C1/L7_bernoulli_binomial.ipynb

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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "import pandas as pd \n",
    "from collections import defaultdict\n",
    "\n",
    "import sys\n",
    "sys.path.insert(0, '..')\n",
    "from utils.plot_lib import set_default\n",
    "\n",
    "set_default(figsize=(6, 4))"
   ]
  },
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   "source": [
    "Suppose we are giving two students a multiple-choice exam with 40 questions, \n",
    "where each question has four choices. We don't know how much the students\n",
    "have studied for this exam, but we think that they will do better than just\n",
    "guessing randomly.\n",
    "\n",
    "1. What are the parameters of interest?\n",
    "2. What is our likelihood?\n",
    "3. What prior should we use?\n",
    "4. What is the prior probability P(theta>.25)? P(theta>.5)? P(theta>.8)?\n",
    "5. Suppose the first student gets 33 questions right. What is the posterior\n",
    "   distribution for theta1? P(theta1>.25)? P(theta1>.5)? P(theta1>.8)?\n",
    "   What is a 95% posterior credible interval for theta1?\n",
    "6. Suppose the second student gets 24 questions right. What is the posterior\n",
    "   distribution for theta2? P(theta2>.25)? P(theta2>.5)? P(theta2>.8)?\n",
    "   What is a 95% posterior credible interval for theta2?\n",
    "7. What is the posterior probability that theta1>theta2, i.e., that the \n",
    "   first student has a better chance of getting a question right than\n",
    "   the second student?"
   ],
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   "source": [
    "### Solutions\n",
    "\n",
    "1.  Parameters of interest are $theta1=true$ probability the first student\n",
    "    will answer a question correctly, and $theta2=true$ probability the second\n",
    "    student will answer a question correctly.\n",
    "\n",
    "\n",
    "2.  Likelihood is Binomial(40, theta), if we assume that each question is \n",
    "    independent and that the probability a student gets each question right \n",
    "    is the same for all questions for that student.\n",
    "\n",
    "3.  The conjugate prior is a beta prior. Plot the density with python."
   ],
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   "cell_type": "code",
   "execution_count": 2,
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   "source": [
    "from scipy.stats import beta\n",
    "\n",
    "n = 40\n",
    "theta = np.arange(0, 1, 0.01)"
   ]
  },
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   "cell_type": "code",
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "a, b = 1, 1 # Prio mean of 1 alpha / alpha +  eta\n",
    "rv = beta(a, b)\n",
    "pdf_val = rv.pdf(theta)\n",
    "\n",
    "plt.plot(theta, pdf_val, label = 'Beta function')\n",
    "plt.legend()\n",
    "plt.title('Beta function with a = {} and b = {}'.format(a, b))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 600x400 with 1 Axes>",
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     },
     "metadata": {}
    }
   ],
   "source": [
    "a, b = 4, 2 # Prio mean of 2 / 3\n",
    "rv = beta(a, b)\n",
    "pdf_val = rv.pdf(theta)\n",
    "\n",
    "plt.plot(theta, pdf_val, label = 'Beta function')\n",
    "plt.legend()\n",
    "plt.title('Beta function with a = {} and b = {}'.format(a, b))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "a, b = 8, 4 # Prio mean of 2 / 3\n",
    "rv = beta(a, b)\n",
    "pdf_val = rv.pdf(theta)\n",
    "\n",
    "plt.plot(theta, pdf_val, label = 'Beta function')\n",
    "plt.legend()\n",
