P02 - probability (hypothesis).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "############################# Гипотеза о посещаемости избирательных участков #############################\n",
    "# H0 - данные имеют распределение, отличное от нормального, или \"между данными и распределениеи связи нет\"\n",
    "# H1 - данные имеют нормальное распределение с некоторысми неизвестными параметрами (сложная)\n",
    "##########################################################################################################\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import requests\n",
    "\n",
    "# установите модуль чтения Excel-файлов: pip install xlrd\n",
    "import xlrd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "from scipy.stats import norm, chi2, expon\n",
    "from decimal import Decimal\n",
    "\n",
    "plt.rcParams.update({'font.size': 20})\n",
    "\n",
    "# центр-юг-Волга кроме Москвы\n",
    "center = set([\n",
    "    \"Краснодарский край\",\n",
    "    \"Ставропольский край\",\n",
    "    \"Астраханская область\",\n",
    "    \"Белгородская область\",\n",
    "    \"Брянская область\",\n",
    "    \"Владимирская область\",\n",
    "    \"Волгоградская область\",\n",
    "    \"Вологодская область\",\n",
    "    \"Воронежская область\",\n",
    "    \"Ивановская область\",\n",
    "    \"Калужская область\",\n",
    "    \"Кировская область\",\n",
    "    \"Костромская область\",\n",
    "    \"Курская область\",\n",
    "    \"Липецкая область\",\n",
    "    \"Нижегородская область\",\n",
    "    \"Новгородская область\",\n",
    "    \"Орловская область\",\n",
    "    \"Пензенская область\",\n",
    "    \"Ростовская область\",\n",
    "    \"Рязанская область\",\n",
    "    \"Самарская область\",\n",
    "    \"Саратовская область\",\n",
    "    \"Смоленская область\",\n",
    "    \"Тамбовская область\",\n",
    "    \"Тверская область\",\n",
    "    \"Тульская область\",\n",
    "    \"Ульяновская область\",\n",
    "    \"Ярославская область\"\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "http://www.vybory.izbirkom.ru/servlet/ExcelReportVersion?region=0&sub_region=0&root=1&global=1&vrn=100100084849062&tvd=100100084849066&type=453&vibid=100100084849066&condition=&action=show&version=null&prver=0&sortorder=0\n"
     ]
    }
   ],
   "source": [
    "# скачаем данные о посещаемости избирательных участков\n",
    "url = (\"http://www.vybory.izbirkom.ru/servlet/ExcelReportVersion?\" + \n",
    "            \"region=0&sub_region=0&root=1&global=1&\" + \n",
    "            \"vrn=100100084849062&tvd=100100084849066&\" + \n",
    "            \"type=453&vibid=100100084849066&condition=&\" + \n",
    "            \"action=show&version=null&prver=0&sortorder=0\"\n",
    "      )\n",
    "c = requests.get(url).content\n",
    "print(url)\n",
    "\n",
    "# сохраним их в файл\n",
    "with open('data/votes.xlsx', 'wb') as f:\n",
    "    f.write(c)\n",
    "\n",
    "# откроем\n",
    "rb = xlrd.open_workbook(file_contents=c)\n",
    "sheet = rb.sheet_by_index(0)\n",
    "regions = [sheet.row_values(i)[-5] for i in range(13, 98)]\n",
    "regions_to_take = list(map(lambda r : r in center, regions))\n",
    "\n",
    "# явка к 10 часам\n",
    "data10 = [float(sheet.row_values(i)[-4][:-1]) for i, r in zip(range(13, 98), regions_to_take) if r]\n",
    "# явка к 12 часам\n",
    "data12 = [float(sheet.row_values(i)[-3][:-1]) for i, r in zip(range(13, 98), regions_to_take) if r]\n",
    "# явка к 18 часам\n",
    "data18 = [float(sheet.row_values(i)[-1][:-1]) for i, r in zip(range(13, 98), regions_to_take) if r]\n",
    "data = data12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data - данные, которые мы проверяем на соответствие гипотизе\n",
    "# H1 - гипотеза о распределении\n",
    "# bin_count - сколько столбиков в гистограмме (bin_count - 1 = число степеней свободы)\n",
    "# α - значимость, или, другими словами допустимая вероятность \n",
    "#     ошибки 1 рода - что, приняв гипотезу H1 мы отвергнем корректную H0\n",
    "def test_data(data, H1, bin_count, α = 0.1, verbose = True):\n",
    "    # разложение данных + попадёт на график\n",
    "    h = plt.hist(data, bin_count, color=\"gray\")\n",
