ has no closed form, so between every pair of limits a and b, probabilities relating to normal distributions are usually obtained numerically and recorded in special tables.\n",
    "\n",
    "These tables apply to the standard normal distribution $Z~N(0,1)$ -- a normal distribution with parameters $\\mu=0, \\sigma = 1$ and their entries values are:\n",
    "$$F_z(z) = \\frac{1}{\\sqrt{2\\pi}}\\int^z_{-\\infty} e^{-t^2/2}dt$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### b. Exponential distribution:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To answer this, we referenced: https://en.wikipedia.org/wiki/Exponential_distribution\n",
    "\n",
    "This signify that the samples have the form of the continuous analague of the goemetric distribution. It is of highest value near the beginning of the function then smoothly and continuously descend until it reaches near zero but never actually touch zero. If samples $X$ is of exponential distribution, we can use the notation $X~EXP(\\lambda)$.\n",
    "\n",
    "Its CDF is given as:\n",
    "\n",
    "The pdf of it is:\n",
    "$$f(x) =\n",
    "  \\begin{cases}\n",
    "    \\lambda e^{-\\lambda x}       & \\quad \\text{if } x>0\\\\\n",
    "    0  & \\quad \\text{otherwise } \n",
    "  \\end{cases}\n",
    "$$\n",
    "\n",
    "One of the most important properties of the exponential distribution is its memoryless properties. Which essentially states that the probability of something will happen only depend on the probabilityof that happening from that point, despite the past. Its fomula is:\n",
    "$$P(T>s+t|T>s) = P(T>t)$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### c. Weibull distribution:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To answer this, we referenced: https://en.wikipedia.org/wiki/Weibull_distribution\n",
    "\n",
    "This distribution signify two parameter continuous probability distributions with $\\lambda$ defines the scale and $k$ defines the shape, resulting in very different forms for the distribution depending on the parameters.\n",
    "\n",
    "Shape paremeters $\\alpha$ and $\\beta$:\n",
    "$$f(x;\\lambda,k) =\n",
    "  \\begin{cases}\n",
    "    \\frac{k}{\\lambda} \\left(\\frac{x}{\\lambda}\\right)^{k-1} e^{\\left(-x/\\lambda\\right)^k}      & \\quad \\text{if } x\\geq 0\\\\\n",
    "    0  & \\quad \\text{otherwise } \n",
    "  \\end{cases}\n",
    "$$\n",
    "\n",
    "Shape parameter $k$ indicates:\n",
    "<ul>\n",
    "    <li>$k<1$: failure rate decreases over time</li>\n",
    "    <li>$k=1$: failure rate is constant over time</li>\n",
    "    <li>$k>1$: failure rate increases over time</li>\n",
    "</ul>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n",
      "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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ddxyxWIxQKMRll13G1772NQKBrosImzdvZvHixVxyySVeNjfv+a4s01ZzF6fnTjxKSThEU9TKMsZkW1FREatWrWL16tU8/fTTLFiwoMeJvzZv3sz8+fMPUQvzh+/CPb3nrkGn514SDlnP3ZhDbPjw4dxzzz3cddddqCqbN29m9uzZzJgxgxkzZrB48WIArrvuOhYtWsT06dO54447ulzP7M+3ZRlE0EABJOMUh4TG1gSqal8gbMwhdPjhh5NMJtm5cyfDhw/n6aefJhKJsH79eubMmcOyZcu45ZZbuP3223nssccA5yrzztYz+/NtuIsIyYCz+5FgkoQqDa1xyiIF/dk8Y3wn9X8yFosxd+5cVq1aRTAY7HTSsN6s53c+D3fnq/YiOPX2vY1RC3djDqFNmzYRDAYZPnw4N954IyNGjOC1114jmUy2f6FOB3fccUdG6/md72rubbNC0t5zD4tTb7cv7TDm0Nm1axdXXXUVc+fORUTYt28fo0aNIhAI8MADD5BIOJ2ujtPidrWe2Z9/e+4BIRFweukFbs+9xsLd+EgmQxe9lvoe0dRQyM997nN8/etfB+A//uM/+OQnP8nDDz/M+9//fkpKSgCYNm0aoVCI448/nssvv7zL9cz+/BvuCAlJhbv13I05FLrrZU+ePJnXX3+97f6Pf/xjwPkGp2eeeWa/dTtbz+wvo7KMiJwtIutEZIOIXNfJ4+NF5DkRWSkir4vIud431Rtto2UCQsIty4Rw5pexr9szxuSLHsNdRILA3cA5wFRgjohM7bDafwEPqeoJwMXAL7xuqFfaJw4T4rgnT+MxQgGxsowxJm9k0nM/CdigqptUNQo8CFzYYR0FBrm3y4Ft3jXRW+nj3FM991i0lZJwyMoyJu/11zevmd7r67HKJNzHAO+k3a92l6W7AbhURKqBBcBXOtuQiHxJRJaJyLJdu3YdRHP7LvWGJVQh6AyFjEVbKS4MUttk4W7yVyQSYc+ePRbwOUBV2bNnT5+GeWZyQrWzSzY7/nbMAe5T1Z+KyCzgARE5VlWT+z1J9R7gHnC+Q/VgGtxXqV/spLrTDwDxaCuRgiB1LTYFgclfY8eOpbq6mv7qWJneiUQijB079qCfn0m4VwPj0u6P5cCyyxeAswFU9WURiQDDgJ0H3bIsaeu5JwE33GOtLYQHBWiwcDd5rKCggIkTJ/Z3M8whkklZZikwWUQmikghzgnTRzussxX4IICITAEiwIDsHqROqHYsy0QKgtS3xvqzacYY45kew11V48Bc4ElgLc6omNUicpOIfNRd7RvAF0XkNeCPwOU6QAt76WUZAkEQIRZtJRyynrsxJn9kdBGTqi7AOVGavux7abfXAKd527Ts2O+EqgihgnB7z70lbjNDGmPygu/mlmkPdyfAQ4VhYq0tREIB4kmlNZ7s7unGGJMTfBfuqZp7MumEfKgwTDwWJVwQBKCuxeruxpjc57twT/Xc4+4ZgYLCMLFWpywDWN3dGJMXfBfuKcn0cI+2Egk5b0W9hbsxJg/4Ltzbh0I69wvCEWLRlrayTIN9l6oxJg/4LtzbT6g699t67gWpnrvV3I0xuc934Z7qucfdukxhOFWWcXruVpYxxuQD34V7es9dgMLCMPHWVsIFVnM3xuQP34Z7MgkFwYBbc28lHLKauzEmf/g23OOqhIJCYThCtLWZYEAoKghazd0Ykxd8F+5to2XcnnthUTHRlmY0maQsErKeuzEmL/gu3NMvYioIBghHigGItjZTGgnZnO7GmLyQ0cRh+aR9PnelICiEC5xwb21uoixSYFeoGmPygm977omkOGUZt+fe2tJMWThkNXdjTF7wbbjHk84J1XCRW5ZpbqIsErKhkMaYvOC7cG87oYpSEAgQjhQB0NrSRGnYTqgaY/KD78I9JZ6AgpAzWgbaa+7WczfG5APfhXvb9AOqFASkfbRMcxOl7lDI1FzvxhiTq3wX7u01d3coZFH7CdVBEWfwUEPUeu/GmNzmu3Bvv4jJGQpZmKq5NzdSGnbD3Uozxpgc57twT++5h4IBQgWFBEMFRFuaKYsUADZ5mDEm9/k23JM449wBwkXFzmiZVFmm1ca6G2Nym2/DHYSCoAAQjhS7o2WccLcpCIwxuc6/4S609dwLI0VEW5oos5q7MSZP+C7cUydU9+u5FxW3jXMHq7kbY3Kf78K9jQihtp67M+2v1dyNMfnCd+Ge3nMvTD+h2txESWEQEeu5G2Nyn+/Cvf2EKoTSyjLRlmZEhNKwTR5mjMl9vgv3tp67CAWB9hOqrc2NAAyy+WWMMXnAd+HeTvbruceircTjcXdmSKu5G2Nym+/CPb3nHgw44Z76wo6mJpvT3RiTH3wX7ukXMQWk/SImgIaGhraZIY0xJpf5N9wFQoH2sgxAY2OjzelujMkL/g130ssyzsyQDQ0N7mgZq7kbY3Kbf8M9reae3nMvKQzSFE30V/OMMcYTvgv39IuY2sO9BHDCvTgcojmWsG9jMsbktIzCXUTOFpF1IrJBRK7rYp3PiMgaEVktIvO9baZ39uu5y4FlmeLCIKrQErfeuzEmd4V6WkFEgsDdwFlANbBURB5V1TVp60wGvgOcpqo1IjI8Ww3uq1TPXeGAskxDQwPFo4MANEUTFBf2+PYYY8yAlEnP/SRgg6puUtUo8CBwYYd1vgjcrao1AKq609tmZoMQ6BDu9fX1FBU44d5sdXdjTA7LJNzHAO+k3a92l6U7EjhSRF4SkVdE5OzONiQiXxKRZSKybNeuXQfX4j5K9dwDgfZx7oFAkHBRCXV1dZS4c7rbSVVjTC7LJNylk2UdzzaGgMnAmcAc4F4RqTjgSar3qGqVqlZVVlb2tq2eSNXcg4H9d72otIza2lqKCp2ee2PUxrobY3JXJuFeDYxLuz8W2NbJOo+oakxV/wWswwn7Aac93Pf/mxUpLqWuro5iK8sYY/JAJuG+FJgsIhNFpBC4GHi0wzp/B94PICLDcMo0m7xsqFdS4R7opOe+8d2dvPD2bgCeePM95i/ZesjbZ4wxXugx3FU1DswFngTWAg+p6moRuUlEPuqu9iSwR0TWAM8B31LVPdlqdF90VZaJFJfS3FBPYchZHo0nD3iuMcbkiozG+qnqAmBBh2XfS7utwNfdnwEtdUI1GOzQcy8po6WpwcLdGJMXfHeFalc196LSMpob6ylwl0cTFu7GmNzl43DvWJYpI5lIQKIVsHA3xuQ2/4Z7J2UZgFhzI0ERK8sYY3Ka78K9reYuHYZClpQCOKWZkIW7MSa3+S7c23vu+59LTvXcWxrrKQwGrCxjjMlp/g33Dnve1nN3h0Naz90Yk8v8G+5d1NxTwyFj1nM3xuQw/4Z7ILjf8lS4N7tlmVbruRtjcpjvwr2ri5gKwhECwRDNjdZzN8bkPt+Fe6rnHuowzl1EKCoppaWxnoKg1dyNMbnNt+HeceIwgEiJc5VqOGSjZYwxuc234R7qOFwGrOdujMkbvgv3tpp74MDvICkqKWuruVu4G2Nyme/CXVVRhFAn4R4pKWu7iCmeVJLa8QunjDEmN/gy3JH2709NV+TW3FPT/sas926MyVG+C3enLCOdl2VKy2htbiIkTqi32klVY0yO8mG4K0jnNfeSMvc7vVsbAeu5G2Nyl+/CPZ5weu6d1dyLBznhnmyuB2xOd2NM7vJfuCeTIJ2XZUo6hrv13I0xOcp34Z5we+6BznruZeUAxJvrAAt3Y0zu8l+4uydUQ52Mlkn13GNNVpYxxuQ234V7PNF1WSZSXEogGCTauA+wnrsxJnf5LtwT3VyhKiKUlFXQ2uiWZaznbozJUf4L92567uCMmGkLd+u5G2NylP/CvZuLmMCpuzfXu2UZ67kbY3KUD8O964uYwLmQqam+llBA7CImY0zO8l+4JxJ033Mvp7Gu1pkZ0nruxpgc5b9wTzoThwU7GQoJTs091tpCgcas5m6MyVk+DPeea+4AoXiThbsxJmdZuHeQuko1FG20sowxJmf5L9wT2u1QyFTPPRBrJBq3L+swxuQm34V7UpMo3Y+WAQhEG4gmEoewZcYY4x3fhXt30w9A+7S/0tpgPXdjTM7yXbgnkwp0PVqmMByhMFKENtcRs5q7MSZH+S/cNdntRUwAZRVDSTTV2mgZY0zO8l24O/O5B7oP98HDSDRauBtjcldG4S4iZ4vIOhHZICLXdbPep0RERaTKuyZ6K6ndTz8AUDZ4KLGGWhKqVpoxxuSkHsNdRILA3cA5wFRgjohM7WS9MuAaYInXjfRS6puYeuq5RxtqQJM0RW3EjDEm92TScz8J2KCqm1Q1CjwIXNjJej8AbgVaPGyf55LqnFANdHFCFZyauyYTEG2k2cLdGJODMgn3McA7afer3WVtROQEYJyqPtbdhkTkSyKyTESW7dq1q9eN9UIimUC6CXZwyjIA0lxHQ2vsUDTLGGM8lUm4d5