c3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import statistics\n",
    "import numpy as np\n",
    "import scipy.stats \n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Веројатност на петка или глава"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.1171875])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 7,       # петки\n",
    "size = 10,   # вкупно фрлања\n",
    "prob = 0.5   # шансата за петка или глава на фер паричка\n",
    "\n",
    "scipy.stats.binom.pmf(x, size, prob)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.24609375])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 5,       # петки\n",
    "size = 10,   # вкупно фрлања\n",
    "prob = 0.5   # шансата за петка или глава на фер паричка\n",
    "\n",
    "scipy.stats.binom.pmf(x, size, prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Процена со решетка"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# вредности на параметарот кои сакаме да ги евалуираме\n",
    "reshetka = [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]\n",
    "\n",
    "# повторување на пресметувањето за секој од можните вредности на параметарот\n",
    "vozmoznost = []\n",
    "for i in range(0, len(reshetka)):\n",
    "    vozmoznost.append(scipy.stats.binom.pmf(67, 100, reshetka[i]))\n",
    "\n",
    "# конвертирај ги листите во np.array\n",
    "reshetka = np.array(reshetka)\n",
    "vozmoznost = np.array(vozmoznost)\n",
    "\n",
    "\n",
    "# сега правиме графикон од резултатите\n",
    "plt.plot(reshetka, vozmoznost, marker='.')\n",
    "#plt.bar(reshetka, vozmoznost, width=.08)\n",
    "#plt.gca().set(xticks=reshetka, xlim=(0, 1))\n",
    "plt.show\n",
    "\n",
    "fig, axes = plt.subplots(1, 2)\n",
    "axes[0].plot(reshetka, vozmoznost, marker='.')\n",
    "axes[1].bar(reshetka, vozmoznost, width=.08)\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Баесово ажурирање"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "prethodni_verojatnosti = np.repeat(1, len(reshetka))\n",
    "posteriorni_verojatnosti = prethodni_verojatnosti * vozmoznost\n",
    "posteriorni_verojatnosti = posteriorni_verojatnosti / sum(posteriorni_verojatnosti)\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(1, 2)\n",
    "axes[0].plot(reshetka, prethodni_verojatnosti, marker='.')\n",
    "axes[1].plot(reshetka, posteriorni_verojatnosti, marker='.')\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6899807280766883"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(posteriorni_verojatnosti)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "prethodni_verojatnosti = np.array([0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0])\n",
    "posteriorni_verojatnosti = prethodni_verojatnosti * vozmoznost\n",
    "posteriorni_verojatnosti = posteriorni_verojatnosti / sum(posteriorni_verojatnosti)\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(1, 2)\n",
    "axes[0].plot(reshetka, prethodni_verojatnosti, marker='.')\n",
    "axes[1].plot(reshetka, posteriorni_verojatnosti, marker='.')\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6956783613104962"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(posteriorni_verojatnosti)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Примероци од постериорната дистрибуција"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2733e3f340>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Креираме вектор можни вредности на параметарот за проценка со решетка\n",
    "# Сакаме да ја најдеме вредноста која ја максимизира можноста\n",
    "p_grid = np.linspace(0, 1, num = 1000)\n",
    "\n",
    "# Користиме униформна приорна дистрибуција\n",
    "# Вектор со илјада единици за секој елемент на мрежата\n",
    "prior = np.repeat(1, 1000)\n",
    "\n",
    "likelihood = scipy.stats.binom.pmf(6, 9,  p_grid ) # 6 W; 3 L\n",
    "\n",
    "posterior = likelihood * prior \n",
    "# Стандардизираме\n",
    "posterior = posterior / sum(posterior) \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(1, 1)\n",
    "axes.plot(p_grid, posterior)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = np.random.choice( p_grid,  # можните вредности на параметарот\n",
    "                   size = int(1e4),  # колку вредности да извлечеме (мора int() бидејќи 1e4 по default е float)\n",
    "                   replace = True,   # со замена \n",
    "                   p = posterior     # веројантоста со која секоја вредност ќе биде извлечена\n",
    "                   )\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([   4.,   48.,  273.,  682., 1291., 2117., 2316., 2024., 1047.,\n",
       "         198.]),\n",
       " array([0.0970971 , 0.18458458, 0.27207207, 0.35955956, 0.44704705,\n",
       "        0.53453453, 0.62202202, 0.70950951, 0.796997  , 0.88448448,\n",
       "        0.97197197]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ht5c0/HW7U4gkSY3xEJAkNcoAkKRGGQCS1CgDQJIaZQBIUqMMAElqlAEgSY36P5rboe5nI+32AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 1)\n",
    "axes.hist(samples)"
   ]
  }
 ],
 "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": "3.8.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}