Lecture 2. Stat power.ipynb

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   "source": [
    "# Лекция 2. Введение в статистику."
   ]
  },
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   "source": [
    "from scipy.stats import (\n",
    "    binom\n",
    ")\n",
    "import numpy as numpy\n",
    "from seaborn import distplot\n",
    "from matplotlib import pyplot\n",
    "import seaborn\n",
    "import random\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "import sys\n",
    "sys.path.append('.')"
   ]
  },
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   "execution_count": 3,
   "id": "39c02b52-7849-4b2f-8321-9ef40cc35ed3",
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   "source": [
    "def inverse_plot_colorscheme():\n",
    "    import cycler\n",
    "    def invert(color_to_convert): \n",
    "        table = str.maketrans('0123456789abcdef', 'fedcba9876543210')\n",
    "        return '#' + color_to_convert[1:].lower().translate(table).upper()\n",
    "    update_dict = {}\n",
    "    for key, value in pyplot.rcParams.items():\n",
    "        if value == 'black':\n",
    "            update_dict[key] = 'white'\n",
    "        elif value == 'white':\n",
    "            update_dict[key] = 'black'\n",
    "    \n",
    "    old_cycle = pyplot.rcParams['axes.prop_cycle']\n",
    "    new_cycle = []\n",
    "    for value in old_cycle:\n",
    "        new_cycle.append({\n",
    "            'color': invert(value['color'])\n",
    "        })\n",
    "    pyplot.rcParams.update(update_dict)\n",
    "    pyplot.rcParams['axes.prop_cycle'] = cycler.Cycler(new_cycle)\n",
    "    lec = pyplot.rcParams['legend.edgecolor']\n",
    "    lec = str(1 - float(lec))\n",
    "    pyplot.rcParams['legend.edgecolor'] = lec"
   ]
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   "execution_count": 4,
   "id": "3b784c12-d5bd-41e8-a326-ac307f35d432",
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   "outputs": [],
   "source": [
    "inverse_plot_colorscheme()"
   ]
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   "source": [
    "______\n",
    "\n"
   ]
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   "source": [
    "## Часть 1. Статистическая мощность\n",
    "\n",
    "### Ошибка False Negative\n",
    "\n",
    "На прошлом занятии при построении критериев мы обращали внимание только на $\\alpha$, уровень значимости критерия. Но этот параметр контролирует лишь ошибку False Positive, а именно вероятность, что критерий выдаст 1 (примет $\\mathsf{H}_1$ и отвергнет $\\mathsf{H}_0$), когда правильный ответ &mdash; 0 (верна $\\mathsf{H}_0$).\n",
    "\n",
    "Уже в части 2 на прошлом уроке было введено понятие ошибки False Negative, а именно выдача 0, когда верный ответ &mdash; 1.\n",
    "\n",
    "Случай, когда вероятность FPR $< \\alpha$, но при этом вероятность False Negative (False Negative Rate, FNR) огромна, можно привести легко. Для этого достаточно **никогда** не отвергать гипотезу, взяв критерий $S \\equiv 0$.\n",
    "\n",
    "Приведём пример, когда ошибки False Negative происходят не всегда, но критерии являются всё ещё бесполезными."
   ]
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   "source": [
    "### Критерии для времени года ☁️☀️❄️\n",
    "\n",
    "Поставим гипотезу о том, что сейчас на улице лето. Для проверки можно было бы конечно посмотреть в календарь, но мы поступим иначе.\n",
    "\n",
    "$$ \\mathsf{H}_0: \\text{ на улице лето} $$\n",
    "$$ \\mathsf{H}_1: \\text{ на улице не лето} $$\n",
    "\n",
    "Гипотеза очень полезная, ведь если она отвергается, а вы студент, необходимо ходить на пары Академии Аналитиков Авито и делать задания!"
   ]
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   "source": [
    "**Критерий Тимура**\n",
    "\n",
    "Посмотрим в окно и определим, идёт ли там снег. Если он идёт, то это неплохое доказательство того, что сейчас не лето, а значит можно отвергнуть $\\mathsf{H}_0$.\n",
    "\n",
    "Посчитаем вероятность ошибки False Positive.\n",
    "\n",
    "$$ FPR(S) = P(\\text{идёт снег}\\ |\\ \\text{сейчас лето}) < 0.001 $$\n",
    "\n",
    "Мы знаем, что летом снег идёт очень редко (вероятность ошибки заведомо ниже $0.1\\%$), так что это точно критерий уровня значимости $0.001$, чего обычно с лихвой достаточно для критериев.\n",
    "\n",
    "Но что с ошибкой False Negative? Рассмотрим конкретный случай: сейчас сентябрь. \n",
    "\n",
    "\n",
    "$$ FNR(S) = P(\\text{не идёт снег}\\ |\\ \\text{сейчас сентябрь}) > 0.9 $$\n",
    "\n",
    "Поскольку в сентябре почти всегда нет снега, можно сказать, что вероятность ошибки False Negative больше $90\\%$, значит этот критерий на самом деле бесполезен. Действительно, если применять его для принятия решения о том, пойти ли на занятия, посещаемость составит всего 10 процентов, за чем последует отчисление..."
   ]
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    "**Тривиальный критерий**\n",
    "\n",
    "Сформулируем другой критерий уровня значимости $\\alpha$, причём в данном случае уровень значимости можно выбрать произвольным.\n",
    "\n",
    "$$\n",
    "S(\\xi) = \\begin{cases}\n",
    "    1, \\text{ если монетка с вероятностью орла } \\alpha \\text{ выпала орлом} \\\\\n",
    "    0, \\text{ иначе}\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "Получается, этот критерий случаен, и он не использует вообще никакой информации о погоде. Однако требованиям к уровню значимости он удовлетворяет.\n",
    "\n",
    "$$ FPR = P(\\text{выпал орёл}\\ |\\ \\text{сейчас лето}) = P(\\text{выпал орёл}) = \\alpha $$\n",
    "\n",
    "Вычислим вероятность ошибки False Negative.\n",
    "\n",
    "$$ FNR = P(\\text{не выпал орёл}\\ |\\ \\text{сейчас не лето}) = P(\\text{не выпал орёл}) = 1 - \\alpha $$\n",
    "\n",
    "При $\\alpha = 0.001$, как у критерия Тимура, получаем вероятность ошибки False Negative $0.999 > 0.9$, то есть при одинаковом уровне значимости с критерием Тимура, тривиальный критерий чаще допускает ошибку False Negative."