aEbQPARSQA3AF8o6cNqeo9qlqlqlWVlZWZt9JDSXfisO4MGjwMAGnZR22ThbsxJvdkEu7VwLi0+2OBbWn3y4BjgedFZDNwCvDoQD2pmkwmM++5t9RRY+FujMlBmYT7UmCyiEwUkULgYuDR1IOquk9Vh6nqBFWdALwCfFRVl2WlxX3kjJbpPtxLy4cgEkBa9lHTGD1ELTPGGO/0GO6qGgfmAk8Ca4GHVHW1iNwkIh/NdgO9lkxqp3WmdIFgkJJBFUjzPvY2WbgbY3JPKJOVVHUBsKDDsu91se6ZfW9W9iSTSZCeP7CUDR5KXXMdNRbuxpgc5LsrVJNJ7bHmDk64B6wsY4zJUT4M955PqIJzIZO01LG30U6oGmNyj//CPYMTquBeyNTayN66hkPQKmOM8Zbvwl0z7LmXDxsBwO6d72W7ScYY4znfhXtSM6u5V7jhXrt7R7abZIwxnvNfuGd4QrWiciQATTU7SSTtG5mMMbnFd+GumuEJ1fIhSDAEjTXUNdtJVWNMbvFduGd6QlUCAYorhiFNe+1CJmNMzvFduGuGZRmA0iHDCTTtpdbC3RiTY3wX7pmeUAWoGDbS6bnbWHdjTI7xXbg7QyEz2+3BlSORaCM79u7LcquMMcZb/gt3Mu+5V44cBcCWd6qz2SRjjPGc78I9mdRuv2Iv3dDhznDIbdvezWaTjDHGc74Ld+1FzX3wMCfcd27f1sOaxhgzsPgw3JNIILNwLykfjIQK2LvTrlI1xuQWX4V7IqmgZNxzFxHC5cOp3209d2NMbvFVuMcSSUAzHi0DUFY5mqa927PXKGOMyQL/hXsvau4AQ0aOJVG3m1jMxrobY3KHz8JdoRdDIQFGjhkPmmTL1ney1zBjjPGYz8Ld6bkHApnv9tjxhwGwZt2GbDXLGGM8579wJ/MTqgCTDj8cgLc2bMxKm4wxJht8Fu7a65r7qMrBaLiUTZs2ZbFlxhjjLZ+FuzNaJtMrVAGGlBSSLK3kna1bstcwY4zxmK/CPRp3R8v0ouY+pKQQLankveqtWWyZMcZ4y1fhfjA991HlRQQGDaepfh+1tbXZa5wxxnjIV+EeT7o19wynHwAIBoQRYycCsGGDjZgxxuQGX4V7LO6MlulNzx1g8pGTAVi3bp3nbTLGmGzwVbhHU9MP9KLmDjDl8HFoYTFr176VnYYZY4zHfBXuqaGQve25TxpeSnLQKN60cDfG5AhfhXv8IC5iAphUWYoOGs2/Nm4gkUhko2nGGOMpX4V71J1+INjLsszhlU7PPdrawjvv2BwzxpiBz1fhfjAThwGUhkMMGT0BgLffftv7hhljjMd8Fu69nzgs5YjJR4AIb71ldXdjzMDnv3A/iJ47wBEjB0PZCNasWeN9w4wxxmM+C3ftdc19/pKtzF+ylZqmKPGKcby6fCX/+4rNM2OMGdh8Fu5JBHp1hWpKZVmY5ODxNDfUUbvrPe8bZ4wxHsoo3EXkbBFZJyIbROS6Th7/uoisEZHXReQZETnM+6b2nXOFqhLoxXeoplSWhklWjAfg3U1WdzfGDGw9ppyIBIG7gXOAqcAcEZnaYbWVQJWqTgP+DNzqdUO9EG37DtXeP3dQUQEFg0cjoULe3WjhbowZ2DLpwp4EbFDVTaoaBR4ELkxfQVWfU9Um9+4rwFhvm+mNhtY4Ir2/iAmeZT2EAAARGklEQVSc+WiGVxRTMHQ82/5lc8wYYwa2TMJ9DJB+5U61u6wrXwAe7+wBEfmSiCwTkWW7du3KvJUeaWiJIwcxt0zKyEERouXj2L55A9Fo1OPWGWOMdzJJuc66udrpiiKXAlXAbZ09rqr3qGqVqlZVVlZm3kqPNLTGnROqne5Sz0aWR2gtH0siHrMhkcaYAS2TcK8GxqXdHwts67iSiHwIuB74qKq2etM8b9Wneu4HU3TH6bknhzpfmL106VIvm2aMMZ7KJNyXApNFZKKIFAIXA4+mryAiJwC/xgn2nd430xv1rXHnRh/CnXAZxZVjWbJkiYctM8YYb/UY7qoaB+YCTwJrgYdUdbWI3CQiH3VXuw0oBR4WkVUi8mgXm+tXDS0xRA++514cDjEoEqJw5JGsWLHC6u7GmAErlMlKqroAWNBh2ffSbn/I43ZlRUNrnIOdfiBlZHmEPUMOp7n5Wd58801mzJjhXQONMcYjvrpCtaHFKcv0KdwHFVFbMh4RsdKMMWbA8k24J5JKYzQBqgddcwen554oKGbCpMksXrzYwxYaY4x3fBPuDamTqShyENMPpIwsjwAw4dgqVq5cyb59+zxonTHGeMt/4a7a+cj9DFWWhgmKEBl/HIlEghdffNGbBhpjjIf8E+4taT33PqR7MCAMHxRmT+FIhgwZwsKFC71poDHGeMg34V7fEgNAVQ9qyt90o8ojrN5ezxlnnMELL7xAPB7v+UnGGHMI+Sfc08syfanLAIcNKWF3Q5QpM05h3759rFixou8NNMYYD/km3FNlGdW+nVAFOGxYMQAyagpFRUUsWLCgh2cYY8yh5Z9wb00P975tq7I0zNCSQlZta+YDH/gATzzxhF2taowZUHwT7vvV3PvYcxcRqiYMZunmvZx33nns27fPxrwbYwYU34R7ai53oE8XMaWcOGEIW/c2MXlaFeXl5Tz22GN93qYxxnjFN+Fe3xqnpDAI9G36gZQTJwwBYGV1Peeeey5PP/00NTU1fd6uMcZ4wTfh3tASpyzsXbgfM3oQxYVBlm7ey8UXX0w0GuWRRx7p83aNMcYL/gn31jilEWcSTC/CPRQMMGP8YF79116OPPJIZsyYwYMPPkgymezzto0xpq98E+71LXFKCt3d9SDc5y/ZSqQgwLr36rn1ibcYV/UhtmzZYidWjTEDgn/CvTVOadjtuffxIqaUkyYOpaK4gPsXb2bklJMZPnw4v/nNbzzZtjHG9IVvwr2hJUZp6oRqH6cfSCkNh7j81IkkFR5Y+i5zLr2MV199lZUrV3qyfWOMOVj+CffWOKXuCdW+Tj+QrrIszKWnHMaexijxw06ivLycX//6155t3xhjDoZvwt2puXs3WibdxGEljB1cxD/W1nDFFVewcOFCXn31VU9fwxhjesMX4Z5IKk3RRNbCHWD6uArWbq/jlI98nJEjR3LbbbfZyBljTL/xRbin5pXJZrhPG1tBMCA8vnYPX/va13jzzTdt3Lsxpt/4K9zD3g2F7Kg0HGL25GE8svJdzjvvfGbMmMFPfvIT9uzZ4/lrGWNMT/wR7u50v21DIfs4cVhXPn7CGLbta2H51lpuuukmmpqauPnmm1HVrLyeMcZ0xRfhnpoRsrjA2d0sdNwBOGvqCIoKgjz2+nYmTZrE1VdfzRNPPMFf//rX7LygMcZ0wR/h7pZligu9HwqZrrgwxGlHDOW5dTtRVa688kpOOeUUbr75ZtatW5eV1zTGmM74ItxTZZm2nrtHFzF15syjhlNd08zGXY0Eg0FuvfVWysrK+PKXv8zOnTuz9rrGGJPOH+HedkLVHS2TpZ47wJlHVQLw/DonyCsrK/nlL3/Jvn37uOqqq6irq8vaaxtjTIovwr295p6afiB7uz12cDGTh5fy/LpdbcuOOeYYfvazn7F+/Xq+8IUvWMAbY7Iu1N8NOBQaWuKIQCSU3b9l85dsBWDEoAgvb9rDvJf+RVCEN7ftY8UWaKm6jNVL7+P8T3yGB3//O0aPHp3V9hhj/MsfPffWOKWFobZRMtkaCply1MgyEkll6eYafrVwIw8tq2ZPYysVk6YTn/Ul9u3ZxUUXXcSSJUuy2g5jjH/5ItwbWpwv6khNB5CNK1TTHTa0mMJQgAVvbKemKcYlJ43nGx8+ii/MnkjR2KNJnnkNRSWlXHHFFfz0pz+lqakJgOZogoVv7yKZtHHxxpi+8Ue4u3O5py4myna4hwIBqg4bzMRhJcx9/xEcO6acgAiDIgX826zDaC0ZTsGHv8EFF36Me++9l/PPP5/Hn3qaL9y/lMt+9yo/efKtrLbPGJP/fFFz393QSlmkPdyzdhVTmvOndV5PH1VexMVV4/jDki2Mm/oJfv/xj3PTTTfx9a9eQ2LYJEbPPIdfP6+8W9PMqZOGAXDJyeOz3l5jTH7J+577ttpmlm+p4bQjhh2ynntPjh41iOvPm8oTq9/j6qdqWXvMF4keeyHFrTXUPHkX5S/9nCce/RurNrzbr+00xuSuvO+5P7ysmqTCZ6rGkax3hyf2c7gDXHHaBJJJ5bXqWsYNKeakz59M9e4v8uYrz7N4wcNEX/szj77+N944dibFl3ycWbNmMWLEiLbnN7TGuX/xZsoiIaaOGsTx4yooCOb932pjTIbyOtwTSeWhZe9w+hHDGDekmM11bs89ixcxZeqPr75DSTjUVnrZXttCMFTA8aefxbTTPsT6dWv5018fYcuGlXznO98BYNKkSVRVVXH01GO4e1Ur78QHQcAZuz+6IsKcE8fzlQ9O7rd9MsYMHBmFu4icDfwcCAL3quotHR4PA78HZgJ7gItUdbO3Te29lzbs5t3aZq4752iA9rJMFqcf8IKIcOTRU5lz5XjmvbiRyZF6Zg+qYcvalTz2j3/wpz/9CYDiQJCKylEUlA9npw7irteHsXX1VKYfOZ6Tp0xk4tgRBIPBHl7NmP5V1xIjFk8ytDTc303JKz2Gu4gEgbuBs4BqYKmIPKqqa9JW+wJQo6pHiMjFwE+Ai7LR4N7409J3qCgu4MPHOOWM9ql3B3a4pxwxvJQ5J0/gn2t38Ntd5Rx21FT2DLsQ6ndTNaiBQbE97H2vmr07thHa8SbxWJTHVsJjqQ2IUDqogvLycoZUlDOorIzi0lLiwQj74kH2NCfZ06w0xoXDR1Yw7bBhHD5iMGOHDWJQSRHhcJhQKEQwGNzvJxAIEAgEaIwp1bWtvLGtnhfW7+Ffe5sZN6SEiZWlTB83mJkThjB2cBGl4QKCaSUjEWn7Sb+fum3yWzyRZNPuRl6v3seTq99j4bpdxJJJZh0+lHOPG8X0cRVMHlFKONT/HZPWeILdDVHW76jnhbd3s2JrDbFEEhE4asQgTjtiKNPGljO6oojiwoFVCMmkNScBG1R1E4CIPAhcCKSH+4XADe7tPwN3iYhoFiYyv//++7nzzjszWrcxmqAgIJz6iBMsqXHugSxOP+C1Y8eUM3l4KQvf3sWO+lY+MGUkhw87gonDSvZbT5NJ6mv3sGPnDt7dtoOt296jevt71DbUURtrZuv2ZmTrXoi1IPFmiDUjyUTb8ze6P321yf15ps9bSgv5/QJf0h6SDvd7Z2BfTeCPP3IiEA4EKFBlpSorDuKgZPJOeXWsA22dENio8I+0DYukzzzbve985zt86lOf8qhVncsk3McA76TdrwZO7modVY2LyD5gKLA7fSUR+RLwJfdug4j0yzy4P7zmc8Po0LY8kq/7lq/7Bfm7b/m6X9DHffv0pz/dl9c+LJOVMgn3zv4wdvxDmMk6qOo9wD0ZvGZWicgyVa3q73ZkQ77uW77uF+TvvuXrfkFu7Fsm9YlqYFza/bHAtq7WEZEQUA7s9aKBxhhjei+TcF8KTBaRiSJSCFwMPNphnUeBy9zbnwKezUa93RhjTGZ6LMu4NfS5wJM4QyF/p6qrReQmYJmqPgr8FnhARDbg9NgvzmajPdDvpaEsytd9y9f9gvzdt3zdL8iBfRPrYBtjTP7JnTGBxhhjMmbhbowxech34S4iZ4vIOhHZICLX9Xd7vCIim0XkDRFZJSLL+rs9fSEivxORnSLyZtqyISLytIisd/8d3J9tPBhd7NcNIvKue9xWici5/dnGgyUi40TkORFZKyKrReSr7vKcPm7d7NeAP26+qrm7Uym8TdpUCsCcDlMp5CQR2QxUqWrOXzQiImcADcDvVfVYd9mtwF5VvcX9ozxYVf+zP9vZW13s1w1Ag6re3p9t6ysRGQWMUtUVIlIGLAc+BlxODh+3bvbrMwzw4+a3nnvbVAqqGgVSUymYAURVX+DA6yQuBO53b9+P8x8sp3SxX3lBVber6gr3dj2wFufK9Zw+bt3s14Dnt3DvbCqFnDhQGVDgKRFZ7k7zkG9GqOp2cP7DAcP7uT1emisir7tlm5wqW3RGRCYAJwBLyKPj1mG/YIAfN7+Fe0bTJOSo01R1BnAOcLVbAjAD3y+BScB0YDvw0/5tTt+ISCnwF+BrqlrX3+3xSif7NeCPm9/CPZOpFHKSqm5z/90J/A2nBJVPdrj1z1QddGc/t8cTqrpDVROqmgR+Qw4fNxEpwAnA/1XVv7qLc/64dbZfuXDc/BbumUylkHNEpMQ92YOIlAAfBt7s/lk5J32Ki8uAR/qxLZ5JBZ/r4+TocRNnIv7fAmtV9WdpD+X0cetqv3LhuPlqtAyAO2Tpv2mfSuGH/dykPhORw3F66+BMKTE/l/dLRP4InIkzreoO4PvA34GHgPHAVuDTqppTJye72K8zcT7aK7AZ+PdUjTqXiMjpwCLgDSDpLv4uTn06Z49bN/s1hwF+3HwX7sYY4wd+K8sYY4wvWLgbY0wesnA3xpg8ZOFujDF5yMLdGGPykIW7GVBEJOHOsvemiPyfiFR4vP0zReTUtPtXici/HcR2PpI2I2CDO9PoKhH5vYhUicidXrbbmN6yoZBmQBGRBlUtdW/fD7zt5Zj9bMzCKCLPA99U1ZyeatnkF+u5m4HsZdImdhORb4nIUneyphvTlv/dnTBtdfqkae7c/StE5DURecad+Okq4Fq3lz3bnZf7m+7600XkFXf7f0tNBiUiz4vIT0TkVRF5W0Rmd9do99PBY+7tG0TkfhF5Spw59z8hIreKM/f+E+6l7YjITBFZ6O7Hkx2ugDSm1yzczYDkzr3/QdzpIUTkw8BknDk8pgMz0yZHu0JVZwJVwDUiMlREKnHm/Pikqh6Pc2XkZuBXwB2qOl1VF3V42d8D/6mq03CuSPx+2mMhVT0J+FqH5ZmYBJyHM/3tH4DnVPU4oBk4zw34/wE+5e7H74CcvcLYDAyh/m6AMR0UicgqYALOFyM87S7/sPuz0r1fihP2L+AE+sfd5ePc5ZXAC6r6L4CeLnkXkXKgQlUXuovuBx5OWyU1EdZyt2298biqxkTkDZxpL55wl7/hbuso4FjgaWcqE4I4Mw0ac9As3M1A06yq092wfQy4GrgTZ7rmH6vqr9NXFpEzgQ8Bs1S1ya1/R9z1vTyh1Or+m6D3/29aAVQ1KSIxbT/RlXS3JcBqVZ3lSUuNwcoyZoBS1X3ANcA33bLFk8AV7rzaiMgYERkOlAM1brAfDZzibuJl4H0iMtFdf4i7vB4o6+L1atLq6Z8DFnZcL0vWAZUiMgucKWZF5JhD9NomT1nP3QxYqrpSRF4DLlbVB0RkCvCyW7poAC7FKXFcJSKv44TkK+5zd7knV/8qIgGcecTPAv4P+LOIXAh8pcNLXgb8SkSKgU3A57O+k05boyLyKeBO9xNLCGfm0tWH4vVNfrKhkMYYk4esLGOMMXnIwt0YY/KQhbsxxuQhC3djjMlDFu7GGJOHLNyNMSYPWbgbY0we+v/oIJZOJiF0dwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "from scipy import stats\n",