    "plt.title('Beta function with a = {} and b = {}'.format(a, b))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "4. Find probabilities using cumulative density function"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The probability with theta = 0.25 is P = 0.9988117218017578\nThe probability with theta = 0.5 is P = 0.88671875\nThe probability with theta = 0.75 is P = 0.2866954803466797\n"
     ]
    }
   ],
   "source": [
    "a, b = 8, 4 # Prio mean of 2 / 3\n",
    "rv = beta(a, b)\n",
    "theta1, theta2, theta3 = 0.25, 0.5, 0.75\n",
    "prob1 = 1 - rv.cdf(theta1)\n",
    "print('The probability with theta = {} is P = {}'.format(theta1, prob1))\n",
    "prob2 = 1 - rv.cdf(theta2)\n",
    "print('The probability with theta = {} is P = {}'.format(theta2, prob2))\n",
    "prob3 = 1 - rv.cdf(theta3)\n",
    "print('The probability with theta = {} is P = {}'.format(theta3, prob3))"
   ]
  },
  {
   "source": [
    "5. Considering that first student gets 33 questions right, what is the posterior for theta1. Posterior    is Beta(8+33,4+40-33) = Beta(41,11)\n",
    "\n",
    "Recall that: \n",
    "\n",
    "$Posterior = Beta(\\alpha + \\sum y_i, \\beta + n - \\sum y_i) $\n",
    "\n",
    "$ Posterior  = Beta(8+33,4+40-33) = Beta(41,11) $"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The posterior mean is: 0.7884615384615384\nThe optimal value of Theta MLE is: 0.825\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 600x400 with 1 Axes>",
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "# Params\n",
    "sum_y = 33\n",
    "n = 40\n",
    "a, b = 41, 11\n",
    "post_mean = 41 / (41 + 11)\n",
    "print('The posterior mean is: {}'.format(post_mean))\n",
    "MLE = 33 / 40\n",
    "print('The optimal value of Theta MLE is: {}'.format(MLE))\n",
    "# Density function (betta) posterior\n",
    "rv = beta(a, b)\n",
    "pdf_val = rv.pdf(theta)\n",
    "# Density function (betta) prior\n",
    "a_p, b_p = 8, 4\n",
    "rv_pr = beta(a_p, b_p)\n",
    "pdf_val_pr = rv_pr.pdf(theta)\n",
    "# Likelihood\n",
    "rv_like = binom(n, theta)\n",
    "pdf_val_like = rv_like.pmf(33)\n",
    "\n",
    "plt.plot(theta, pdf_val, label = 'Beta function posterior')\n",
    "plt.plot(theta, pdf_val_pr, '--', label = 'Beta function prior')\n",
    "# 44 * pdf_val_like is for skiling purpose.\n",
    "plt.plot(theta, 44*pdf_val_like, '--', label = 'Likelihood function')\n",
    "plt.legend()\n",
    "plt.title('Beta function with a = {} and b = {}'.format(a, b))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "It is possible to see how the posterior is more prone to the likelihood rather than the prior! Likelihood is at a different scale as this is not a PMF. This is due to the efective sample size of the likelihood which is of 40 compared with the effective sample size of the prior which is of 11. The likelihood is more important.\n",
    "\n",
    "Now lets compute the posterior probabilities."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The probability with theta = 0.25 is P = 0.9999999999999999\nThe probability with theta = 0.5 is P = 0.9999926311420575\nThe probability with theta = 0.8 is P = 0.44440438256879644\n"
     ]
    }
   ],
   "source": [
    "a, b = 41, 11\n",
    "rv = beta(a, b)\n",
    "theta1, theta2, theta3 = 0.25, 0.5, 0.8\n",
    "prob1 = 1 - rv.cdf(theta1)\n",
    "print('The probability with theta = {} is P = {}'.format(theta1, prob1))\n",
    "prob2 = 1 - rv.cdf(theta2)\n",
    "print('The probability with theta = {} is P = {}'.format(theta2, prob2))\n",
    "prob3 = 1 - rv.cdf(theta3)\n",
    "print('The probability with theta = {} is P = {}'.format(theta3, prob3))"
   ]
  },
  {
   "source": [
    "With a equal-tailed 95% credible interval"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The value of theta for a 0.95 equal tailed interval between 0.6688426487470713 and 0.8871094002502565\n"
     ]
    }
   ],
   "source": [
