Third_Task.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Проверка статистических гипотез: последовательный критерий Вальда"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для начала импортируем все необходимые для анализа библиотеки:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "import pandas as pd\n",
    "%matplotlib inline\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Пусть в результате экспериментов наблюдаются значения случайной величины: $x_1 , x_2, …,$ которые являются независимыми и одинаково распределенными. Эксперименты продолжаются до тех пор, пока не будет принято решение о виде распределения случайной величины. Объем выборки заранее не известен и определяется в процессе последовательной процедуры.<br>\n",
    "\n",
    "Пусть основная гипотеза о виде распределения случайной величины имеет вид $H_0: f(x) = f_0(x, \\theta),$ где $f(x)$ - функция плотности, а $\\theta$ - известный в случае простой и неизвестный в случае сложной гипотезы параметр распределения. Конкурирующая гипотеза имеет вид $H_1: f(x) = f_1(x, \\theta)$. При проверке сложной гипотезы оценка параметра $\\hat \\theta$ вычисляется по той же выборке, по которой проверяется гипотеза.\n",
    "\n",
    "Последовательный критерий отношения правдоподобия строится сле-\n",
    "дующим образом: сначала выбирают критические границы $c_0$ и $c_1$ ($c_0$ < $c_1$). После наблюдения $x_1$ вычисляют значение статистики критерия:\n",
    "\n",
    "$$\n",
    "\\lambda_1 = ln\\begin{pmatrix}\\frac{L_1(X_1)}{L_0(X_1)}\\end{pmatrix} = ln\\begin{pmatrix}\\frac{f_1(x_1)}{f_0(x_1)}\\end{pmatrix} = ln(f_1(x_1)) - ln(f_0(x_1)),\n",
    "$$\n",
    "\n",
    "где $L_0$ - функция правдоподобия при законе, соответствующем гипотезе $H_0$, $L_1$ - при законе, соответствующем гипотезе $H_1$.\n",
    "\n",
    "Если $\\lambda_1 < c_0$, то принимают гипотезу $H_0$; если $\\lambda_1 > c_1$, то принимают гипотезу $H_1$; если $c_0 < \\lambda_1 < c_1$, то производят второе наблюдение $x_2$ и также исследуют величину:\n",
    "\n",
    "$$\n",
    "\\lambda_1 = ln\\begin{pmatrix}\\frac{L_1(X_2)}{L_0(X_2)}\\end{pmatrix} = ln\\begin{pmatrix}\\frac{f_1(x_1)f_1(x_2)}{f_0(x_1)f_0(x_2)}\\end{pmatrix} = ln(f_1(x_1)f_1(x_2)) - ln(f_0(x_1)f_0(x_2)) = ln(f_1(x_1)) - ln(f_0(x_1)) + ln(f_1(x_2)) - ln(f_0(x_2)).\n",
    "$$\n",
    "\n",
    "С вероятностью, равной единице, процесс оканчивается либо выбором $H_0$, либо $H_1$, т.е. на каком-то шаге $n$ статистика\n",
    "\n",
    "$$\n",
    "\\lambda_n = ln\\begin{pmatrix}\\frac{L_1(X_n)}{L_0(X_n)}\\end{pmatrix} = \\sum_{i=1}^{n} [ln(f_1(x_i)) - ln(f_0(x_i))],\n",
    "$$\n",
    "\n",
    "выйдет за интервал $(c_0,\\ c_1)$.\n",
    "\n",
    "Отсюда первое, что можно определить, это функцию вида:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def lambda_stat(pdf_1, pdf_0):\n",
    "    return math.log(pdf_1) - math.log(pdf_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Величины $c_0$ и $c_1$ определяются из условия, чтобы вероятности ошибок первого и второго рода имели заданные значения $\\alpha$ и $\\beta$. \n",
    "\n",
    "**Теорема:** *Критические значения $c_0$ и $c_1$ критерия Вальда удовлетворяют условиям:*\n",
    "\n",
    "$$c_0 \\geq ln\\begin{pmatrix}\\frac{\\beta}{1 - \\alpha}\\end{pmatrix}, \\ c_1 \\leq ln\\begin{pmatrix}\\frac{1 - \\beta}{\\alpha}\\end{pmatrix}.$$\n",
    "\n",
    "В критерии Вальда критические границы неизвестны, поэтому на практике используют оценки этих границ, которые в явном виде зависят от вероятностей ошибок первого и второго рода. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def c0(alpha, beta):\n",
    "    return math.log(beta/(1 - alpha))\n",
