NaiveBayes.ipynb

{
 "cells": [
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "P(D) is the probability of a person having Diabetes. It's value is 0.01 or in other words, 1% of the general population has diabetes(Disclaimer: these values are assumptions and are not reflective of any medical study).\n",
    "\n",
    "P(Pos) is the probability of getting al positive test result.\n",
    "\n",
    "P(Neg) is the probability of getting a negative test result.\n",
    "\n",
    "P(Pos|D) is the probability of getting a positive result on a test done for detecting diabetes, given that you have diabetes. This has a value 0.9. In other words the test is correct 90% of the time. This is also called the Sensitivity or True Positive Rate.\n",
    "\n",
    "P(Neg|~D) is the probability of getting a negative result on a test done for detecting diabetes, given that you do not have diabetes. This also has a value of 0.9 and is therefore correct, 90% of the time. This is also called the Specificity or True Negative Rate.\n",
    "\n",
    "The Bayes formula is as follows:\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "P(A) is the prior probability of A occuring independantly. In our example this is P(D). This value is given to us.\n",
    "\n",
    "P(B) is the prior probability of B occuring independantly. In our example this is P(Pos).\n",
    "\n",
    "P(A|B) is the posterior probability that A occurs given B. In our example this is P(D|Pos). That is, the probability of an individual having diabetes, given that, that individual got a positive test result. This is the value that we are looking to calculate.\n",
    "\n",
    "P(B|A) is the likelihood probability of B occuring, given A. In our example this is P(Pos|D). This value is given to us.\n",
    "\n",
    "Putting our values into the formula for Bayes theorem we get:\n",
    "\n",
    "P(D|Pos) = (P(D) * P(Pos|D) / P(Pos)\n",
    "\n",
    "The probability of getting a positive test result P(Pos) can be calulated using the Sensitivity and Specificity as follows:\n",
    "\n",
    "P(Pos) = [P(D) * Sensitivity] + [P(~D) * (1-Specificity))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('The probability of getting a positive test result P(Pos) is: {}', '0.108')\n"
     ]
    }
   ],
   "source": [
    "# P(D)\n",
    "p_diabetes = 0.01\n",
    "\n",
    "# P(~D)\n",
    "p_no_diabetes = 0.99\n",
    "\n",
    "# Sensitivity or P(Pos|D)\n",
    "p_pos_diabetes = 0.9\n",
    "\n",
    "# Specificity or P(Neg/~D)\n",
    "p_neg_no_diabetes = 0.9\n",
    "\n",
    "# P(Pos)\n",
    "p_pos = (p_diabetes * p_pos_diabetes) + (p_no_diabetes * (1 - p_neg_no_diabetes))\n",
    "print('The probability of getting a positive test result P(Pos) is: {}',format(p_pos))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Using all of this information we can calculate our posteriors as follows: **\n",
    "\n",
    "The probability of an individual having diabetes, given that, that individual got a positive test result:\n",
    "\n",
    "P(D/Pos) = (P(D) * Sensitivity)) / P(Pos)\n",
    "\n",
    "The probability of an individual not having diabetes, given that, that individual got a positive test result:\n",
    "\n",
    "P(~D/Pos) = (P(~D) * (1-Specificity)) / P(Pos)\n",
    "\n",
    "The sum of our posteriors will always equal 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Probability of an individual having diabetes, given that that individual got a positive test result is:', '0.0833333333333')\n"
     ]
    }
   ],
   "source": [
    "'''\n",
    "Instructions:\n",
    "Compute the probability of an individual having diabetes, given that, that individual got a positive test result.\n",
    "In other words, compute P(D|Pos).\n",
    "\n",
    "The formula is: P(D|Pos) = (P(D) * P(Pos|D) / P(Pos)\n",
    "'''\n",
    "\n",
    "# P(D|Pos)\n",
    "p_diabetes_pos = (p_diabetes * p_pos_diabetes) / p_pos\n",
    "print('Probability of an individual having diabetes, given that that individual got a positive test result is:\\\n",
    "',format(p_diabetes_pos)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of an individual not having diabetes, given that that individual got a positive test result is: 0.916666666667\n"
     ]
    }
   ],
   "source": [
    "'''\n",
    "Instructions:\n",
    "Compute the probability of an individual not having diabetes, given that, that individual got a positive test result.\n",
    "In other words, compute P(~D|Pos).\n",
    "\n",
    "The formula is: P(~D|Pos) = (P(~D) * P(Pos|~D) / P(Pos)\n",
    "\n",
    "Note that P(Pos/~D) can be computed as 1 - P(Neg/~D). \n",
    "\n",
    "Therefore:\n",
    "P(Pos/~D) = p_pos_no_diabetes = 1 - 0.9 = 0.1\n",
    "'''\n",
    "\n",
    "# P(Pos/~D)\n",
    "p_pos_no_diabetes = 0.1\n",
    "\n",
    "# P(~D|Pos)\n",
    "p_no_diabetes_pos = (p_no_diabetes * p_pos_no_diabetes) / p_pos\n",
    "print 'Probability of an individual not having diabetes, given that that individual got a positive test result is:'\\\n",
    ",p_no_diabetes_pos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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