    "\n",
    "#fitting the exponential distribution\n",
    "ax1 =sns.distplot(df_dis['ReactionTime'].dropna(),fit=stats.expon)\n",
    "plt.title('Fitting Distributions (Exponential)')\n",
    "plt.legend(['Exponential fit', 'Data'])\n",
    "plt.show()\n",
    "\n",
    "#fitting the normal distribution\n",
    "ax2 = sns.distplot(df_dis['ReactionTime'].dropna(),fit=stats.norm, kde=True)\n",
    "plt.title('Fitting Distributions (Normal)')\n",
    "plt.legend(['Normal fit', 'Data'])\n",
    "plt.show()\n",
    "\n",
    "#fitting the weibull_min distribution\n",
    "ax3 = sns.distplot(df_dis['ReactionTime'].dropna(),fit=stats.weibull_min, kde=True)\n",
    "plt.title('Fitting Distributions (Weibull_min)')\n",
    "plt.legend(['weibull_min fit', 'Data'])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the above distribution plots, we can conclude that the reaction time closely follows the $\\bf distribution\\ of\\ exponential\\ and\\ weibull$.\n",
    "\n",
    "Further we observe that the probability that reaction time is less than 3 seconds is high. Therefore, the AVs tend to be safer as they react within a short span of time to externalities that they cannot handle on its own."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average reaction time for the entire duration of the dataset is =  0.9297703252032526\n"
     ]
    }
   ],
   "source": [
    "mean=df_dis['ReactionTime'].mean()\n",
    "print(\"Average reaction time for the entire duration of the dataset is = \", mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Location\n",
       "highway         1.48000\n",
       "urban-street    0.92865\n",
       "Name: ReactionTime, dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_location=df_dis.groupby('Location')['ReactionTime'].mean()\n",
    "mean_location"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$Null\\ Hypothesis\\ (H_o): mean\\ reaction\\ time\\ for\\ humans\\ in\\ non-AV\\ cars\\ = mean\\ reaction\\ time\\ for\\ humans\\ in\\ AV\\ cars$\n",
    "\n",
    "\n",
    "$Alternate\\ Hypothesis\\ (H_a): mean\\ reaction\\ time\\ for\\ humans\\ in\\ non-AV\\ cars\\ \\neq mean\\ reaction\\ time\\ for\\ humans\\ in\\ AV\\ cars$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "reaction_time_non_AV = 1.09 #Given in the question\n",
    "reaction_time_AV = df_dis['ReactionTime'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#importing the library to be used for one-sample t-test\n",
    "from scipy import stats\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Taking onle those rows where the reaction time is not NA\n",
    "df_dis2 = df_dis[np.isfinite(df_dis['ReactionTime'])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=-2.0986037086235854, pvalue=0.03636206696694606)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Performing the one sample t-test using the stats package\n",
    "stats.ttest_1samp(a = np.array(df_dis2['ReactionTime']), popmean = reaction_time_non_AV)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$We\\ can\\ clearly\\ see\\ the\\ the\\ p-value\\ is\\ {\\bf0.03636}\\ which\\ is\\ less\\ than\\ 0.05.$\n",
    "\n",
    "$Therefore,\\ at\\ \\alpha = 0.05, we\\ can\\ reject\\ the\\ null\\ hypothesis\\ and\\ conclude\\ that\\ the\\\\ mean\\ reaction\\ time\\ for\\ humans\\ in\\ non-AV\\ cars\\ \\neq mean\\ reaction\\ time\\ for\\ humans\\ in\\ AV\\ cars$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Frequency')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the histogram of disengagements/mile\n",
    "plt.hist(df_mil['Dis/Mile'], bins = 10, rwidth = 0.6, color = 'darkgreen')\n",
    "plt.title('Histogram of Dis/Mile')\n",
    "plt.xlabel('Dis/Mile')\n",
    "plt.ylabel('Frequency')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above figure represents the histogram of disengagements/mile with monthly granularity. Since, we don't have enough datapoints, it is difficult to plot the probability distribution.\n",
    "\n",
    "Therefore, we have used 'Seaborn' library and its distplot function which plots the probability distribution of sparse data by scaling it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n",
      "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Fitting the Exponential distribution\n",
    "ax=sns.distplot(df_mil['Dis/Mile'].dropna(),fit=stats.expon, kde=False)\n",
    "plt.title('Fitting Distributions (Exponential)')\n",
    "plt.legend(['Exponential fit', 'Data'])\n",
    "plt.show()\n",
    "\n",
    "#Fitting the Normal distribution\n",
    "ax=sns.distplot(df_mil['Dis/Mile'].dropna(),fit=stats.norm, kde=False)\n",
    "plt.title('Fitting Distributions (Normal)')\n",
    "plt.legend(['Normal fit', 'Data'])\n",
    "plt.show()\n",
    "\n",
    "#Fitting the Weibull distribution\n",
    "ax=sns.distplot(df_mil['Dis/Mile'].dropna(),fit=stats.weibull_min, kde=False)\n",
    "plt.title('Fitting Distributions (Weibull)')\n",
    "plt.legend(['weibull fit', 'Data'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see in the above distribution plots that disengagements/mile follows ${\\bf exponential\\ distribution}$ the best.\n",
    "\n",
    "This signifies that the majority of the occurences of disengagements/mile lie in the range of 0 - 0.0050 dis/mile. It is because the number of disengagements/mile decreased exponentially with time, which lead to higher number of occurences in the 0 - 0.0050 dis/mile range and lesser number of occurences in the higher dis/mile range.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\bf{Given\\ Assumptions}$:\n",
    "- There can be at most one disengagement in a mile\n",
    "- A day can be either clear or cloudy, but not both. The probability of a day being clear in California is 72%\n",
    "- The AV is equally likely to drive on a cloudy day as on a clear day"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the above assumption number 2, we can define that $\\bf{P(clear) = 0.72}$ and $\\bf{P(cloudy) = 0.28}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The assumption on maximum number of disengagements in a mile allows us to treat the occurrence of a disengagement in a mile as a random variable with a  $\\bf{Bernoulli}$ distribution  (the number of disengagements per mile takes two values 0 or 1). Sequence of such events is binomially distributed.\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as st"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Disengagements per mile in cloudy conditions\n",
    "total_miles_cloudy = int(round(df_mil['miles driven in autonomous mode'].sum()*0.28,0))\n",
    "prob_diseng_per_mile = 0.5\n",
    "diseng_under_cloudy_conditions = df_dis[df_dis['Weather'] == 'cloudy'].count()[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using the normal approximation:\n",
    "mean_a = total_miles_cloudy*prob_diseng_per_mile\n",
    "variance_a = total_miles_cloudy*prob_diseng_per_mile*(1-prob_diseng_per_mile)\n",