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   "source": [
    "### Мощность"
   ]
  },
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   "metadata": {},
   "source": [
    "В статистике принято положительным результатом считать отвержение нулевой гипотезы, потому что обычно подтверждение альтернативы означает наличие бизнес-результата. Поэтому считается хорошим критерий, который чаще позволяет выявить бизнес-результат. И считают тогда не вероятность ошибки False Negative, а *мощность*, которая равна вероятности отвергнуть нулевую гипотезу при верности $\\mathsf{H}_1$, то есть True Positive Rate.\n",
    "\n",
    "$$ \\text{Power}_S = 1 - FNR $$\n",
    "\n",
    "Когда альтернатива $\\mathsf{H}_1$ состоит из множества исходов, мощность рассматривают как функцию от исхода. Например, можно посчитать мощность критерия Тимура и тривиального критерия зимой и осенью.\n",
    "\n",
    "$$ \\text{Power}_S(\\mu) = 1 - FNR(\\mu) $$\n",
    "\n",
    "**Критерий Тимура**\n",
    "\n",
    "$$ \\text{Power}_S(\\text{май}) = P(\\text{идёт снег } | \\text{ май}) \\approx 0.00001 $$\n",
    "$$ \\text{Power}_S(\\text{октябрь}) = P(\\text{идёт снег } | \\text{ октябрь}) \\approx 0.1 $$\n",
    "$$ \\text{Power}_S(\\text{январь}) = P(\\text{идёт снег } | \\text{ январь}) \\approx 0.5 $$\n",
    "\n",
    "**Тривиальный критерий**\n",
    "\n",
    "$$ \\text{Power}_S(\\text{май}) = P(\\text{выпал орёл } | \\text{ май}) = \\alpha = 0.001 $$\n",
    "$$ \\text{Power}_S(\\text{октябрь}) = P(\\text{выпал орёл } | \\text{ октябрь}) = \\alpha = 0.001 $$\n",
    "$$ \\text{Power}_S(\\text{январь}) = P(\\text{выпал орёл } | \\text{ январь}) = \\alpha = 0.001 $$\n",
    "\n",
    "Обычно задача поиска лучшего критерия формулируется как поиск как можно более мощного критерия при заданном уровне значимости $FPR \\leqslant \\alpha$. Но мы сказали, что мощность &mdash; функция от параметра, в нашем случае от месяца.\n",
    "\n",
    "Если мы будем применять критерий в январе, то мощнее критерий Тимура, а если в мае, то мощнее траивиальный критерий. Поэтому нужно понимать, когда будет применяться критерий, а значит мы ищем самый мощный критерий в интересующей нас области.\n",
    "\n",
    "Хотя в реальности в мае мощность обоих критериев настолько низкая, что они просто бесполезны, и использовать их не имеет смысла."
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   "source": [
    "## Часть 2. Мощность для задачи с доставкой"
   ]
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   "source": [
    "Применим новые знания о мощности для нашей задачи с доставкой. Из бизнес-соображений мы уже выбрали $\\alpha = 0.05$, а значит знаем, что мы неправильно отвергаем гипотезу $\\mathsf{H}_0:\\ \\mu = 0.5$ с вероятностью не более, чем $5\\%$. То есть этим ограничена вероятность ошибки False Positive.\n",
    "\n",
    "А с какой вероятностью мы будем *правильно* отвергать гипотезу? И какая у нас будет вероятность ошибки False Negative? На этот вопрос как раз ответит формула мощности.\n",
    "\n",
    "Вспомним критерий, по которому мы принимаем решение:\n",
    "\n",
    "$$ Q(\\xi) = \\sum\\limits_{i=1}^n \\xi_i - \\text{количество успешных доставок} $$\n",
    "\n",
    "$$ S = \\{Q \\geqslant 20\\} $$\n",
    "\n",
    "То есть если получаем хотя бы $20$ успешных доставок, то отвергаем $\\mathsf{H}_0$.\n",
    "\n",
    "Заметим, что, как и в прошлом пункте, мощность зависит от того, какое значение $\\mu$ в нашей генеральной совокупности. Зафиксируем сначала параметр $\\mu = 0.6$ и посчитаем мощность для него. Если истинный параметр такой, то статистика $Q$ имеет распределение $Binom(30, 0.6)$."
   ]
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   "id": "2bee71a2",
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   "source": [
    "binom_h0 = binom(n=30, p=0.5)\n",
    "binom_alternative = binom(n=30, p=0.6)"
   ]
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_grid = numpy.arange(1, 31)\n",
    "crit_reg = x_grid >= 20\n",
    "\n",
    "pyplot.figure(figsize=(16, 8))\n",
    "\n",
    "# строим распределение при H0 и критическую область\n",
    "probs_h0 = binom_h0.pmf(x_grid)\n",
    "pyplot.vlines(x_grid, 0, probs_h0, linewidth=15.0, color='#AAAAAA', label='PMF, $Binom(0.5, 30)$', alpha=0.5)\n",
    "\n",
    "# строим распределение при mu > 0.5\n",
    "probs_alternative = binom_alternative.pmf(x_grid)\n",
    "pyplot.vlines(x_grid, 0, probs_alternative, linewidth=15.0, color='white', label='PMF, $Binom(0.6, 30)$')\n",
    "pyplot.vlines(x_grid[crit_reg], 0, probs_alternative[crit_reg], linewidth=15.0, label='Rejection of H0', color='red')\n",
    "\n",
    "pyplot.title('Binomial distribution', fontsize=20)\n",
    "pyplot.legend(fontsize=18)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae275033",
   "metadata": {},
   "source": [
    "Как и раньше, нас интересует вероятность получить $20$ или более успехов. Но если раньше мы смотрели на неё для распределения с $\\mu=0.5$ и хотели, чтобы она была меньше $5\\%$, то теперь мы смотрим при $\\mu = 0.6$ и стремимся сделать эту величину как можно больше. По сравнению с вычислением FPR формула не поменяется, изменяется только $\\mu$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0acd7770",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False Positive Rate is 4.9%\n",
      "Power is 29.1%\n"
     ]
    }
   ],
   "source": [
    "critical_value = 20\n",
    "power = 1 - binom(n=30, p=0.6).cdf(critical_value - 1)\n",
    "fpr   = 1 - binom(n=30, p=0.5).cdf(critical_value - 1)\n",
    "\n",
    "print('False Positive Rate is {:.1%}'.format(fpr))\n",
    "print('Power is {:.1%}'.format(power))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b7866c0",
   "metadata": {},
   "source": [
    "Видно, что мощность около $30\\%$. Это довольно маленькое значение, ведь если наш продукт прибылен, то мы увидим это с помощью нашего теста только с вероятностью в $30$ процентов. Мы легко можем пропустить эффект.\n",
    "\n",
