sem13_bootstrap/sem13_bootstrap_simulations_bonus.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Свойства бутсрапа\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from scipy import stats as sts\n",
    "\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from tqdm import tqdm\n",
    "\n",
    "plt.style.use('ggplot')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Скопируем из лекции функцию для бустрапирования, которую мы написали. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_bootstrap_sample(x, B_sample=1):\n",
    "    N = x.size \n",
    "    sample = np.random.choice(x, size=(N, B_sample), replace=True)\n",
    "    \n",
    "    if B_sample == 1:\n",
    "        sample = sample.T[0]\n",
    "    return sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 1, 4],\n",
       "       [3, 1, 5],\n",
       "       [3, 3, 3],\n",
       "       [3, 2, 4],\n",
       "       [2, 5, 1]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1,2,3,4,5])\n",
    "\n",
    "get_bootstrap_sample(x, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 0. Подготовка\n",
    "\n",
    "Реализуем все три процедуры для строительства доверительного интервала, изученные нами на лекции. Начнём с перцентильного доверительного интервала."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-728a5e22fe1a2dee",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "### ╰( ͡° ͜ʖ ͡° )つ▬▬ι═══════  bzzzzzzzzzz\n",
    "# will the code be with you\n",
    "\n",
    "def quantile_ci(x_boot, alpha=0.05):\n",
    "    ### BEGIN SOLUTION\n",
    "    left = np.quantile(x_boot, alpha/2)\n",
    "    right = np.quantile(x_boot, 1-alpha/2)\n",
    "    ### END SOLUTION\n",
    "    return left, right"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-6c3c44716327f49f",
     "locked": true,
     "points": 0,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# Убедимся, что функция реализована правильно\n",
    "x = np.array([1,2,3,4])\n",
    "l, r = quantile_ci(x)\n",
    "\n",
    "assert np.abs(l - 1.07) < 1e-2\n",
    "assert np.abs(r - 3.92) < 1e-2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь обратный перцентильный доверительный интервал."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-14e45785658fd375",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "### ╰( ͡° ͜ʖ ͡° )つ▬▬ι═══════  bzzzzzzzzzz\n",
    "# will the code be with you\n",
    "\n",
    "def reverse_quantile_ci(x_boot, theta_hat, alpha=0.05):\n",
    "    ### BEGIN SOLUTION\n",
    "    d = x_boot - theta_hat\n",
    "    left = theta_hat - np.quantile(d, 1-alpha/2)\n",
    "    right = theta_hat - np.quantile(d, alpha/2)\n",
    "    ### END SOLUTION\n",
    "    return left, right"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-e55cf45d4ef901a6",
     "locked": true,
     "points": 0,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# Убедимся, что функция реализована правильно\n",
    "l, r = reverse_quantile_ci(x, 2)\n",
    "\n",
    "assert np.abs(l - 0.07) < 1e-2\n",
    "assert np.abs(r - 2.92) < 1e-2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Остался только $t$-перцентильный доверительный интервал."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-67f8e3d93971d6e0",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "### ╰( ͡° ͜ʖ ͡° )つ▬▬ι═══════  bzzzzzzzzzz\n",
    "# will the code be with you\n",
    "\n",
    "def t_ci(x_boot, std_boot, theta_hat, sd_hat, alpha=0.05):\n",
    "    ### BEGIN SOLUTION\n",
    "    d = (x_boot - theta_hat)/std_boot\n",
    "    left = theta_hat - np.quantile(d, 1-alpha/2)*sd_hat\n",
    "    right = theta_hat - np.quantile(d, alpha/2)*sd_hat\n",
    "    ### END SOLUTION\n",
    "    return left, right"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-ce884867876a84df",
     "locked": true,
     "points": 0,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# Убедимся, что функция реализована правильно\n",
    "l, r = t_ci(x, x/10, 2, 2/10)\n",
    "\n",
    "assert np.abs(l - 1.025) < 1e-2\n",
    "assert np.abs(r - 3.85) < 1e-2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Бутстрап для симметричное распределения\n",
    "\n",
    "Давайте сгенерируем $10^4$ раз выборку из симметричного распределения и построим для его среднего разные доверительные интервалы. Для каждого из них оценим, с какой вероятностью интервал действительно накрывает неизвестное среднее. Будем это делать на уровне значимости $5\\%$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100000, 100)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_int = 10**5      # число интервалов \n",
    "sample_size = 100  # размеры выборок\n",
    "\n",
    "rv = sts.uniform(3,2)\n",
    "theta_real = 4     # настоящий параметр\n",
    "\n",
    "# генерируем n_int выборок\n",