    "prob_a = st.norm(mean_a, variance_a).cdf(diseng_under_cloudy_conditions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of disengagement per mile on a cloudy day is:  0.0241\n"
     ]
    }
   ],
   "source": [
    "print(\"The probability of disengagement per mile on a cloudy day is: \", round(prob_a,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Disengagements per mile in clear conditions\n",
    "total_miles_clear = int(round(df_mil['miles driven in autonomous mode'].sum()*0.72,0))\n",
    "prob_diseng_per_mile = 0.5\n",
    "diseng_under_clear_conditions = df_dis[df_dis['Weather'] == 'clear'].count()[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using the normal approximation:\n",
    "mean_b = total_miles_clear*prob_diseng_per_mile\n",
    "variance_b = total_miles_clear*prob_diseng_per_mile*(1-prob_diseng_per_mile)\n",
    "prob_b = st.norm(mean_b, variance_b).cdf(diseng_under_clear_conditions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of disengagement per mile on a clear day is:  0.0229\n"
     ]
    }
   ],
   "source": [
    "print(\"The probability of disengagement per mile on a clear day is: \", round(prob_b,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the probability of disengagement per mile is higher during cloudy conditions compared to clear conditions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Automatic disengagement per mile on a cloudy day"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Creating a separate dataframe for automatic disengagements:\n",
    "df_dis_automatic = df_dis[df_dis['TypeOfTrigger'] == 'automatic']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculating total miles travelled by the AV in cloudy conditions\n",
    "total_miles_cloudy = int(round(df_mil['miles driven in autonomous mode'].sum()*0.28,0))\n",
    "prob_diseng_per_mile = 0.5\n",
    "diseng_under_cloudy_conditions = df_dis_automatic[df_dis_automatic['Weather'] == 'cloudy'].count()[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using the normal approximation:\n",
    "mean_a = total_miles_cloudy*prob_diseng_per_mile\n",
    "variance_a = total_miles_cloudy*prob_diseng_per_mile*(1-prob_diseng_per_mile)\n",
    "prob_a = st.norm(mean_a, variance_a).cdf(diseng_under_cloudy_conditions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of automatic disengagement per mile on a cloudy day is:  0.0234\n"
     ]
    }
   ],
   "source": [
    "print(\"The probability of automatic disengagement per mile on a cloudy day is: \", round(prob_a,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Automatic disengagement per mile on a clear day\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculating total miles travelled by the AV in clear conditions\n",
    "total_miles_clear = int(round(df_mil['miles driven in autonomous mode'].sum()*0.72,0))\n",
    "prob_diseng_per_mile = 0.5\n",
    "diseng_under_clear_conditions = df_dis_automatic[df_dis_automatic['Weather'] == 'clear'].count()[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using the normal approximation:\n",
    "mean_b = total_miles_clear*prob_diseng_per_mile\n",
    "variance_b = total_miles_clear*prob_diseng_per_mile*(1-prob_diseng_per_mile)\n",
    "prob_b = st.norm(mean_b, variance_b).cdf(diseng_under_clear_conditions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of automatic disengagement per mile on a clear day is:  0.0228\n"
     ]
    }
   ],
   "source": [
    "print(\"The probability of automatic disengagement per mile on a clear day is: \", round(prob_b,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (E)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability that there are more than 150 disengagements in 10000 miles is : 0.9738\n"
     ]
    }
   ],
   "source": [
    "# assuming 10000 Miles are covered in cloudy conditions\n",
    "no_of_miles = 10000\n",
    "no_of_disengagements = 150\n",
    "prob_diseng_per_mile = 0.5\n",
    "mean_c = no_of_miles*prob_diseng_per_mile\n",
    "var_c = no_of_miles*prob_diseng_per_mile*(1-prob_diseng_per_mile)\n",
    "prob_c = 1 - st.norm(mean_c,var_c).cdf(no_of_disengagements)\n",
    "print(\"The probability that there are more than 150 disengagements in 10000 miles is :\", round(prob_c,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given information:\n",
    "\n",
    "$\\alpha$ = 0.05\n",
    "\n",
    "$\\bf{Ask}$: Test the hypothesis that AV has more disengagements on cloudy days than clear days"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\bf{Null\\ hypothesis}$: Disengagements on cloudy days <= Disengagements on clear days\n",
    "\n",
    "$\\bf{Alternate\\ hypothesis}$: Disengagements on cloudy days > Disengagements on clear days"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$z=\\frac{(\\hat{p_1}-\\hat{p_2})-(p_1-p_2)}{\\sqrt{\\hat{p}.(1-\\hat{p}).(\\frac{1}{n_1}+\\frac{1}{n_2})}}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\hat{p}= \\frac{X_1+X_2}{n_1+n_2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculating the parameters which are needed for z-value\n",
    "proportion_clear = df_dis.groupby('Weather').count()['Month'][0]/df_dis.groupby('Weather').count()['Month'].sum()\n",
    "proportion_cloudy = df_dis.groupby('Weather').count()['Month'][1]/df_dis.groupby('Weather').count()['Month'].sum()\n",
    "total_count = df_dis.groupby('Weather').count()['Month'].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculating p_hat for the given data\n",
    "p_hat = (df_dis.groupby('Weather').count()['Month'][0] + df_dis.groupby('Weather').count()['Month'][1]) / \\\n",
    "            (total_count + total_count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The calculated Z_Value is 28.5494\n"
     ]
    }
   ],
   "source": [
    "#Calculating the Z_value\n",
    "z_value = (proportion_cloudy - proportion_clear) / ((p_hat*(1-p_hat)*((1 / total_count) + (1 / total_count)))**0.5)\n",
    "print(\"The calculated Z_Value is\", round(z_value,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6448536269514722"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Checking the Z critical value at alpha = 0.05\n",
    "z_critical = st.norm.ppf(0.95)\n",
    "z_critical"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see that the calculated z-value from the given data is greater than the critical z-value at $\\bf{\\alpha=0.05}$.\n",
    "\n",
    "Therefore, we can reject the null hypothesis and conclude that $\\bf{the\\ number\\ of\\ disengagements\\ on\\ cloudy\\ days\\ is\\ more\\ than\\ the\\ number\\ of\\ disengagements\\ on\\ clear\\ days.}$\n",
    "\n",
    "Also, it is fair to conclude that cloudy weather has severe effect on the safety of AVs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\bf{Using\\ Bayes\\ theorem:}$\n",
    "\n",
    "\n",
    "\\begin{equation*}\n",
    "P(react\\_time>0.5\\ |\\ disengagements\\ occuring\\ in \\ cloudy\\ condition) = \\frac{P(\\ disengagements\\ occuring\\ in \\ cloudy\\ condition\\ |\\ react\\_time>0.5) * P(react\\_time > 0.5)}{P(\\ disengagements\\ occuring \\ in \\ cloudy\\ condition)}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Creating a separate dataframe for automatic disengagements:\n",
    "df_dis_automatic = df_dis[df_dis['TypeOfTrigger'] == 'automatic']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "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>Month</th>\n",