    "Что же можно сделать, чтобы сделать мощность выше? Чтобы разобраться, реализуем функцию мощности в общем виде."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a7e097ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_stat_power(N, mu_h0, mu_alternative, alpha):\n",
    "    '''Вычисляет статистическую мощность критерия для биномиального распределения\n",
    "    \n",
    "    Параметры:\n",
    "        N - количество бернуллиевских экспериментов (размер выборки)\n",
    "        mu_h0 - вероятность успеха в нулевой гипотезе\n",
    "        mu_alternative - предполагаемая вероятность успеха в эксперименте\n",
    "        alpha - уровень значимости критерия\n",
    "    '''\n",
    "    binom_h0 = binom(n=N, p=mu_h0)\n",
    "    binom_alternative = binom(n=N, p=mu_alternative)\n",
    "\n",
    "    # вычисляем критическое значение\n",
    "    critical_value = binom_h0.ppf(1 - alpha) + 1\n",
    "    # вычисляем мощность по формуле\n",
    "    return 1 - binom_alternative.cdf(critical_value - 1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "452ad466",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.29147186122349644"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_stat_power(30, 0.5, 0.6, alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10f342a5",
   "metadata": {},
   "source": [
    "Когда в жизни мы наблюдаем какое-то явление и видим его всего несколько раз, мы не уверены в том, что оно не случайно. Если же видим его достаточно часто, то уже составляем закономерности. Так и в статистике. Когда мы посмотрели на 30 пробных доставок, мы замечаем, что доля доставок больше половины. Но мы всё ещё не уверены. Чтобы получить больше уверенности, нужно провести больше наблюдений, то есть найти больше пробных клиентов.\n",
    "\n",
    "Посмотрим, что будет, если мы проведём эксперимент на 300 клиентах."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "53462b32",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9655326717180854"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_stat_power(300, 0.5, 0.6, alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c09a6d9",
   "metadata": {},
   "source": [
    "Видим, что мощность уже очень близка к $100\\%$. Но провести 300 пробных доставок гораздо затратнее, чем 30. И по ресурсам, и по времени. Поэтому обычно балансируют между мощностью и длительностью/затратами эксперимента.\n",
    "\n",
    "Принято считать, что приемлемой для работы мощностью считается $80\\%$. Посмотрим, как изменяется мощность при росте размера выборки, и сколько нужно провести экспериментов, чтобы детектировать эффект при $\\mu = 0.6$ в $80\\%$ случаев."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b1cb51de",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_grid = numpy.arange(10, 600, 10)\n",
    "# можем вычислить \n",
    "power = get_stat_power(n_grid, 0.5, 0.6, alpha=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "640fe469",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(12, 7))\n",
    "pyplot.title('Power for $\\mu = 0.6$', fontsize=18)\n",
    "pyplot.xlabel('Number of trial deliveries', fontsize=15)\n",
    "pyplot.ylabel('Power', fontsize=15)\n",
    "\n",
    "pyplot.plot(n_grid, power)\n",
    "pyplot.axhline(0.8, ls='--', color='red', label='Power = 80%')\n",
    "\n",
    "# считаем минимальный размер выборки для мощности в 80% \n",
    "min_n = n_grid[power >= 0.8].min()\n",
    "pyplot.axvline(min_n, ls='--', color='white', label=f'N = {min_n}')\n",
    "\n",
    "pyplot.legend(fontsize=15)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51ab2b4c",
   "metadata": {},
   "source": [
    "Видим, что для мощности в $80\\%$ достаточно набрать 160 доставок.\n",
    "\n",
    "А что, если мы хотим детектировать ещё меньший эффект? Например, если хотим отвергать гипотезу при $\\mu = 0.51$. Часто улучшение вероятности успеха на $1\\%$ может быть значимым для продукта, поэтому этот вопрос не лишен смысла."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "19364f9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_grid = numpy.arange(10, 30000, 59)\n",
    "# можем вычислить \n",
    "power = get_stat_power(n_grid, 0.5, 0.51, alpha=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5b80a8f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(12, 7))\n",
    "pyplot.title('Power for $\\mu = 0.51$', fontsize=18)\n",
    "pyplot.xlabel('Number of trial deliveries', fontsize=15)\n",
    "pyplot.ylabel('Power', fontsize=15)\n",
    "\n",
    "pyplot.plot(n_grid, power)\n",
    "pyplot.axhline(0.8, ls='--', color='red', label='Power = 80%')\n",
    "\n",
    "# считаем минимальный размер выборки для мощности в 80% \n",
    "min_n = n_grid[power >= 0.8].min()\n",
    "pyplot.axvline(min_n, ls='--', color='white', label=f'N = {min_n}')\n",
    "\n",
    "pyplot.legend(fontsize=15)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "308bafcc",
   "metadata": {},
   "source": [
    "Видим, что потребуется более 15 тысяч клиентов, чтобы детектировать такой эффект! Очень сложно найти столько пробных клиентов. Но нужно задаться вопросом, а стоит ли это делать? В нашем случае, если вероятность успеха $51\\%$, то прибыль с заказов будет небольшая, и вложения инвесторов конечно будут окупаться, но очень долго. Поэтому увеличение на $1%$ для нашей задачи не значимо *практически*, а значит не нужно стараться набирать 15 тысяч людей, а можно остановиться и на 160.\n",
    "\n",
    "Перед каждым экспериментом аналитику стоит задумываться над вопросом длительности теста и количества участников. Для этого нужно понять:\n",
    "\n",
    "* какой эффект является для задачи практически значимым?\n",
    "* сколько потребуется испытуемых, чтобы детектировать этот эффект чаще, чем в $80\\%$ случаев? "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4557cbd0",
   "metadata": {},
   "source": [
    "По графикам видно, что для детектирования меньшего эффекта нужен больший размер выборки. Посмотрим, как для фиксированного $N=30$ меняется мощность для разных параметров $\\mu$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "02f5b9f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_grid = numpy.linspace(0.5, 1, 500)\n",
    "# можем вычислить сразу для всех mu\n",
