Last active
December 20, 2020 06:35
-
-
Save tatamiya/ed434f786826c6c3666e73b924a06b80 to your computer and use it in GitHub Desktop.
Visual understanding of law of large numbers and central limit theorem with dices
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| { | |
| "cells": [ | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:53.336287Z", | |
| "end_time": "2020-12-20T06:34:53.717582Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "import numpy as np\nimport matplotlib.pyplot as plt\n%matplotlib inline", | |
| "execution_count": 1, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "# サイコロで見る大数の法則と中心極限定理\n\nサイコロを複数回振って出た目の平均値から、大数の法則と中心極限定理を視覚的に理解する" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "## サイコロの目の期待値と標準偏差\n\n理論的には、期待値$\\mu = 3.5$, 標準偏差$\\sigma = \\sqrt{35/12} \\fallingdotseq 1.708$" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:53.719486Z", | |
| "end_time": "2020-12-20T06:34:53.722196Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "mu = np.mean([1, 2, 3, 4, 5, 6])\nsigma = np.std([1, 2, 3, 4, 5, 6])\n\nprint(f'mu: {mu}, sigma: {sigma}')", | |
| "execution_count": 2, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "mu: 3.5, sigma: 1.707825127659933\n", | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "100000サンプルで計算してみる：" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:53.723383Z", | |
| "end_time": "2020-12-20T06:34:53.727935Z" | |
| }, | |
| "trusted": true, | |
| "scrolled": true | |
| }, | |
| "cell_type": "code", | |
| "source": "dice_sample = np.random.randint(1, 6+1, 100000)\nprint('mean: ', dice_sample.mean()) \nprint('standard deviation: ', dice_sample.std())", | |
| "execution_count": 3, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": "mean: 3.49876\nstandard deviation: 1.7066629609855601\n", | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "## n回試行平均値\n「n回振る」試行を10000回繰り返し、各試行の平均値をみる\n\n$$\n\\bar{X}_n = \\frac{1}{n}\\sum_{i=1}^n X_i\n$$" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:53.729429Z", | |
| "end_time": "2020-12-20T06:34:53.731679Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "def sample_mean_iterations(n, iteration=1000):\n\n samples = np.random.randint(1,6+1, n * iteration).reshape(-1, n)\n return samples.mean(1)", | |
| "execution_count": 4, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T01:25:43.328434Z", | |
| "end_time": "2020-12-20T01:25:43.332098Z" | |
| } | |
| }, | |
| "cell_type": "markdown", | |
| "source": "n = 1, 10, 100, 1000で見てみる。" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:53.733133Z", | |
| "end_time": "2020-12-20T06:34:53.752990Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "sample_mean1 = sample_mean_iterations(1)\nsample_mean10 = sample_mean_iterations(10)\nsample_mean100 = sample_mean_iterations(100)\nsample_mean1000 = sample_mean_iterations(1000)", | |
| "execution_count": 5, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "## 各試行平均値の分布と大数の法則\n試行回数を増やすほど、各試行平均値の分布は期待値3.5を中心に尖っていく。" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:53.755410Z", | |
| "end_time": "2020-12-20T06:34:54.259318Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "plt.hist(sample_mean1, bins=20, density=True, label='n=1')\nplt.hist(sample_mean10, bins=20, density=True, label='n=10')\nplt.hist(sample_mean100, bins=20, density=True, label='n=100')\nplt.hist(sample_mean1000, bins=20, density=True, label='n=1000')\nplt.legend()\n\nplt.xlabel('$\\\\bar{X}_n$', fontsize=15);", | |
| "execution_count": 6, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": "<Figure size 432x288 with 1 Axes>", | |
| "image/png": "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\n" | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "この時の$\\mu=3.5$からの「ずれ」を表す$\\bar{X_n} - \\mu$の分散は、$n\\to0$につれ小さくなり0に収束する（大数の法則）\n\n$$\nE\\left[\\left(\\bar{X}_n - \\mu\\right)^2\\right]=\\frac{\\sigma^2}{N} \\xrightarrow{N\\to\\infty} 0.\n$$" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:54.263314Z", | |
| "end_time": "2020-12-20T06:34:54.268168Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "(sample_mean1 - mu).var()", | |
| "execution_count": 7, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 7, | |
| "data": { | |
| "text/plain": "2.847696" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:54.270664Z", | |
| "end_time": "2020-12-20T06:34:54.274075Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "(sample_mean10 - mu).var()", | |
| "execution_count": 8, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 8, | |
| "data": { | |
| "text/plain": "0.29415244" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:54.276167Z", | |
| "end_time": "2020-12-20T06:34:54.279808Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "(sample_mean100 - mu).var()", | |