       "      <th>Car</th>\n",
       "      <th>Location</th>\n",
       "      <th>Weather</th>\n",
       "      <th>TypeOfTrigger</th>\n",
       "      <th>ReactionTime</th>\n",
       "      <th>Cause</th>\n",
       "      <th>month</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>837</th>\n",
       "      <td>15-Jul</td>\n",
       "      <td>WDD2221851A001072</td>\n",
       "      <td>urban-street</td>\n",
       "      <td>cloudy</td>\n",
       "      <td>automatic</td>\n",
       "      <td>NaN</td>\n",
       "      <td>System Tuning and Calibration</td>\n",
       "      <td>Jul</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>889</th>\n",
       "      <td>15-Sep</td>\n",
       "      <td>WDD2221851A001072</td>\n",
       "      <td>urban-street</td>\n",
       "      <td>cloudy</td>\n",
       "      <td>automatic</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Unwanted Driver Discomfort</td>\n",
       "      <td>Sep</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Month                Car      Location Weather TypeOfTrigger  \\\n",
       "837  15-Jul  WDD2221851A001072  urban-street  cloudy     automatic   \n",
       "889  15-Sep  WDD2221851A001072  urban-street  cloudy     automatic   \n",
       "\n",
       "     ReactionTime                          Cause month  \n",
       "837           NaN  System Tuning and Calibration   Jul  \n",
       "889           NaN     Unwanted Driver Discomfort   Sep  "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Checking if there are (reaction time) null values in automatic disengagements\n",
    "df_dis_automatic[df_dis_automatic['ReactionTime'].isnull()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Removing the null values from automatic disengagements\n",
    "df_dis_automatic = df_dis_automatic[~df_dis_automatic['ReactionTime'].isnull()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "react_time_gt_05 = df_dis_automatic['ReactionTime'] > 0.5\n",
    "prob_react_time_gt_05 = (df_dis_automatic[react_time_gt_05].count()[5]) /\\\n",
    "(df_dis_automatic.count()[5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Probability of the day being cloudy in California is given as 0.28\n",
    "cloudy = df_dis_automatic['Weather'] == 'cloudy'\n",
    "prob_cloudy = (df_dis_automatic[cloudy].count()[5]) / (df_dis_automatic.count()[4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob_cloudy_given_react_time_gt_05 = \\\n",
    "df_dis_automatic[react_time_gt_05][df_dis_automatic[react_time_gt_05]['Weather'] == 'cloudy'].count()[5]/\\\n",
    "df_dis_automatic[react_time_gt_05].count()[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using Bayes theorem to calculate the needed conditional probability\n",
    "prob_react_time_gt_05_given_cloudy = (prob_cloudy_given_react_time_gt_05 * prob_react_time_gt_05)/prob_cloudy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of reaction time is greater than 0.5 secs given the weather is cloudy is:  0.5418\n"
     ]
    }
   ],
   "source": [
    "print(\"The probability of reaction time is greater than 0.5 secs given the weather is cloudy is: \", round(prob_react_time_gt_05_given_cloudy,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\bf{By\\ Bayes\\ theorem:}$\n",
    "\n",
    "\n",
    "\\begin{equation*}\n",
    "P(react\\_time>0.7\\ |\\ disengagements\\ occuring\\ in \\ clear\\ condition) = \\frac{P(\\ disengagements\\ occuring\\ in \\ clear\\ condition\\ |\\ react\\_time>0.7) * P(react\\_time > 0.7)}{P(\\ disengagements\\ occuring\\ in \\ clear\\ condition)}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "react_time_gt_07 = df_dis_automatic['ReactionTime'] > 0.7\n",
    "prob_react_time_gt_07 = (df_dis_automatic[react_time_gt_07].count()[5]) /\\\n",
    "(df_dis_automatic.count()[5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "clear = df_dis_automatic['Weather'] == 'clear'\n",
    "prob_clear = (df_dis_automatic[clear].count()[5]) / (df_dis_automatic.count()[4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob_clear_given_react_time_gt_07 = \\\n",
    "df_dis_automatic[react_time_gt_07][df_dis_automatic[react_time_gt_07]['Weather'] == 'clear'].count()[5]/\\\n",
    "df_dis_automatic[react_time_gt_07].count()[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using Bayes theorem to calculate the needed conditional probability\n",
    "prob_react_time_gt_07_given_clear = (prob_clear_given_react_time_gt_07 * prob_react_time_gt_07)/prob_clear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of reaction time is greater than 0.7 secs given the weather is clear is:  0.3854\n"
     ]
    }
   ],
   "source": [
    "print(\"The probability of reaction time is greater than 0.7 secs given the weather is clear is: \", round(prob_react_time_gt_07_given_clear,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Calculating the probability of accident under given conditions in cloudy weather"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "total_miles_cloudy = int(round(df_mil['miles driven in autonomous mode'].sum()*0.28,0))\n",
    "total_diseng_react_time_gt_05 = int(df_dis_automatic[react_time_gt_05].count()[5])\n",
    "prob_diseng_per_mile = 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As disengagement/mile follows binomial distribution and the given number of miles travelled by the vehicle is large, we can use normal approximation to calculate the required probability.\n",
    "\n",
    "As we know, the normal approximation for our binomial variable has a mean of $\\bf{np}$ and a standard deviation of $\\bf{\\sqrt{np(1 - p)}}$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The total number of disengagements under cloudy condition given the accident conditions is:  267\n",
      "Total miles covered by the vehicle under cloudy conditions is:  141464\n"
     ]
    }
   ],
   "source": [
    "print(\"The total number of disengagements under cloudy condition given the accident conditions is: \", total_diseng_react_time_gt_05)\n",
    "print(\"Total miles covered by the vehicle under cloudy conditions is: \", total_miles_cloudy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using the normal approximation:\n",
    "mean_a = total_miles_cloudy*prob_diseng_per_mile\n",
    "variance_a = total_miles_cloudy*prob_diseng_per_mile*(1-prob_diseng_per_mile)\n",
    "prob_a = st.norm(mean_a, variance_a).cdf(total_diseng_react_time_gt_05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of accident under given conditions in cloudy weather is:  0.0232\n"
     ]
    }
   ],
   "source": [
    "print(\"The probability of accident under given conditions in cloudy weather is: \", round(prob_a, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Calculating the probability of accident under given conditions in clear weather"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "total_miles_clear = int(round(df_mil['miles driven in autonomous mode'].sum()*0.72,0))\n",
    "total_diseng_react_time_gt_07 = int(df_dis_automatic[react_time_gt_07].count()[5])\n",
    "prob_diseng_per_mile = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The total number of disengagements under cloudy condition given the accident conditions is:  191\n",