    "X = rv.rvs((n_int, sample_size))\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Напишем цикл для эксперимента: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|                                       | 19/100000 [00:00<18:26, 90.33it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quantile: 3.823020299803376 4.038749019138487\n",
      "quantile: 3.8235542344614197 4.039282953796531\n",
      "t-percentile: 3.822961136104111 4.042974025938029\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████| 100000/100000 [19:13<00:00, 86.67it/s]\n"
     ]
    }
   ],
   "source": [
    "B = 10**4 # сколько делть бустрап-выборок\n",
    "\n",
    "# счётчики для проверки как часто мы попали в интервал реальным параметром\n",
    "i_q, i_rq, i_t = 0, 0, 0\n",
    "\n",
    "for i in tqdm(range(n_int)):\n",
    "    x = X[i] # взяли i-ую выборку \n",
    "    \n",
    "    # оценки по выборке \n",
    "    theta_hat, sd_hat = np.mean(x), np.std(x)  \n",
    "    \n",
    "    # бутстрап-статистики \n",
    "    x_boot = get_bootstrap_sample(x, B_sample=B)\n",
    "    std_boot = np.std(x_boot, axis=0)\n",
    "    x_boot = np.mean(x_boot, axis=0)\n",
    "    \n",
    "    # quantile CI\n",
    "    left1, right1 = quantile_ci(x_boot)\n",
    "    i_q += (left1 < theta_real < right1)\n",
    "    \n",
    "    # reverse quantile CI\n",
    "    left2, right2 = reverse_quantile_ci(x_boot, theta_hat)\n",
    "    i_rq += (left2 < theta_real < right2)\n",
    "\n",
    "    # t-percentile CI\n",
    "    left3, right3 = t_ci(x_boot, std_boot, theta_hat, sd_hat)\n",
    "    i_t += (left3 < theta_real < right3)\n",
    "    \n",
    "    # Напечатать интервалы после первой итерации\n",
    "    if i == 0: \n",
    "        print('quantile:', left1, right1)\n",
    "        print('quantile:', left2, right2)\n",
    "        print('t-percentile:', left3, right3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Исходный уровень доверия был $95\\%$. Посмотрим как часто настоящее значение параметра оказывается внутри соотвествующего доверительного интервала. Если способ построения доверительного интервала хороший, полученная в ходе эксперимента частота, должна слабо отличаться от заявленного уровня доверия. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.94703, 0.94417, 0.95381)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i_q/n_int, i_rq/n_int, i_t/n_int"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видим, что доверительные интервалы оказываются похожими, а частота попадания истиного среднего в доверительный интервал близка к $0.95$. То есть уровень значимости близок к $5\\%$. Если сделать больше итераций эксперимента (в районе $10^7$, мы получим числа совсем-совсем близкие к $0.95$. __Все три процедуры бутстрапирования хорошо себя показывают при работе с симметричным распределением.__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Несимметричное распределение \n",
    "\n",
    "Сделаем то же самое для несимметричного случая. Сгенерируйте $10^4$ выборок размера $100$ из экспоненциального распределения со `scale = 20`. Постройте для одной из выборок гистограмму, убедитесь что наше распределение несимметрично относительно нуля и обладает длинным хвостом. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-3708dc179a8575f8",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100000, 100)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### ╰( ͡° ͜ʖ ͡° )つ▬▬ι═══════  bzzzzzzzzzz\n",
    "# will the code be with you\n",
    "\n",
    "### BEGIN SOLUTION\n",
    "n_int = 10**5      # число интервалов \n",
    "sample_size = 100  # размеры выборок\n",
    "\n",
    "#rv = sts.expon(scale=30)\n",
    "rv = sts.chi2(df=1)\n",
    "theta_real = rv.mean()   # настоящий параметр\n",
    "\n",
    "# генерируем n_int выборок\n",
    "X = rv.rvs((n_int, sample_size))\n",
    "X.shape\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(X[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Повторите тот же самый эксперимент, что и выше. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-2382533bfab87032",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|                                       | 16/100000 [00:00<21:28, 77.62it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quantile: 0.7599585133026329 1.2733383735499413\n",
      "quantile: 0.7283267120019936 1.241706572249302\n",
      "t-percentile: 0.7741298303259918 1.323539979806154\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████| 100000/100000 [18:17<00:00, 91.08it/s]\n"
     ]
    }
   ],
   "source": [
    "### ╰( ͡° ͜ʖ ͡° )つ▬▬ι═══════  bzzzzzzzzzz\n",
    "# will the code be with you\n",
    "\n",
    "B = 10**4 # сколько делть бустрап-выборок\n",
    "\n",
    "# счётчики для проверки как часто мы попали в интервал реальным параметром\n",
    "i_q, i_rq, i_t = 0, 0, 0\n",
    "\n",
    "### BEGIN SOLUTION\n",