    "    h_vals, h_borders = h[0], h[1]\n",
    "    N = len(data)\n",
    "    μ_ = sum(data) / N\n",
    "    σ2_ = sum( (x-μ_) ** 2 for x in data ) / N\n",
    "    if verbose:\n",
    "        print(\"{} значений в интервале {:.2f}-{:.2f}\".format(len(data), h_borders[0], h_borders[-1]))\n",
    "        print('(μ\\', σ2\\') = ({:.3f}, {:.3f})'.format(μ_, σ2_))\n",
    "    \n",
    "    χ2 = chi2(bin_count - 1)\n",
    "    if verbose:\n",
    "        print(\"Для проверки гипотезы используется распределение χ2 c {} степенями свободы\".format(bin_count - 1))\n",
    "    \n",
    "    # критическое значение вычисляется путём применения функции, обратной функции распределения\n",
    "    # такая функция есть, потому что функция распределения χ2 строго возрастающая\n",
    "    χ2α = χ2.ppf(α)\n",
    "    if verbose:\n",
    "        print(\"Критическое значение для α={} и {} степеней свободы равно {:.2f}\".format(\n",
    "            α, bin_count - 1, χ2α\n",
    "        ))\n",
    "\n",
    "    P = []\n",
    "    for i in range(bin_count):\n",
    "        P.append(H1.cdf(h_borders[i+1]) - H1.cdf(h_borders[i]))\n",
    "\n",
    "    P_ = [p * N for p in P]\n",
    "    step = h_borders[1] - h_borders[0]\n",
    "    if verbose:\n",
    "        plt.plot([x + step/2 for x in h_borders[:-1]], P_, color=\"black\", linestyle=\":\", lw=4)\n",
    "        plt.show()\n",
    "    χ2n = Decimal(0.0)\n",
    "    for i in range(bin_count):\n",
    "        # !!! Важно !!! при малых значениях P[i] возможно деление на машинный ноль\n",
    "        # обработаем как-нибудь эту ситуацию\n",
    "        if P[i] == 0.0:\n",
    "            continue\n",
    "        χ2n += Decimal(h_vals[i] / N - P[i]) ** 2 / Decimal(P[i])\n",
    "    χ2n *= Decimal(N)\n",
    "    if verbose:\n",
    "        print('χ2n = {:.3f}'.format(χ2n))\n",
    "    χ2n = float(χ2n)\n",
    "    \n",
    "    p_value = 1 - χ2.cdf(χ2n)\n",
    "    if verbose:\n",
    "        print(\"Вероятность, что если H0 (гипотеза, что связи между данными и распределением нет) верна,\")\n",
    "        print(\"то величина ошибки больше либо равна полученному χ2n: p-value = {:.2f}%.\".format(p_value * 100))\n",
    "        print(\"Чем больше эта вероятность, тем лучше для альтернативной гипотезы H1,\")\n",
    "        print(\"однако, если эта величина близка к 1, данные можно заподозрить в фальсификации.\")\n",
    "    return (χ2n, p_value, bin_count, α, H1)\n",
    "    # NB: Запомните, это абсолютно ничего не говорит о тот, что гипотеза H0 верна!!!\n",
    "    # Да, это сложно принять :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "29 значений в интервале 20.44-34.14\n",
      "(μ', σ2') = (27.772, 11.073)\n",
      "Для проверки гипотезы используется распределение χ2 c 4 степенями свободы\n",
      "Критическое значение для α=0.2 и 4 степеней свободы равно 1.65\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "χ2n = 1.393\n",
      "Вероятность, что если H0 (гипотеза, что связи между данными и распределением нет) верна,\n",
      "то величина ошибки больше либо равна полученному χ2n: p-value = 84.55%.\n",
      "Чем больше эта вероятность, тем лучше для альтернативной гипотезы H1,\n",
      "однако, если эта величина близка к 1, данные можно заподозрить в фальсификации.\n"
     ]
    }
   ],
   "source": [
    "N = len(data)\n",
    "μ_ = sum(data) / N\n",
    "σ2_ = sum( (x-μ_) ** 2 for x in data ) / N\n",
    "\n",
    "H1 = norm(μ_, σ2_ ** .5)\n",
    "_ = test_data(data, H1, 5, 0.20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NormaltestResult(statistic=0.2096711124947861, pvalue=0.9004725875031654)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# конечно же провести тест на нормальное распределение можно и гораздо проще :)\n",
    "# это немного другой тест D'Agostino-Pearson Test:\n",
    "stats.normaltest(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "####################### Гипотеза о времени ответов сервиса #######################################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min = 119.0, Max = 129.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with open('data/times.log', 'r') as f:\n",
    "    # убираем сервисные строчки, приводим к числу и берём первые 100\n",