      "Total miles covered by the vehicle under cloudy conditions is:  363765\n"
     ]
    }
   ],
   "source": [
    "print(\"The total number of disengagements under cloudy condition given the accident conditions is: \", total_diseng_react_time_gt_07)\n",
    "print(\"Total miles covered by the vehicle under cloudy conditions is: \", total_miles_clear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using the normal approximation:\n",
    "mean_b = total_miles_clear*prob_diseng_per_mile\n",
    "variance_b = total_miles_clear*prob_diseng_per_mile*(1-prob_diseng_per_mile)\n",
    "prob_b = st.norm(mean_b, variance_b).cdf(total_diseng_react_time_gt_07)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of accident under given conditions in clear weather is:  0.0229\n"
     ]
    }
   ],
   "source": [
    "print(\"The probability of accident under given conditions in clear weather is: \", round(prob_b, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Calculating the probability of accident using the theorem of total probability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$P(Accident) = P(Accident|Cloudy) * P(Cloudy) + P(Accident|Clear) * P(Clear)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of accident is:  0.0229\n"
     ]
    }
   ],
   "source": [
    "prob_accident = (prob_a*0.28) +(prob_b*0.72)\n",
    "print(\"The probability of accident is: \", round(prob_accident,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, it is given that the probability of a human driver causing a car accident is $2\\times10^{-6}$. We have found above that AVs display a probability of $\\approx 2\\times10^{-2}$ of causing accidents. This value is significantly higher than that of a human, showing that AVs have a long way to go in terms of safety and performance. AVs are still incapable of reacting faster during adverse external conditions such as Incorrect traffic light detection, adverse road surface conditions etc as compared to humans.   \n",
    "\n",
    "This statistics show that it is relatively more dangerous to give complete control to the AVs without any human supervision. We see that despite having a very low probability for humans, we still witness accidents frequently. So we can deduce that AVs are much more likely to cause severe casualties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Getting rid of month column which we no longer require\n",
    "df_dis = df_dis.drop('month', axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Modifying the dataframe and adding the Class column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculating the number of records:\n",
    "n = len(df_dis)\n",
    "\n",
    "#Defining the list for each classes\n",
    "Controller = ['Incorrect behavior prediction of others', 'Recklessly behaving agent', 'Unwanted Driver Discomfort']\n",
    "Perception_System = ['Adverse road surface conditions', 'Emergency Vehicle', 'Position Estimation Failure', 'Incorrect Traffic Light Detection']\n",
    "Computer_System = ['System Tuning and Calibration', 'Hardware Fault', 'Software Froze']\n",
    "\n",
    "#Defining an empty class list\n",
    "Disengagement_class = list()\n",
    "\n",
    "for i in range(0,n):\n",
    "    if df_dis['Cause'][i] in Controller:\n",
    "        Disengagement_class.append('Controller')\n",
    "    elif df_dis['Cause'][i] in Perception_System:\n",
    "        Disengagement_class.append('Perception System')\n",
    "    elif df_dis['Cause'][i] in Computer_System:\n",
    "        Disengagement_class.append('Computer System')\n",
    "\n",
    "#Adding the Class column to the data frame\n",
    "df_dis['Class'] = Disengagement_class\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Randomly splitting the dataset into training-testing(80-20 split)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Counting the number of records\n",
    "n = len(df_dis)\n",
    "\n",
    "#Defining a serial number list for the dataframe:\n",
    "S_No = np.arange(1,n+1)\n",
    "\n",
    "#Importing random package\n",
    "import random\n",
    "random.seed(2) #Setting the seed to ensure same result is obtained everytime the file is run\n",
    "\n",
    "#Shuffling the list of serial number\n",
    "random.shuffle(S_No)\n",
    "\n",
    "#Assigning the shuffled serial number list to the data frame\n",
    "df_dis['S_No'] = S_No\n",
    "\n",
    "#Sorting the data frame as per the shuffled serial number:\n",
    "df_dis = df_dis.sort_values(by=['S_No'])\n",
    "\n",
    "#Splitting the dataset into training and testing\n",
    "#Also, I'm subsetting the main dataframe and taking the columns required to build the Naive Bayes model\n",
    "disengagement_train = df_dis.iloc[0:820, [2,3,4,7]]\n",
    "disengagement_train = disengagement_train.reset_index()\n",
    "disengagement_train = disengagement_train.drop('index', axis = 1)\n",
    "\n",
    "disengagement_test = df_dis.iloc[820:n, [2,3,4,7]]\n",
    "disengagement_test = disengagement_test.reset_index()\n",
    "disengagement_test = disengagement_test.drop('index', axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Building the Naive Bayes function for our dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Creating a Naive Bayes training function\n",
    "\n",
    "def naive_bayes_training(disengagement_train):\n",
    "    \n",
    "    \"\"\"This is the naive bayes training function which takes the train dataframe as input and\n",
    "    calculate the necessary probabilities required for classifying the class in test dataset\"\"\"\n",
    "    \n",
    "    #Definging the global variables which will be needed in classifying the test set\n",
    "    global prob_controller, prob_perception_system, prob_computer_system, prob_urban_given_controller, prob_highway_given_controller, \\\n",
    "    prob_urban_given_perception_system, prob_highway_given_perception_system, prob_urban_given_computer_system, prob_highway_given_computer_system, \\\n",
    "    prob_clear_given_controller, prob_cloudy_given_controller, prob_clear_given_perception_system, prob_cloudy_given_perception_system, \\\n",
    "    prob_clear_given_computer_system, prob_cloudy_given_computer_system, prob_automatic_given_controller, prob_manual_given_controller, \\\n",
    "    prob_automatic_given_perception_system, prob_manual_given_perception_system, prob_automatic_given_computer_system, prob_manual_given_computer_system\n",
    "    \n",
    "    \n",
    "    #Calculating the total records in the train dataset\n",
    "    total_records = len(disengagement_train)\n",
    "\n",
    "    #Defining the boolean vectors for all classes which I will be using later to calculate different probabilities\n",
    "    controller_bool = disengagement_train['Class'] == 'Controller'\n",
    "    perception_bool = disengagement_train['Class'] == 'Perception System'\n",
    "    computer_bool = disengagement_train['Class'] == 'Computer System'\n",
    "\n",
    "\n",
    "    #from the training data, I first need to calculate the probability of each class separately\n",
    "    prob_controller = disengagement_train[controller_bool].count()[0] / total_records\n",
    "    prob_perception_system = disengagement_train[perception_bool].count()[0] / total_records\n",