    "# 95% interval\n",
    "q1 = rv.ppf(0.025)\n",
    "q2 = rv.ppf(0.975)\n",
    "print('The value of theta for a 0.95 equal tailed interval between {} and {}'.format(q1, q2))"
   ]
  },
  {
   "source": [
    "Therefore, most of the mass of theta is between 0.66 and 0.88. Consistent with the plot above."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "6. Considering that second student gets 24 questions right, what is the posterior for theta1. Posterior    is Beta(8+24,4+40-24) = Beta(32,20)\n",
    "\n",
    "Recall that: \n",
    "\n",
    "$Posterior = Beta(\\alpha + \\sum y_i, \\beta + n - \\sum y_i) $\n",
    "\n",
    "$ Posterior  = Beta(8+24,4+40-24) = Beta(32,20) $"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The posterior mean is: 0.6153846153846154\nThe optimal value of Theta MLE is: 0.6\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 600x400 with 1 Axes>",
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "# Params\n",
    "sum_y = 24\n",
    "n = 40\n",
    "a, b = 32, 20\n",
    "post_mean = a / (a + b)\n",
    "print('The posterior mean is: {}'.format(post_mean))\n",
    "MLE = sum_y / n\n",
    "print('The optimal value of Theta MLE is: {}'.format(MLE))\n",
    "# Density function (betta) posterior\n",
    "rv = beta(a, b)\n",
    "pdf_val = rv.pdf(theta)\n",
    "# Density function (betta) prior\n",
    "a_p, b_p = 8, 4\n",
    "rv_pr = beta(a_p, b_p)\n",
    "pdf_val_pr = rv_pr.pdf(theta)\n",
    "# Likelihood\n",
    "rv_like = binom(n, theta)\n",
    "pdf_val_like = rv_like.pmf(sum_y)\n",
    "\n",
    "plt.plot(theta, pdf_val, label = 'Beta function posterior')\n",
    "plt.plot(theta, pdf_val_pr, '--', label = 'Beta function prior')\n",
    "# 44 * pdf_val_like is for skiling purpose.\n",
    "plt.plot(theta, 44*pdf_val_like, '--', label = 'Likelihood function')\n",
    "plt.legend()\n",
    "plt.title('Beta function with a = {} and b = {}'.format(a, b))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The probability with theta = 0.25 is P = 0.9999999863130408\nThe probability with theta = 0.5 is P = 0.9540427250920729\nThe probability with theta = 0.8 is P = 0.001248189858039872\n"
     ]
    }
   ],
   "source": [
    "a, b = 32, 20\n",
    "rv = beta(a, b)\n",
    "theta1, theta2, theta3 = 0.25, 0.5, 0.8\n",
    "prob1 = 1 - rv.cdf(theta1)\n",
    "print('The probability with theta = {} is P = {}'.format(theta1, prob1))\n",
    "prob2 = 1 - rv.cdf(theta2)\n",
    "print('The probability with theta = {} is P = {}'.format(theta2, prob2))\n",
    "prob3 = 1 - rv.cdf(theta3)\n",
    "print('The probability with theta = {} is P = {}'.format(theta3, prob3))"
   ]
  },
  {
   "source": [
    "With a equal-tailed 95% credible interval"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The value of theta for a 0.95 equal tailed interval between 0.4808021582419634 and 0.7415563647178172\n"
     ]
    }
   ],
   "source": [
    "# 95% interval\n",
    "q1 = rv.ppf(0.025)\n",
    "q2 = rv.ppf(0.975)\n",
    "print('The value of theta for a 0.95 equal tailed interval between {} and {}'.format(q1, q2))"
   ]
  },
  {
   "source": [
    "The results are consistent as the second student did not get as many questions good as the first student."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "7. Estimate by simulation: draw 1,000 samples from each and see how often \n",
    "   we observe theta1>theta2"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The mean value that theta1 is greather than theta2 is 0.968\n"
     ]
    }
   ],
   "source": [
    "beta_1 = beta.rvs(41, 11, size=1000)\n",
    "beta_2 = beta.rvs(32, 20, size=1000)\n",
    "mean_val = np.mean(beta_1 > beta_2)\n",
    "print('The mean value that theta1 is greather than theta2 is {}'.format(mean_val))"
   ]
  }
 ]
}