    "\n",
    "def c1(alpha, beta):\n",
    "    return math.log((1 - beta)/alpha)\n",
    "\n",
    "def vald_criterion(rv_1, rv_0, c_0, c_1, sample):\n",
    "    lambda_n = 0\n",
    "    i = 0\n",
    "    while lambda_n >= c_0 and lambda_n <= c_1 and i <= len(sample):\n",
    "        lambda_n += lambda_stat(rv_1.pdf(sample[i]), rv_0.pdf(sample[i]))\n",
    "        i += 1\n",
    "    return (lambda_n, i - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Далее необходимо сгенерировать выборки объема $n$ из нормальных распределений $N(\\mu_0, \\ \\sigma), \\ N(\\mu_1, \\ \\sigma)$, где $\\sigma$ известно, а $\\mu_0, \\ \\mu_1$ - задаваемые параметры:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = 10000\n",
    "\n",
    "sigma = 5\n",
    "\n",
    "mu_0 = 2\n",
    "\n",
    "mu_1 = 1\n",
    "\n",
    "rv_0 = norm(loc=mu_0, scale=sigma)\n",
    "rv_1 = norm(loc=mu_1, scale=sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для моделирования будем использовать значения $\\alpha$ и $\\beta$, равные 0.02 и 0.03 соответственно:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alpha = 0.01\n",
    "beta = 0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь необходимо проводить процедуру накапливания значения $\\lambda_n$ до тех пор пока ее значение не выйдет за границы интервала $(c_0, \\ c_1)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def genearateMeans_0(alpha, beta):\n",
    "    array = [vald_criterion(rv_1, rv_0, c0(alpha, beta), c1(alpha, beta), rv_0.rvs(size=n))[1] for i in range(1000)]\n",
    "    return sum(array)/len(array)\n",
    "def genearateMeans_1(alpha, beta):\n",
    "    array = [vald_criterion(rv_1, rv_0, c0(alpha, beta), c1(alpha, beta), rv_1.rvs(size=n))[1] for i in range(1000)]\n",
    "    return sum(array)/len(array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 20min 12s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "alphas = [0.01, 0.02, 0.03, 0.04, 0.05]\n",
    "betas = [0.01, 0.02, 0.03, 0.04, 0.05]\n",
    "\n",
    "means_0 = [[genearateMeans_0(alpha, beta) for alpha in alphas] for beta in betas]\n",
    "means_1 = [[genearateMeans_1(alpha, beta) for alpha in alphas] for beta in betas]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(768.727,0.5,'Beta')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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0bkEFs1wBTI/xfU5ItjIvshPjfn+XkEDOAK4k3GD4I8JxLCT0/KQ95+5TfkH4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x23f3b4b6080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "means_0 = list(map(lambda x: list(map(math.ceil, x)), means_0))\n",
    "means_1 = list(map(lambda x: list(map(math.ceil, x)), means_1))\n",
    "\n",
    "means_0_df = pd.DataFrame(data=means_0, index=alphas, columns=betas)\n",
    "means_1_df = pd.DataFrame(data=means_1, index=alphas, columns=betas)\n",
    "\n",
    "f, axarr = plt.subplots(1, 2, figsize=(20,10))\n",
    "\n",
    "sns.heatmap(means_0_df, annot=True, fmt=\"d\", linewidths=.5, ax=axarr[0])\n",
    "axarr[0].set_title(\"Среднее количество наблюдений\\n в зависимости от вероятностей ошибок\\n I-го и II-го рода при справедливости нулевой гипотезы\")\n",
    "axarr[0].set_xlabel(\"Alpha\")\n",
    "axarr[0].set_ylabel(\"Beta\")\n",
    "\n",
    "sns.heatmap(means_1_df, annot=True, fmt=\"d\", linewidths=.5, ax=axarr[1])\n",
    "axarr[1].set_title(\"Среднее количество наблюдений\\n в зависимости от вероятностей ошибок\\n I-го и II-го рода при справедливости альтернативной гипотезы\")\n",
    "axarr[1].set_xlabel(\"Alpha\")\n",
    "axarr[1].set_ylabel(\"Beta\")"
   ]
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}