    "    prob_computer_system = disengagement_train[computer_bool].count()[0] / total_records\n",
    "\n",
    "    #Calculating conditional probabilites for all features given classes:\n",
    "\n",
    "    #Location\n",
    "    prob_urban_given_controller = list(disengagement_train[controller_bool]['Location']== 'urban-street').count(True) / list(controller_bool).count(True)\n",
    "    prob_highway_given_controller = list(disengagement_train[controller_bool]['Location']== 'highway').count(True) / list(controller_bool).count(True)\n",
    "\n",
    "    prob_urban_given_perception_system = list(disengagement_train[perception_bool]['Location']== 'urban-street').count(True) / list(perception_bool).count(True)\n",
    "    prob_highway_given_perception_system = list(disengagement_train[perception_bool]['Location']== 'highway').count(True) / list(perception_bool).count(True)\n",
    "\n",
    "    prob_urban_given_computer_system = list(disengagement_train[computer_bool]['Location']== 'urban-street').count(True) / list(computer_bool).count(True)\n",
    "    prob_highway_given_computer_system = list(disengagement_train[computer_bool]['Location']== 'highway').count(True) / list(computer_bool).count(True)\n",
    "\n",
    "    #Weather\n",
    "    prob_clear_given_controller = list(disengagement_train[controller_bool]['Weather']== 'clear').count(True) / list(controller_bool).count(True)\n",
    "    prob_cloudy_given_controller = list(disengagement_train[controller_bool]['Weather']== 'cloudy').count(True) / list(controller_bool).count(True)\n",
    "\n",
    "    prob_clear_given_perception_system = list(disengagement_train[perception_bool]['Weather']== 'clear').count(True) / list(perception_bool).count(True)\n",
    "    prob_cloudy_given_perception_system = list(disengagement_train[perception_bool]['Weather']== 'cloudy').count(True) / list(perception_bool).count(True)\n",
    "\n",
    "    prob_clear_given_computer_system = list(disengagement_train[computer_bool]['Weather']== 'clear').count(True) / list(computer_bool).count(True)\n",
    "    prob_cloudy_given_computer_system = list(disengagement_train[computer_bool]['Weather']== 'cloudy').count(True) / list(computer_bool).count(True)\n",
    "\n",
    "    #Type of trigger\n",
    "    prob_automatic_given_controller = list(disengagement_train[controller_bool]['TypeOfTrigger']== 'automatic').count(True) / list(controller_bool).count(True)\n",
    "    prob_manual_given_controller = list(disengagement_train[controller_bool]['TypeOfTrigger']== 'manual').count(True) / list(controller_bool).count(True)\n",
    "\n",
    "    prob_automatic_given_perception_system = list(disengagement_train[perception_bool]['TypeOfTrigger']== 'automatic').count(True) / list(perception_bool).count(True)\n",
    "    prob_manual_given_perception_system = list(disengagement_train[perception_bool]['TypeOfTrigger']== 'manual').count(True) / list(perception_bool).count(True)\n",
    "\n",
    "    prob_automatic_given_computer_system = list(disengagement_train[computer_bool]['TypeOfTrigger']== 'automatic').count(True) / list(computer_bool).count(True)\n",
    "    prob_manual_given_computer_system = list(disengagement_train[computer_bool]['TypeOfTrigger']== 'manual').count(True) / list(computer_bool).count(True)\n",
    "    \n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calling the Naive Bayes training function:\n",
    "naive_bayes_training(disengagement_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Building the Naive Bayes testing function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Creating a Naive Bayes Testing Function:\n",
    "\n",
    "def naive_bayes_testing(test):\n",
    "    \"\"\" This function is to be run after the naive_bayes_train function is run, which trains the model.\n",
    "    This function takes a test dataframe as input which should have three features mainly Location, Weather, and TypeOfTrigger.\n",
    "    This function will give a list of predicted class for each test input\"\"\"\n",
    "\n",
    "    total_test_records = len(test)\n",
    "\n",
    "    #Defining a class predicted list:\n",
    "    global class_predicted\n",
    "    class_predicted = list()\n",
    "\n",
    "    for i in range(0,total_test_records):\n",
    "        #Calculating the probability of class to be Controller\n",
    "        if test['Location'][i] == 'urban-street':\n",
    "            l = prob_urban_given_controller\n",
    "        else:\n",
    "            l = prob_highway_given_controller\n",
    "\n",
    "        if test['Weather'][i] == 'clear':\n",
    "            w = prob_clear_given_controller\n",
    "        else:\n",
    "            w = prob_cloudy_given_controller\n",
    "\n",
    "        if test['TypeOfTrigger'][i] == 'automatic':\n",
    "            t = prob_automatic_given_controller\n",
    "        else:\n",
    "            t = prob_manual_given_controller\n",
    "\n",
    "        total_prob_controller = l * w * t * prob_controller\n",
    "\n",
    "        #Calculating the probability of class to be Perception System\n",
    "        if test['Location'][i] == 'urban-street':\n",
    "            l = prob_urban_given_perception_system\n",
    "        else:\n",
    "            l = prob_highway_given_perception_system\n",
    "\n",
    "        if test['Weather'][i] == 'clear':\n",
    "            w = prob_clear_given_perception_system\n",
    "        else:\n",
    "            w = prob_cloudy_given_perception_system\n",
    "\n",
    "        if test['TypeOfTrigger'][i] == 'automatic':\n",
    "            t = prob_automatic_given_perception_system\n",
    "        else:\n",
    "            t = prob_manual_given_perception_system\n",
    "\n",
    "        total_prob_perception_system = l * w * t * prob_perception_system\n",
    "\n",
    "        #Calculating the probability of class to be Computer System\n",
    "        if test['Location'][i] == 'urban-street':\n",
    "            l = prob_urban_given_computer_system\n",
    "        else:\n",
    "            l = prob_highway_given_computer_system\n",
    "\n",
    "        if test['Weather'][i] == 'clear':\n",
    "            w = prob_clear_given_computer_system\n",
    "        else:\n",
    "            w = prob_cloudy_given_computer_system\n",
    "\n",
    "        if test['TypeOfTrigger'][i] == 'automatic':\n",
    "            t = prob_automatic_given_computer_system\n",
    "        else:\n",
    "            t = prob_manual_given_computer_system\n",
    "\n",
    "        total_prob_computer_system = l * w * t * prob_computer_system\n",
    "\n",
    "        #Using MAP rule to classify the class for the given set of features\n",
    "        max_prob = max([total_prob_controller, total_prob_perception_system, total_prob_computer_system])\n",
    "\n",
    "        if max_prob == total_prob_controller:\n",
    "            class_predicted.append(\"Controller\")\n",
    "        elif max_prob == total_prob_perception_system:\n",
    "            class_predicted.append(\"Perception System\")\n",
    "        else:\n",
    "            class_predicted.append(\"Computer System\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Running the naive bayes testing function on the test dataset:\n",