    "for i in tqdm(range(n_int)):\n",
    "    x = X[i] # взяли i-ую выборку \n",
    "    \n",
    "    # оценки по выборке \n",
    "    theta_hat, sd_hat = np.mean(x), np.std(x)  \n",
    "    \n",
    "    # бутстрап-статистики \n",
    "    x_boot = get_bootstrap_sample(x, B_sample=B)\n",
    "    std_boot = np.std(x_boot, axis=0)\n",
    "    x_boot = np.mean(x_boot, axis=0)\n",
    "    \n",
    "    # quantile CI\n",
    "    left1, right1 = quantile_ci(x_boot)\n",
    "    i_q += (left1 < theta_real < right1)\n",
    "    \n",
    "    # reverse quantile CI\n",
    "    left2, right2 = reverse_quantile_ci(x_boot, theta_hat)\n",
    "    i_rq += (left2 < theta_real < right2)\n",
    "\n",
    "    # t-percentile CI\n",
    "    left3, right3 = t_ci(x_boot, std_boot, theta_hat, sd_hat)\n",
    "    i_t += (left3 < theta_real < right3)\n",
    "    \n",
    "    # Напечатать интервалы после первой итерации\n",
    "    if i == 0: \n",
    "        print('quantile:', left1, right1)\n",
    "        print('quantile:', left2, right2)\n",
    "        print('t-percentile:', left3, right3)\n",
    "### END SOLUTION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Помиотрим на оценку получившихся частот."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.93414, 0.92431, 0.9492)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i_q/n_int, i_rq/n_int, i_t/n_int"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Близкой к 0.95 оказалась только последняя частота. Первые две довольно сильно от неё отличаются. Мы оказываемся в ситуации, когда перцентильный и обратный перцентильные интервалы приводят нас к смещённым оценкам границ доверительного интервала. При этом $t$-процентильный интервал показывает результаты на заявленном уровне доверия. \n",
    "\n",
    "Обратите внимание на границы, которые получились для разных доверительных интервалово. $t$-процентильный интервал уважительнее всего отнесся к тому, что исходное распределение скошено и выдал более далеко расположенные друг от друга критические значения. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Бутсрап? А это точно? \n",
    "\n",
    "Мы сказали с вами, что бутстрап - это асимптотическая техника, которая при больших размерах выборки позволяет получать критические значения. \n",
    "\n",
    "Кроме размера выборки в бутстрапе фигурирует ещё и число испытаний, $B$. С ним связан интересный практический вопрос: как быстро бустрап сходится. Достаточно ли $10000$ испытаний? А достаточно ли $1000$ или $100$? \n",
    "\n",
    "В целом, чем больше тем лучше, но сейчас мы увидим, что даже для оценки CDF распределения верно, что $B_k$ сходится к $B_{\\infty}$ (значение статистики при бесконечном количестве ресемплов) как $\\frac{1}{\\sqrt{n}}$.\n",
    "\n",
    "Смотреть на то, как устроена эта сходимость, будем на треугольном распределении. Так обычно называют сумму двух равномерных случайных величин. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 5000 # размер изначальной выборки\n",
    "X = np.random.uniform(0, 1, size=N) + np.random.uniform(0, 1, size=N)\n",
    "plt.hist(X, bins=100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Это распределение называют треугольным, так как его плотность распределения выглядит как треугольник. Вобьём его функцию распределения. Её можно найти в аналитическом виде. Она будет выглядеть вот так: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def TrueTriangularDistrubition(x):\n",
    "    if x < 0:\n",
    "        return 0\n",
    "    elif x < 1:\n",
    "        return x**2 / 2\n",
    "    elif x < 2:\n",
    "        return 2*x - x**2 / 2 - 1\n",
    "    else:\n",
    "        return 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Давайте сделаем $B=800$ бутсрап-выборок и для каждой из них построим эмпирическую функцию распределения. На этом же графике нарисуем исходную эмпирическую функцию распределения и теоретическую функцию распределения. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(300, 800)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 300 # размер изначальной выборки\n",
    "B = 800 # размер бутстрепной выборки\n",
    "\n",
    "x = np.random.uniform(0, 1, size=N) + np.random.uniform(0, 1, size=N)\n",
    "Xb = get_bootstrap_sample(x, B_sample=B)\n",
    "Xb.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-0000b435be0ffb97",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### ╰( ͡° ͜ʖ ͡° )つ▬▬ι═══════  bzzzzzzzzzz\n",
    "# will the code be with you\n",
    "\n",
    "from statsmodels.distributions.empirical_distribution import ECDF\n",
    "\n",
    "plt.figure(figsize = (16, 8))\n",
    "\n",
    "# CDF для каждого бутстрепной выборки\n",
    "for bootstrap_sample in Xb:\n",
    "    ### BEGIN SOLUTION\n",
    "    ecdf = ECDF(bootstrap_sample)\n",
    "    plt.step(ecdf.x, ecdf.y, alpha = 0.1, color='grey')\n",