    "power = get_stat_power(30, 0.5, mu_grid, alpha=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "252be5dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(12, 7))\n",
    "pyplot.title('Power for $N = 30$', fontsize=18)\n",
    "pyplot.xlabel('$\\mu$', fontsize=15)\n",
    "pyplot.ylabel('Power', fontsize=15)\n",
    "\n",
    "pyplot.plot(mu_grid, power)\n",
    "pyplot.axhline(0.8, ls='--', color='red', label='Power = 80%')\n",
    "# считаем минимальный эффект мощности в 80% \n",
    "min_mu = mu_grid[power >= 0.8].min()\n",
    "pyplot.axvline(min_mu, ls='--', color='white', label='$\\mu$ = {:.2f}'.format(min_mu))\n",
    "\n",
    "pyplot.legend(fontsize=15)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a1358ab",
   "metadata": {},
   "source": [
    "В нашем эксперименте мы хорошо детектируем эффект, только если вероятность успеха в генеральной совокупности хотя бы $72\\%$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb6ae78f",
   "metadata": {},
   "source": [
    "### MDE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ab897ac",
   "metadata": {},
   "source": [
    "Выше на графике мы увидели, что с хорошей мощностью больше $80\\%$ мы можем заметить эффект в $22$ процентных пункта. Причём это можно посчитать даже до проведения эксперимента. В нашем случае такое увеличение успешности относительно $0.5$ вполне возможно, и с ним можно работать. Но когда аналитики проверяют изменения, зачастую ожидаемый эффект колеблется в районе одного, максимум двух процентов! Для подобных изменений не подойдёт выбранная постановка эксперимента, а значит и проводить его не имеет смысла.\n",
    "\n",
    "Поэтому перед запуском экспериментов аналитики сообщают минимальную величину эффекта, которую можно задетектировать. Она так и называется, **минимальный детектируемый эффект**, сокращённо MDE (Minimal Detectable Effect). В нашем случае $MDE = +22$ п.п. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea95017c-4c0b-43ae-be6d-6d881bf44e79",
   "metadata": {},
   "source": [
    "Более формально, $MDE$ для гипотезы $\\mathsf{H}_0: \\mu = \\mu_0$ &mdash; это минимальный эффект $\\delta$, при котором критерий уровня значимости $\\alpha$ для проверки этой гипотезы при истинном параметре $\\mu = \\mu_0 + \\delta$ и размере выборки $N$ будет отвергать $\\mathsf{H}_0$ с мощностью большей, чем $1 - \\beta$.\n",
    "\n",
    "Чаще всего берут $1 - \\beta = 80\\%$. Напишем функцию, которая будет вычислять MDE подбором."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "0edf6b55-2ba5-4f7d-8240-1405752a6da5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def binom_test_mde_one_sided(N, mu0, alpha=0.05, min_power=0.8):\n",
    "    '''Вычисляет MDE одностороннего критерия для проверки гипотезы mu = mu0 в задаче с доставкой\n",
    "    \n",
    "    Параметры:\n",
    "        N (int) - размер выборки\n",
    "        mu0 (float) - вероятность успеха в нулевой гипотезе\n",
    "        alpha (float) - уровень значимости критерия\n",
    "        min_power (float) - желаемая мощность\n",
    "        \n",
    "    Возвращает:\n",
    "        float - MDE'''\n",
    "    delta_grid = numpy.linspace(0, 1 - mu0, 500) \n",
    "    power = get_stat_power(N, mu0, mu0 + delta_grid, alpha=alpha)\n",
    "    # выберем подходящие delta и вернем первую\n",
    "    fit_delta = delta_grid[power >= min_power]\n",
    "    return fit_delta[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cafc517-8676-43e2-81ce-af6f4bfa9155",
   "metadata": {},
   "source": [
    "Вызовем функцию для нашего случая"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b92fbcf1-8d7a-49c0-b153-49a34bda116c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.21843687374749496"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binom_test_mde_one_sided(30, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d97fea1-db32-40c7-aad0-63afdb0bbb03",
   "metadata": {},
   "source": [
    "Результат совпадает с вычислениями по графику"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de2415fe-f55a-4272-9e91-1f1a0ffd43d3",
   "metadata": {},
   "source": [
    "Обычно MDE считают не просто так, а неразрывно с ним идёт вопрос об определении размера выборки.\n",
    "\n",
    "**Определение размера выборки**\n",
    "\n",
    "В нашей задаче мы нашли $30$ клиентов, не вычисляя изначально, сколько их понадобится. Но что если полученный MDE слишком велик и нужно сделать его меньше, поскольку ожидаемые изменения гораздо меньше? Тогда решается обратная задача, По требуемому MDE определить объём выборки. Если мы говорим, что хотим детектировать +10 п.п., то есть 60% успешных доставок, то потребуется найти 160 пробных клиентов, это видно из предыдущих графиков. Если 30 человек нам, например, искать месяц, такой тест может затянуться почти на полгода. Поэтому стоит подумать о том, чтобы выделить дополнительные ресурсы на поиск клиентов, например, привлечь маркетологов.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cb17b4c",
   "metadata": {},
   "source": [
    "## Часть 3. Доверительные интервалы"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be9b8e8b",
   "metadata": {},
   "source": [
    "В предыдущих частях мы научились проверять гипотезу $\\mathsf{H}_0: \\mu = 0.5$. В качестве ответа мы получаем лишь вердикт \"отвергаем $\\mathsf{H}_0$\" или \"не отвергаем $\\mathsf{H}_0$\". Однако в выборке содержится гораздо больше информации, и мы можем больше понять про параметр, чем сравнение с числом $0.5$.\n",
    "\n",
    "Если гипотеза $\\mathsf{H}_0$ не отвергается, это значит, что значение $\\mu = 0.5$ допустимо для нашей выборки. Полученные значения можно объяснить значением $\\mu = 0.5$. Но если у нас есть механизм проверки для любого $\\mu$, мы можем для всех значений узнать, какие из них допустимы и получить множество возможных значений $\\mu$. Такое множество называется доверительным интервалом.\n",
    "\n",
    "*Доверительный интервал* уровня доверия $1 - \\alpha$ &mdash; множество значений параметра $\\mu_0$, для которых гипотеза $\\mu = \\mu_0$ не отвергается критерием уровня значимости $\\alpha$.\n",
    "\n",
    "\n",
