Posterior Probability.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import random\n",
    "import sys\n",
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "def plot_normal(gloc, gscale):\n",
    "    x = np.linspace(0,10,1000)\n",
    "    y = norm.pdf(x, loc=gloc, scale=gscale)    # for example\n",
    "    plt.plot(x,y)\n",
    "    axes = plt.gca()\n",
    "    axes.set_ylim([0,0.6])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "pi_1 = 0.3\n",
    "pi_2 = 0.7\n",
    "\n",
    "# assume normal distribution\n",
    "x_c2_mu = 4.5\n",
    "x_c2_sigma = 0.9\n",
    "x_c1_mu = 7.0\n",
    "x_c1_sigma = 1.2\n",
    "\n",
    "x_obs = 5.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,10,1000)\n",
    "y1 = norm.pdf(x, loc=x_c1_mu, scale=x_c1_sigma)\n",
    "y2 = norm.pdf(x, loc=x_c2_mu, scale=x_c2_sigma)\n",
    "plt.plot(x,y1)\n",
    "plt.plot(x,y2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.046, 0.167)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior_c1 = round(scipy.stats.norm(x_c1_mu, x_c1_sigma).pdf(x_obs)*pi_1,3)\n",
    "posterior_c2 = round(scipy.stats.norm(x_c2_mu, x_c2_sigma).pdf(x_obs)*pi_2,3)\n",
    "posterior_c1, posterior_c2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if(posterior_c1 > posterior_c2):\n",
    "    predicted_c = 1\n",
    "else:\n",
    "    predicted_c = 2\n",
    "predicted_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decision boundary 6.05\n"
     ]
    }
   ],
   "source": [
    "for val in np.arange(0.0, 10.0, 0.01):\n",
    "    posterior_c1 = round(scipy.stats.norm(x_c1_mu, x_c1_sigma).pdf(val)*pi_1,3)\n",
    "    posterior_c2 = round(scipy.stats.norm(x_c2_mu, x_c2_sigma).pdf(val)*pi_2,3)\n",
    "    if(posterior_c1 > posterior_c2):\n",
    "        print(\"Decision boundary\",val)\n",
    "        break"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49"
  },
  "kernelspec": {
   "display_name": "Python 3.9.7 64-bit",
   "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": "3.9.7"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}