    "    ### END SOLUTION\n",
    "    \n",
    "# Настоящая функция распределения\n",
    "xs = np.linspace(0, 2, 100)\n",
    "cdf = [TrueTriangularDistrubition(item) for item in xs]\n",
    "plt.plot(xs, cdf, lw = 3, label='Функция распределения')\n",
    "\n",
    "# эмпирическая функция распределения \n",
    "### BEGIN SOLUTION\n",
    "ecdf = ECDF(x)\n",
    "plt.step(ecdf.x, ecdf.y, lw = 3, label='Эмпирическая функция распределения')\n",
    "### END SOLUTION\n",
    "\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы не знаем теоретической функции распределения на практике. Мы используем эмпирическую функцию распределения, как бутсрап-аналог для реальности. Мы делаем вид, что у нас есть вся генеральная совокупность, а симуляции это наши независимые наблюдения из неё. \n",
    "\n",
    "По картинке видно, что все наши бустрап-выборки вытягиваются именно вдоль эмпирической функции, а не вдоль теоретической. __Мы действуем в предпосылке, что наша выборка хорошо описывает генеральную совокупность.__ Если это не так, мы будем получать неверные выводы.\n",
    "\n",
    "Посмотрим на то, насколько хорошо, в среднем, бустраповыские эмпирические функции распределения, приближают наше исходное, теоретическое, распределение, при разных значениях $B$ (число бутсрап-выборок размера $N$).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|█████████████████████████████████████████| 999/999 [00:20<00:00, 47.68it/s]\n"
     ]
    }
   ],
   "source": [
    "bins = np.linspace(0, 2, N)\n",
    "\n",
    "# Настоящее распределение\n",
    "true_distr = np.array([TrueTriangularDistrubition(item) for item in np.linspace(0, 2, N - 1)])\n",
    "\n",
    "# диапазон количества испытаний для которых будем смотреть на зависимость\n",
    "Bs = np.arange(1, 1000, 1)\n",
    "\n",
    "means = []\n",
    "\n",
    "for B in tqdm(Bs):\n",
    "    # бутстрап выборки\n",
    "    Xb = np.random.choice(x, (B, N), replace=True)\n",
    "    \n",
    "    cdfs = []\n",
    "    for bootstrap_sample in Xb:\n",
    "        \n",
    "        # считаем насколько сильно CDF полученная бутстрапом отличается от настоящей\n",
    "        # bins - те точки, где нам надо считать значения CDF, для удобства они всегда фиксированы\n",
    "        # мы сначала находим гистограмму, а потом считаем по ней кумулятивную сумму, получается ECDF\n",
    "        \n",
    "        cdfs.append(\n",
    "            true_distr - np.cumsum(np.histogram(bootstrap_sample, bins=bins)[0] / N)\n",
    "        )\n",
    "    # считаем среднее отличие по всем B функциям в каждой точке\n",
    "    means.append(np.array(cdfs).mean(axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Внутри вектора `means` записана средняя разница между бустрап-распределениями и теоретической функцией при разных $B$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(999, 299)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "means = np.array(means)\n",
    "means.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Чем больше $B$, тем меньше должна быть эта разница. Тем не менее, объём исходной выборки, $N$, ограничен. То есть рано или поздно мы должны исчерпать повышение качества за счёт увелечиня $B$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(999,)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = means.mean(axis=1) # усредним разницу по всем бинам\n",
    "r.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Если построить график средней ошибки, можно увидеть, что её дисперсия с ростом $B$ становится всё меньше. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Bs[:len(r)], r);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вопрос в том, как именно себя эта дисперсия ведёт. Давайте сгладим ёё. Для этого пройдёмся по полученному вектору ошибок скользящим окном. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def rolling_window(a, window):\n",
    "    shape = a.shape[:-1] + (a.shape[-1] - window + 1, window)\n",
    "    strides = a.strides + (a.strides[-1],)\n",
    "    return np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)\n",
    "\n",
    "# считаем скользящее стандартное отклонение, чтобы получить более гладкий график\n",
    "r = np.std(rolling_window(r, 15), -1)\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.plot(Bs[:len(r)], r)\n",
    "plt.plot(Bs, 1e-2 / np.sqrt(Bs));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Что мы видим? \n",
    "\n",
    "Мы видим, что ошибка постепенно уменьшается. Её стандартное отклонение падает. Причём оно падает как $\\frac{1}{\\sqrt{n}}$. Эта функция нанесена на картинку синим цветом. На практике для бутсрапа рекомендуется использовать размер бутстрепной выборки порядка $10000$ и больше."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Create Assignment",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}