    "Из определения следует, что разные критерии могут порождать разные доверительные интервалы. В этой части рассмотрим, какие интервалы порождаются двусторонним критерием. Для этого с шагом $0.001$ переберём значения $\\mu \\in [0, 1]$ и проверим гипотезы."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e96c0a23",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Функция из прошлой лекции\n",
    "def two_sided_criterion_nonsym(n, mu, alpha):\n",
    "    '''Строит двусторонний критерий для несимметричной задачи с доставкой\n",
    "    \n",
    "    Параметры:\n",
    "        n: количество доставок в эксперименте\n",
    "        mu: вероятность успеха в нулевой гипотезе\n",
    "        alpha: уровень значимости критерия\n",
    "        \n",
    "    Возвращает:\n",
    "        C1, C2 для критерия S = {Q <= C1 или Q >= C2}\n",
    "    '''\n",
    "    binom_h0 = binom(n=n, p=mu)\n",
    "    \n",
    "    # аналогично одностороннему критерию\n",
    "    c2 = binom_h0.ppf(1 - alpha/2) + 1\n",
    "        \n",
    "    # по выкладкам выше\n",
    "    c1 = binom_h0.ppf(alpha/2) - 1\n",
    "    \n",
    "    return c1, c2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9e31ff2b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence interval: 0.439 -- 0.8\n"
     ]
    }
   ],
   "source": [
    "success_cnt = 19\n",
    "mu_grid = numpy.arange(0, 1, 0.001)\n",
    "mu_no_rejection = []\n",
    "\n",
    "for mu_h0 in mu_grid:\n",
    "    c1, c2 = two_sided_criterion_nonsym(30, mu_h0, alpha=0.05)\n",
    "    if success_cnt > c1 and success_cnt < c2:\n",
    "        mu_no_rejection.append(mu_h0)\n",
    "\n",
    "print('95% confidence interval: {} -- {}'.format(min(mu_no_rejection), max(mu_no_rejection)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f05f304",
   "metadata": {},
   "source": [
    "Можно проверить, что допустимые значения образуют именно интервал. Впоследствии это можно будет увидеть по графикам."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "501d9b74",
   "metadata": {},
   "source": [
    "Получив такой интервал, мы сразу можем сделать вывод, что гипотеза $\\mathsf{H}_0: \\mu = 0.5$ не отвергается, поскольку $0.5$ лежит в доверительном интервале. Но при этом сразу понятно, что $\\mu \\neq 0.4$ на уровне значимости $\\alpha$.\n",
    "\n",
    "Конечно же, в доверительном интервале лежит значение $\\mu = \\frac{19}{30}$, для которого $19$ успехов &mdash; это самый правдоподобный результат. При этом интервал несимметричен относительно точки $\\frac{19}{30}$.\n",
    "\n",
    "Посмотрим, как можно визуально найти границу интервала. Мы получили $19$ успехов. Для каждого $\\mu_0$ статистика $Q$ имеет распределение $Binom(30, \\mu_0)$. Будем рисовать это распределение и смотреть, попадает ли $19$ в критическую область."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1cd93230",
   "metadata": {},
   "outputs": [],
   "source": [
    "mus_h0 = [0.2, 0.438, 0.439, 0.8, 0.81, 0.9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f8b18932",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1500x1500 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = pyplot.subplots(3, 2, figsize=(15, 15))\n",
    "\n",
    "for mu_h0, ax in zip(mus_h0, axes.flatten()):\n",
    "    binom_h0 = binom(n=30, p=mu_h0)\n",
    "    probs = binom_h0.pmf(x_grid)\n",
    "\n",
    "    # строим вертикальные столбцы от 0 до вероятности\n",
    "    ax.vlines(x_grid, 0, probs, linewidth=8.0, color='white', label=f'PMF, $Binom({mu_h0}, 30)$')\n",
    "    # отдельно изобразим критическую области критерия\n",
    "    c1, c2 = two_sided_criterion_nonsym(30, mu_h0, alpha=0.05)\n",
    "    crit_reg = (x_grid <= c1) | (x_grid >= c2)\n",
    "    ax.vlines(x_grid[crit_reg], 0, probs[crit_reg], linewidth=8.0, label='Critical region for S')\n",
    "\n",
    "    is_rejection = success_cnt <= c1 or success_cnt >= c2\n",
    "    ax.axvline(success_cnt, ls='--', label=f'Q = {success_cnt} ' + ('is rejected' if is_rejection else 'is not rejected'), color='gray', alpha=0.4)\n",
    "\n",
    "    rejection_prob = probs[crit_reg].sum()\n",
    "    ax.set_title(f'$\\mu = {mu_h0}$', fontsize=12)\n",
    "    ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "395b26f4",
   "metadata": {},
   "source": [
    "Видно, что с ростом $\\mu_0$ гистограмма сдвигается вправо. И сначала $19$ попадает в правую критическую область. Потом, начиная с точки $0.439$, значение $19$ уже оказывается вне критической области, и только с $\\mu_0 = 0.81$ начинает попадать в левую критическую область.\n",
    "\n",
    "Таким образом, левая граница доверительного интервала &mdash; это первая точка, когда значение статистики перестало попадать в критическую область, а правая граница &mdash; последняя точка, когда значение не попадает в правую критическую область."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00c7322e",
   "metadata": {},
   "source": [
    "## Часть 4. Односторонние доверительные интервалы"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78c9ca16",
   "metadata": {},
   "source": [
    "В прошлой части мы использовали двусторонний критерий, и из него получился доверительный интервал. Но на прошлой лекции мы говорили, что двусторонний критерий нужен крайне редко. Контролировать ошибку False Positive нам нужно только для отклонений в сторону, полезную для бизнеса. В случае задачи с доставкой это получение *большей* конверсии в успех.\n",
    "\n",
    "Попробуем воспользоваться односторонним критерием для построения доверительного интервала.\n",
    "\n",
    "Возьмем критерий с прошлой лекции."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "eedffb68",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_binom_criterion(n, mu=0.5, alpha=0.05):\n",
    "    '''Строит критерий для задачи с доставкой\n",
    "    \n",
    "    Параметры:\n",
    "        n: количество доставок в эксперименте\n",
    "        mu: вероятность успеха в нулевой гипотезе\n",
    "        alpha: уровень значимости критерия\n",
    "        \n",
    "    Возвращает:\n",
    "        C для критерия S = {Q >= C}\n",
    "    '''\n",