    "naive_bayes_testing(disengagement_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\bf{Accuracy}$ of the Naive Bayes classifier can be defined as the percentage of correctly predicted classes on the test dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Making the Accuracy function which will calculate the accuracy of each:\n",
    "def naive_bayes_accuracy(test):\n",
    "    \"\"\" This function will return the accuracy of the naive bayes model which was run on the test dataset\"\"\"\n",
    "    global correct_predictions_count\n",
    "    \n",
    "    correct_predictions_count = list(class_predicted == test['Class']).count(True)\n",
    "    test_data_count = len(test)\n",
    "    accuracy = (correct_predictions_count/test_data_count) * 100\n",
    "    return accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The accuracy of the Naive Bayes classifier is: 75.9804%\n"
     ]
    }
   ],
   "source": [
    "print(\"The accuracy of the Naive Bayes classifier is: {a}%\".\\\n",
    "      format(a=round(naive_bayes_accuracy(disengagement_test),4)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Performing 5-Folds cross validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculating the length of dataset:\n",
    "n = len(df_dis)\n",
    "\n",
    "#Creating 5 folds manually\n",
    "fold_1 = df_dis.iloc[0:205, [2,3,4,7]]\n",
    "fold_1 = fold_1.reset_index()\n",
    "fold_1 = fold_1.drop('index', axis = 1)\n",
    "\n",
    "fold_2 = df_dis.iloc[205:410, [2,3,4,7]]\n",
    "fold_2 = fold_2.reset_index()\n",
    "fold_2 = fold_2.drop('index', axis = 1)\n",
    "\n",
    "fold_3 = df_dis.iloc[410:615, [2,3,4,7]]\n",
    "fold_3 = fold_3.reset_index()\n",
    "fold_3 = fold_3.drop('index', axis = 1)\n",
    "\n",
    "fold_4 = df_dis.iloc[615:820, [2,3,4,7]]\n",
    "fold_4 = fold_4.reset_index()\n",
    "fold_4 = fold_4.drop('index', axis = 1)\n",
    "\n",
    "fold_5 = df_dis.iloc[820:n, [2,3,4,7]]\n",
    "fold_5 = fold_5.reset_index()\n",
    "fold_5 = fold_5.drop('index', axis = 1)\n",
    "\n",
    "#Creating an empty Accuracy list where I will store the accuracy for each cross validation:\n",
    "accuracy_NB = list()\n",
    "\n",
    "#Performing Naive Bayes using fold 1 as test and remaining folds as train\n",
    "test = fold_1\n",
    "train = pd.concat([fold_2, fold_3, fold_4, fold_5], axis=0)\n",
    "naive_bayes_training(train)\n",
    "naive_bayes_testing(test)\n",
    "accuracy_NB.append(round(naive_bayes_accuracy(test),4))\n",
    "\n",
    "#Performing Naive Bayes using fold 2 as test and remaining folds as train\n",
    "test = fold_2\n",
    "train = pd.concat([fold_1, fold_3, fold_4, fold_5], axis=0)\n",
    "naive_bayes_training(train)\n",
    "naive_bayes_testing(test)\n",
    "accuracy_NB.append(round(naive_bayes_accuracy(test),4))\n",
    "\n",
    "#Performing Naive Bayes using fold 3 as test and remaining folds as train\n",
    "test = fold_3\n",
    "train = pd.concat([fold_1, fold_2, fold_4, fold_5], axis=0)\n",
    "naive_bayes_training(train)\n",
    "naive_bayes_testing(test)\n",
    "accuracy_NB.append(round(naive_bayes_accuracy(test),4))\n",
    "\n",
    "#Performing Naive Bayes using fold 4 as test and remaining folds as train\n",
    "test = fold_4\n",
    "train = pd.concat([fold_1, fold_2, fold_3, fold_5], axis=0)\n",
    "naive_bayes_training(train)\n",
    "naive_bayes_testing(test)\n",
    "accuracy_NB.append(round(naive_bayes_accuracy(test),4))\n",
    "\n",
    "#Performing Naive Bayes using fold 5 as test and remaining folds as train\n",
    "test = fold_5\n",
    "train = pd.concat([fold_1, fold_2, fold_3, fold_4], axis=0)\n",
    "naive_bayes_training(train)\n",
    "naive_bayes_testing(test)\n",
    "accuracy_NB.append(round(naive_bayes_accuracy(test),4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the accuracy of cross validation\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(10,7))\n",
    "\n",
    "plt.plot(accuracy_NB, marker='o',\\\n",
    "         markerfacecolor='blue', markersize=8, color='skyblue',\\\n",
    "         linewidth=3, linestyle='dashed')\n",
    "plt.ylim([40,100])\n",
    "plt.title(\"Naive Bayes model accuracy in 5-folds cross validation\", fontsize = 15)\n",
    "plt.xlabel(\"Cross validation run\", fontsize = 12)\n",
    "plt.ylabel(\"Accuracy\", fontsize = 12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average accuracy on the Naive Bayes model in 5 folds cross validation is 79.4888%\n"
     ]
    }
   ],
   "source": [
    "print(\"The average accuracy on the Naive Bayes model in 5 folds cross validation is {a}%\".format(a=round(sum(accuracy_NB)/5,4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The accuracy of the random classifier is: 15.1367%\n"
     ]
    }
   ],
   "source": [
    "# Defining an empty class list\n",
    "Disengagement_class_rand = list()\n",
    "\n",
    "# Randomly assign class based on the calculated probability\n",
    "for i in range(0,n):\n",
    "    Disengagement_class_rand.append(np.random.choice(['Controller', 'Perception System', 'Computer System'], p=[prob_controller, prob_perception_system, prob_computer_system]))\n",
    "\n",
    "#Adding the Class random column to the data frame\n",
    "df_dis['Classrand'] = Disengagement_class_rand\n",
    "\n",
    "# Calculating the Accuracy:\n",
    "correct_predictions_rand_count = list(df_dis['Classrand'] == df_dis['Class']).count(True)\n",
    "\n",
    "print(\"The accuracy of the random classifier is: {accr}%\".format(accr=round((correct_predictions_count/n) * 100,4)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NB model performs much better than chance based on our calculation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The assumptions in NB in the context of this problem includes the NB common assumption that the probability of the features are independent. In this case, we assume that location, weather, and type of trigger are conditionally independent. However, this is not realistic because those factors might influence each other such as bad weather may cause an increase chance in manual type of trigger since humans will be more prone to pay more attention to the road."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1- Take into consideration that in reality, features are conditionally dependent (in this particular dataset). In that case, Naive Bayes is not applicable as it violates the original assumption that the features are conditionally independent.\n",
    "\n",
    "Using domain knowledge we know that weather or location may have a significant effect on the type of trigger. So, we calculate the probability of class given its features using the Bayes theorem without assuming the feature independence. Therefore, it will also inlcude terms such as $\\bf{P(Trigger|Weather)}$ and $\\bf{P(Trigger|Location)}$.\n",
    "\n",
    "2- Improvements can be gained in classification accuracy by changing the current method from Naive Bayes to a more sophisticated classification algorithm such as Logistic Regression, Random Forest etc.\n",
    "\n",
    "3- Having more data and features can train the Naive Bayes model better, which may lead to higher accuracy."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}