    "    data = [float(v) for v in f.readlines()[1:-4]][:100]\n",
    "    \n",
    "print(\"Min = {}, Max = {}\".format(min(data), max(data)))\n",
    "# В отличие от предыдущего пример, здесь с числом корзин нужно быть осторожным\n",
    "# Измерения времени дискретные, поэтому нужно сделать так, чтобы они не \"слипались\"\n",
    "bins = 6\n",
    "h = plt.hist(data, bins, color='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 значений в интервале 119.00-129.00\n",
      "(μ', σ2') = (121.210, 4.366)\n",
      "Для проверки гипотезы используется распределение χ2 c 5 степенями свободы\n",
      "Критическое значение для α=0.2 и 5 степеней свободы равно 2.34\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "χ2n = 37.647\n",
      "Вероятность, что если H0 (гипотеза, что связи между данными и распределением нет) верна,\n",
      "то величина ошибки больше либо равна полученному χ2n: p-value = 0.00%.\n",
      "Чем больше эта вероятность, тем лучше для альтернативной гипотезы H1,\n",
      "однако, если эта величина близка к 1, данные можно заподозрить в фальсификации.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "NormaltestResult(statistic=22.320874453814103, pvalue=1.4226029230845182e-05)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# проверка на нормальность!\n",
    "\n",
    "N = len(data)\n",
    "μ_ = sum(data) / N\n",
    "σ2_ = sum( (x-μ_) ** 2 for x in data ) / N\n",
    "\n",
    "H1 = norm(μ_, σ2_ ** .5)\n",
    "test_data(data, H1, bins, 0.2)\n",
    "\n",
    "# или так тоже можно.\n",
    "stats.normaltest(data)\n",
    "\n",
    "# как видно, по обоим тестам гипотеза провалилась - p-value около 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# а может экспоненциальное?\n",
    "results = []\n",
    "# сделаем Grid Search - поиск по сетке параметров.\n",
    "# параметры экспоненциального распределения - смещение и крутизна\n",
    "for d in [x / 10. for x in range(-10, 10)]:\n",
    "    for λ in [x / 100. for x in range(25, 50)]:\n",
    "        loc = d + min(data) # смещение\n",
    "        H1 = expon(scale=1./λ, loc=loc)\n",
    "        r = test_data(data, H1, bins, 0.2, verbose=False)\n",
    "        results.append((*r, d, λ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d = 119.0 + (0.0); λ = 0.4\n",
      "100 значений в интервале 119.00-129.00\n",
      "(μ', σ2') = (121.210, 4.366)\n",
      "Для проверки гипотезы используется распределение χ2 c 5 степенями свободы\n",
      "Критическое значение для α=0.05 и 5 степеней свободы равно 1.15\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "χ2n = 0.819\n",
      "Вероятность, что если H0 (гипотеза, что связи между данными и распределением нет) верна,\n",
      "то величина ошибки больше либо равна полученному χ2n: p-value = 97.58%.\n",
      "Чем больше эта вероятность, тем лучше для альтернативной гипотезы H1,\n",
      "однако, если эта величина близка к 1, данные можно заподозрить в фальсификации.\n"
     ]
    }
   ],
   "source": [
    "best = sorted(results)[0]\n",
    "H, d, λ = best[-3], best[-2], best[-1]\n",
    "print(\"d = {} + ({}); λ = {}\".format(min(data), d, λ))\n",
    "_ = test_data(data, H, bins, 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 значений в интервале 119.00-129.00\n",
      "(μ', σ2') = (121.210, 4.366)\n",
      "Для проверки гипотезы используется распределение χ2 c 5 степенями свободы\n",
      "Критическое значение для α=0.05 и 5 степеней свободы равно 1.15\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "χ2n = 0.819\n",
      "Вероятность, что если H0 (гипотеза, что связи между данными и распределением нет) верна,\n",
      "то величина ошибки больше либо равна полученному χ2n: p-value = 97.58%.\n",
      "Чем больше эта вероятность, тем лучше для альтернативной гипотезы H1,\n",
      "однако, если эта величина близка к 1, данные можно заподозрить в фальсификации.\n"
     ]
    }
   ],
   "source": [
    "# экспоненциально распределение лишь частный случай хи-квадрат expon = chi2(k=2)\n",
    "# попробуем его\n",
    "λ = 0.4 * 2\n",
    "H1 = chi2(2, loc=min(data), scale=1./λ)\n",
    "_ = test_data(data, H1, bins, 0.05)"
   ]
  }
 ],
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