    "    binom_h0 = binom(n=n, p=mu)\n",
    "    q = binom_h0.ppf(1 - alpha)\n",
    "    return q + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "237dd891",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence interval: 0.467 -- 1.0\n"
     ]
    }
   ],
   "source": [
    "success_cnt = 19\n",
    "mu_grid = numpy.arange(0, 1.001, 0.001)\n",
    "mu_no_rejection = []\n",
    "\n",
    "for mu_h0 in mu_grid:\n",
    "    crit_val = make_binom_criterion(n=30, mu=mu_h0, alpha=0.05)\n",
    "    if success_cnt < crit_val:\n",
    "        mu_no_rejection.append(mu_h0)\n",
    "\n",
    "print('95% confidence interval: {} -- {}'.format(min(mu_no_rejection), max(mu_no_rejection)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0f22e7a",
   "metadata": {},
   "source": [
    "Когда мы использовали двусторонний интервал, мы получили левую границу $0.439 < 0.467$. Получается, что односторонний интервал с точки зрения левой границы даёт нам больше информации. При этом с точки зрения правой границы мы теряем информацию совсем. Она получается равна 1 просто потому что вероятность не может быть больше.\n",
    "\n",
    "На самом деле обычно на правую границу не смотрят при анализе, когда мы ищем положительный эффект.\n",
    "\n",
    "Предположим, мы получили не $19$ успехов, а $22$. Построим 2 вида интервалов."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "063d9ff6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Two-sided 95% confidence interval: 0.542 -- 0.877\n"
     ]
    }
   ],
   "source": [
    "success_cnt = 22\n",
    "mu_grid = numpy.arange(0, 1, 0.001)\n",
    "mu_no_rejection = []\n",
    "\n",
    "for mu_h0 in mu_grid:\n",
    "    c1, c2 = two_sided_criterion_nonsym(30, mu_h0, alpha=0.05)\n",
    "    if success_cnt > c1 and success_cnt < c2:\n",
    "        mu_no_rejection.append(mu_h0)\n",
    "\n",
    "print('Two-sided 95% confidence interval: {:.3f} -- {:.3f}'.format(min(mu_no_rejection), max(mu_no_rejection)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7e319ad9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "One-sided 95% confidence interval: 0.571 -- 1.000\n"
     ]
    }
   ],
   "source": [
    "success_cnt = 22\n",
    "mu_grid = numpy.arange(0, 1.001, 0.001)\n",
    "mu_no_rejection = []\n",
    "\n",
    "for mu_h0 in mu_grid:\n",
    "    crit_val = make_binom_criterion(n=30, mu=mu_h0, alpha=0.05)\n",
    "    if success_cnt < crit_val:\n",
    "        mu_no_rejection.append(mu_h0)\n",
    "\n",
    "print('One-sided 95% confidence interval: {:.3f} -- {:.3f}'.format(min(mu_no_rejection), max(mu_no_rejection)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66d5e9c6",
   "metadata": {},
   "source": [
    "По обоим доверительным интервалам мы делаем вывод, что конверсия значимо отличается от $50\\%$. Но односторонный интервал даёт лучшую нижнюю оценку на вероятность успеха. Мы можем понять, что наша конверсия больше $57\\%$. А информация из двустороннего интервала о том, что вероятность меньше $88\\%$ не добавляет нам пользы.\n",
    "\n",
    "Зачем же мы тогда вообще используем двусторонний интервал? Чтобы это понять, посмотрим, как выглядят визуально границы для одностороннего интервала."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5d339716",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1500x1500 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = pyplot.subplots(3, 2, figsize=(15, 15))\n",
    "\n",
    "for mu_h0, ax in zip(mus_h0, axes.flatten()):\n",
    "    binom_h0 = binom(n=30, p=mu_h0)\n",
    "    probs = binom_h0.pmf(x_grid)\n",
    "\n",
    "    # строим вертикальные столбцы от 0 до вероятности\n",
    "    ax.vlines(x_grid, 0, probs, linewidth=8.0, color='white', label=f'PMF, $Binom({mu_h0}, 30)$')\n",
    "    # отдельно изобразим критическую области критерия\n",
    "    c = make_binom_criterion(30, mu_h0, alpha=0.05)\n",
    "    crit_reg = (x_grid >= c)\n",
    "    ax.vlines(x_grid[crit_reg], 0, probs[crit_reg], linewidth=8.0, label='Critical region for S')\n",
    "\n",
    "    is_rejection = success_cnt >= c\n",
    "    ax.axvline(success_cnt, ls='--', label=f'Q = {success_cnt} ' + ('is rejected' if is_rejection else 'is not rejected'), color='gray', alpha=0.4)\n",
    "\n",
    "    rejection_prob = probs[crit_reg].sum()\n",
    "    ax.set_title(f'$\\mu = {mu_h0}$', fontsize=12)\n",
    "    ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8256711",
   "metadata": {},
   "source": [
    "По сравнению с картинкой из предыдущей части мы видим, что правая критическая область стала больше из-за того, что там теперь находится не $2.5\\%$, а $5\\%$ по построению. При этом левой критической области просто не существует, поэтому при больших $\\mu$ не происходит попадания $19$ в неё, а значит мы не отвергаем гипотезу.\n",
    "\n",
    "Заметим, что если бы мы строили двусторонний интервал, но с вдвое большей $\\alpha$, попадания в правую критическую область случались бы при тех же $\\mu$, что и в одностороннем критерии. Поэтому зачастую для поиска односторонней границы строят двусторонний доверительный интервал с большей $\\alpha$, игнорируя при этом правую границу. Это удобно, поскольку можно пользоваться только одной функцией для критерия.\n",
    "\n",
    "Проверим, что получится при $\\alpha = 0.1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "02d0564d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Two-sided 90% confidence interval: 0.467 -- 0.778\n"
     ]
    }
   ],
   "source": [
    "success_cnt = 19\n",
    "mu_grid = numpy.arange(0, 1, 0.001)\n",
    "mu_no_rejection = []\n",
    "\n",
    "for mu_h0 in mu_grid:\n",
    "    c1, c2 = two_sided_criterion_nonsym(30, mu_h0, alpha=0.1)\n",
    "    if success_cnt > c1 and success_cnt < c2:\n",
    "        mu_no_rejection.append(mu_h0)\n",
    "\n",
    "print('Two-sided 90% confidence interval: {:.3f} -- {:.3f}'.format(min(mu_no_rejection), max(mu_no_rejection)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae60d3fb",
   "metadata": {},
   "source": [
    "Видим, что получили такую же левую границу, как и в одностороннем интервале."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "add7a463",
   "metadata": {},
   "source": [
    "## Часть 5. Свойства доверительных интервалов"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cffb388",
   "metadata": {},
   "source": [
    "Вспомним определение доверительного интервала.\n",
    "\n",
    "Пусть есть критерий $S = \\{Q(\\xi) \\leqslant C\\}$ уровня значимости $\\alpha$ для проверки гипотезы $\\mathsf{H}_0: \\mu = \\mu_0$, $Q$ &mdash; статистика критерия, а $q$ &mdash; её реализация на конкретной выборке $\\xi = \\xi_1, \\dots, \\xi_n$. Тогда **доверительным интервалом** называется множество таких $\\mu_0$, на которых критерий $S$ не отвергает гипотезу $\\mathsf{H}_0: \\mu = \\mu_0$.\n",
    "\n",
    "Процедура подсчёта интервала в прошлой части &mdash; это долгий перебор значений с некоторым шагом. Но это всё ещё остаётся некоторой функцией от выборки, то есть *статистикой* и случайной величиной, причём её распределение зависит от статистики $Q$, а значит и от изначальной выборки, и от параметра $\\mu$ в генеральной совокупности.\n",
    "\n",
    "Обозначим границы интервала за $\\mathcal{L}(Q), \\mathcal{R}(Q)$ &mdash; статистики"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c77a40b2",
   "metadata": {},
   "source": [
    "**Свойство доверительного интервала**\n",
    "\n",
    "Каким бы ни было истинное значение $\\mu = \\mu_0$, вероятность того, что оно находится между $\\mathcal{L}(Q)$ и $\\mathcal{R}(Q)$, не ниже, чем $1 - \\alpha$. Значение $1 - \\alpha$ называется **уровнем доверия** доверительного интервала.\n",
    "\n",
    "$$ P(\\mathcal{L}(Q) < \\mu_0 < \\mathcal{R}(Q)) \\geqslant 1 - \\alpha $$\n",
    "\n",
    "Важно, что случайность здесь скрыта именно в $\\mathcal{L}$ и $\\mathcal{R}$, а не в $\\mu_0$. Параметр $\\mu_0$ неизвестен, но мы предполагаем его константным и не случайным."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0b8cb5d",
   "metadata": {},
   "source": [
    "Проверим справедливость этого свойства. Для этого зафиксируем $\\mu_0$ и проведём множество экспериментов:\n",
    "\n",
    "* Генерируем выборку из распределения с параметром $\\mu_0$\n",
    "* Вычисляем статистику $q$\n",
    "* Считаем доверительный интервал для $\\alpha = 0.05$\n",
    "\n",
    "Проверяем, что доля случаев, когда параметр $\\mu_0$ оказался внутри границ интервала, хотя бы $95\\%$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a65468cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_binomial_confint(n, alpha, q):\n",
    "    '''Вычисляет доверительный интервал для выборки из распределения Бернулли\n",
    "    \n",
    "        n (int) - количество элементов в выборке\n",
    "        alpha (float) - уровень значимости критерия\n",
    "        q (float) - реализация статистики критерия\n",
    "    '''\n",
    "    mu_grid = numpy.arange(0, 1.001, 0.001)\n",
    "    mu_no_rejection = []\n",
    "\n",
    "    for mu_h0 in mu_grid:\n",
    "        c1, c2 = two_sided_criterion_nonsym(30, mu_h0, alpha=0.05)\n",
    "        if q > c1 and q < c2:\n",
    "            mu_no_rejection.append(mu_h0)\n",
    "\n",
    "    return min(mu_no_rejection), max(mu_no_rejection)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "4f25b5b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "numpy.random.seed(202312)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "bbd7045b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.976\n"
     ]
    }
   ],
   "source": [
    "N_EXPERIMENTS = 1000\n",
    "SAMPLE_SIZE = 30\n",
    "latent_mu = 0.5  # \"истинное\" значение параметра\n",
    "binom_true = binom(n=SAMPLE_SIZE, p=latent_mu)  # \"истинное\" распрееление\n",
    "\n",
    "confint_fail_cases = 0\n",
    "\n",
    "for i in range(N_EXPERIMENTS):\n",
    "    q = binom_true.rvs()  # генерируем сразу сумму элементов\n",
    "    L, R = my_binomial_confint(n=SAMPLE_SIZE, alpha=0.05, q=q)\n",
    "    if L < latent_mu < R:\n",
    "        pass # всё хорошо\n",
    "    else:\n",
    "        confint_fail_cases += 1\n",
    "\n",
    "print(1 - confint_fail_cases / N_EXPERIMENTS)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06eb4703",
   "metadata": {},
   "source": [
    "Отметим, что этот код работал больше 5 минут. Это из-за того, что при каждом эксперименте требуется построить доверительный интервал, а значит проверить 1000 возможных параметров $\\mu_0$.\n",
    "\n",
    "Видим, что свойство выполнилось. Мы ожидали хотя бы $95\\%$ попаданий, получили даже $97.5\\%$. На самом деле это сильно больше, чем мы ожидали. Это происходит из-за дискретности распределения. По той же причине при поиске критической области мы не могли выбрать столбцы с суммарной высотой ровно $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77793ce4",
   "metadata": {},
   "source": [
    "**Доказательство свойства**\n",
    "\n",
    "При формулировке свойства мы предполагаем, что есть некоторая $\\mu_0$ &mdash; вероятность успеха в генеральной совокупности. Когда мы проводим искусственный эксперимент, мы фиксируем её и можем считать истинной $\\mu$.\n",
    "\n",
    "Каждый раз мы генерируем $Q \\sim Binom(\\mu_0, 30)$ и проверяем, попала ли $\\mu_0$ в доверительный интервал. Нарисуем распределение статистики $Q$, которое уже нам знакомо. Нарисуем и область вероятности $\\leqslant \\alpha$, как мы делали это раньше."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e26af265",
   "metadata": {},
   "outputs": [],
   "source": [
    "mu0 = 0.5\n",
    "binom_mu0 = binom(n=30, p=mu0)  # раньше это было mu_h0, остальное так же\n",
    "probs = binom_mu0.pmf(x_grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "25b379f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(12, 7))\n",
    "\n",
    "pyplot.title('Распределение статистики при \"истинном mu\"', fontsize=18)\n",
    "\n",
    "pyplot.vlines(x_grid, 0, probs, linewidth=8.0, color='white', label=f'PMF, $Binom({mu0}, 30)$')\n",
    "c1, c2 = two_sided_criterion_nonsym(30, mu0, alpha=0.05)\n",
    "crit_reg = (x_grid >= c2) | (x_grid <= c1)\n",
    "pyplot.vlines(x_grid[crit_reg], 0, probs[crit_reg], linewidth=8.0, label='Region with proba $\\leqslant \\\\alpha$')\n",
    "pyplot.legend(fontsize=15)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f7d8de0",
   "metadata": {},
   "source": [
    "Пусть реализовалось значение статистики $q$. По такой выборке можно построить доверительный интервал на $\\mu$. Он будет как-то расположен, но сейчас нас интересует, попадёт ли в него $\\mu_0$. По определению попадание в интервал произойдёт $\\Leftrightarrow$ не отвергается гипотеза $\\mathsf{H}_0:\\ \\mu = \\mu_0$. Но тогда при справедливости $\\mathsf{H}_0$ статистика имеет то распределение, что и на рисунке. И гипотеза отвергается только при попадании в рыжую критическую область, а это случается с вероятностью $\\leqslant \\alpha$.\n",
    "\n",
    "Значит с вероятностью хотя бы $1 - \\alpha$ $\\mu_0$ будет находиться в доверительном интервале.\n",
    "\n",
    "Часто так и вводят определение доверительного интервала. Для выборки $\\xi_1, \\dots, \\xi_n$ &mdash; это такая пара статистик $\\mathcal{L}(\\xi)$ и $\\mathcal{R}(\\xi)$, что каким бы ни было $\\mu_0$,\n",
    "\n",
    "$$P(L(\\xi) < \\mu_0 < R(\\xi)) \\geqslant 1 - \\alpha$$\n",
    "\n",
    "Снова обращаем внимание, что случайность здесь скрыта не в параметре $\\mu_0$, а в статистиках от выборки."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbceb5eb",
   "metadata": {},
   "source": [
    "**Приближённое построение интервала**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54279e9c",
   "metadata": {},
   "source": [
    "Рассмотренный сейчас алгоритм построение доверительного интервала работает слишком долго. В Python есть функции, которые позволяют быстрее рассчитать интервал. Например, можно воспользоваться методом Уилсона и функцией `proportion_confint`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "4c816de9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.stats.proportion import proportion_confint"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46ded2f8",
   "metadata": {},
   "source": [
    "Повторим эксперименты с новым типом доверительного интервала, тут можем позволить больше реализаций выборки, покольку интервал считается недолго."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "a76b8653",
   "metadata": {},
   "outputs": [],
   "source": [
    "numpy.random.seed(20231212)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "a7306de7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.943\n"
     ]
    }
   ],
   "source": [
    "N_EXPERIMENTS = 1000\n",
    "SAMPLE_SIZE = 30\n",
    "latent_mu = 0.5  # \"истинное\" значение параметра\n",
    "binom_true = binom(n=SAMPLE_SIZE, p=latent_mu)  # \"истинное\" распрееление\n",
    "\n",
    "confint_fail_cases = 0\n",
    "\n",
    "for i in range(N_EXPERIMENTS):\n",
    "    q = binom_true.rvs()  \n",
    "    L, R = proportion_confint(\n",
    "        count=q,  # количество успехов\n",
    "        nobs=SAMPLE_SIZE,  # размер выборки\n",
    "        alpha=0.05,\n",
    "        method='wilson'\n",
    "    )\n",
    "    if L < latent_mu < R:\n",
    "        pass # всё хорошо\n",
    "    else:\n",
    "        confint_fail_cases += 1\n",
    "\n",
    "print(1 - confint_fail_cases / N_EXPERIMENTS)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0aa9eb4",
   "metadata": {},
   "source": [
    " Заметим, что наше $\\mu$ нашлось в доверительном интервале меньше, чем в $95\\%$ случаев. Это происходит из-за того, что быстрые методы работают приближённо, оценивая распределение статистики при увеличении размера выборки. Чем размер выборки больше, тем ближе будет интервал к $95\\%$-ному.\n",
    "\n",
    " Зависимость доли успешных попаданий $\\mu$ в доверительный интервал от размера выборки изобразим на графике."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "499fbdbf",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_grid = numpy.arange(1, 1000, 25).tolist()\n",
    "interval_success_rate = []\n",
    "\n",
    "for n in n_grid:\n",
    "    confint_fail_cases = 0\n",
    "    for i in range(N_EXPERIMENTS):\n",
    "        binom_true = binom(n=n, p=latent_mu)\n",
    "        q = binom_true.rvs()  \n",
    "        L, R = proportion_confint(\n",
    "            count=q,  # количество успехов\n",
    "            nobs=n,  # размер выборки\n",
    "            alpha=0.05,\n",
    "            method='wilson'\n",
    "        )\n",
    "        if L < latent_mu < R:\n",
    "            pass # всё хорошо\n",
    "        else:\n",
    "            confint_fail_cases += 1\n",
    "    interval_success_rate.append(1 - confint_fail_cases / N_EXPERIMENTS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "23c81fb1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(12, 7))\n",
    "pyplot.title('Успешность доверительного интервала Уилсона при разном размере выборки', fontsize=15)\n",
    "pyplot.xlabel('Размер выборки', fontsize=15)\n",
    "pyplot.ylabel('Доля попаданий $\\mu$ в интервал', fontsize=15)\n",
    "\n",
    "pyplot.plot(n_grid, interval_success_rate, label='Успешность в экспериментах')\n",
    "pyplot.axhline(0.95, ls='--', label='Желаемая успешность', color='red')\n",
    "\n",
    "pyplot.legend(fontsize=15)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "499970a4",
   "metadata": {},
   "source": [
    "Видно, что на любом размере выборки при использовании интервала Уилсона можно получить меньше $95\\%$ попаданий, но чем больше размер выборки, тем меньше график отклоняется от $95\\%$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61f8a252",
   "metadata": {},
   "source": [
    "### Итог"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d07131f",
   "metadata": {},
   "source": [
    "Мы рассмотрели понятие мощности и поняли, что не все критерии уровня значимости $\\alpha$ могут быть применимы на практике. Мы определили MDE и способ определения размера выборки, которые помогают правильно запланировать эксперимент и затраты на него.\n",
    "\n",
    "Далее мы рассмотрели доверительные интервалы, которые помогают больше узнать о параметре, чем простой вердикт критерия."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
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