| "execution_count": 9, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 9, | |
| "data": { | |
| "text/plain": "0.027381259899999996" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:54.281573Z", | |
| "end_time": "2020-12-20T06:34:54.285010Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "(sample_mean1000 - mu).var()", | |
| "execution_count": 10, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 10, | |
| "data": { | |
| "text/plain": "0.002833262464" | |
| }, | |
| "metadata": {} | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "... 直感的には、先ほどの図で$n$が大きくなるほど分布が尖って幅0になる、ということ。" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "## 各試行平均値の分布と中心極限定理" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "$$\n\\sqrt{n} (\\bar{X}_n - \\mu)\n$$\n\nの分布が、$n\\to \\infty$につれて正規分布$N(0, \\sigma)$に漸近していく" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:54.286679Z", | |
| "end_time": "2020-12-20T06:34:54.290330Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "sample_mean1_scaled = np.sqrt(1) * (sample_mean1 - mu)\nsample_mean10_scaled = np.sqrt(10) * (sample_mean10 - mu)\nsample_mean100_scaled = np.sqrt(100) * (sample_mean100 - mu)\nsample_mean1000_scaled = np.sqrt(1000) * (sample_mean1000 - mu)", | |
| "execution_count": 11, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:54.292572Z", | |
| "end_time": "2020-12-20T06:34:54.296286Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "def gaussian_function(x, mu=0, sigma=1):\n return np.exp(-(x-mu)**2 / sigma**2 * 0.5) / np.sqrt(2 * np.pi) / sigma\n\nx = np.linspace(-7, 7, 1000)\n\ngaussian_distribution = gaussian_function(x, sigma=sigma)", | |
| "execution_count": 12, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:54.298118Z", | |
| "end_time": "2020-12-20T06:34:54.703030Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "plt.hist(sample_mean1_scaled, bins=20, density=True, label='n=1')\nplt.hist(sample_mean10_scaled, bins=20, density=True, label='n=10')\nplt.hist(sample_mean100_scaled, bins=20, density=True, label='n=100')\nplt.hist(sample_mean1000_scaled, bins=20, density=True, label='n=1000')\nplt.plot(x, gaussian_distribution, color='black', linewidth=3, label='$N(0, \\\\sigma)$')\n\nplt.xlabel('$\\\\sqrt{n}(\\\\bar{X}_n - \\\\mu)$', fontsize=15);\n\nplt.legend()", | |
| "execution_count": 13, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "execution_count": 13, | |
| "data": { | |
| "text/plain": "<matplotlib.legend.Legend at 0x1154ac6a0>" | |
| }, | |
| "metadata": {} | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": "<Figure size 432x288 with 1 Axes>", | |
| "image/png": "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\n" | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "見方を変えると、$\\bar{X}_n$の分布は、$n\\to\\infty$で$N(\\mu, \\sigma/\\sqrt{n})$に近づいていく、とも理解できる" | |
| }, | |
| { | |
| "metadata": { | |
| "ExecuteTime": { | |
| "start_time": "2020-12-20T06:34:54.704270Z", | |
| "end_time": "2020-12-20T06:34:55.029801Z" | |
| }, | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "x = np.linspace(1, 6, 1000)\n\nplt.hist(sample_mean1, bins=20, density=True, label='n=1', alpha=0.5)\n\nplt.hist(sample_mean10, bins=20, density=True, label='n=10', alpha=0.5)\nplt.plot(x, gaussian_function(x, mu=mu, sigma=sigma/np.sqrt(10)), color='tab:orange', linewidth=2)\n\nplt.hist(sample_mean100, bins=20, density=True, label='n=100', alpha=0.5)\nplt.plot(x, gaussian_function(x, mu=mu, sigma=sigma/np.sqrt(100)), color='tab:green', linewidth=2)\n\nplt.hist(sample_mean1000, bins=20, density=True, label='n=1000', alpha=0.5)\nplt.plot(x, gaussian_function(x, mu=mu, sigma=sigma/np.sqrt(1000)), color='tab:red', linewidth=2)\n\nplt.legend()\n\nplt.xlabel('$\\\\bar{X}_n$', fontsize=15);", | |
| "execution_count": 14, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": "<Figure size 432x288 with 1 Axes>", | |
| "image/png": "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\n" | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "", | |
| "execution_count": null, | |
| "outputs": [] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "", | |
| "execution_count": null, | |
| "outputs": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "name": "python3", | |
| "display_name": "Python 3", | |
| "language": "python" | |
| }, | |
| "toc": { | |
| "nav_menu": {}, | |
| "number_sections": true, | |
| "sideBar": true, | |
| "skip_h1_title": false, | |
| "base_numbering": 1, | |
| "title_cell": "Table of Contents", | |
| "title_sidebar": "Contents", | |
| "toc_cell": false, | |
| "toc_position": {}, | |
| "toc_section_display": true, | |
| "toc_window_display": false | |
| }, | |
| "language_info": { | |
| "name": "python", | |
| "version": "3.8.5", | |
| "mimetype": "text/x-python", | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "pygments_lexer": "ipython3", | |
| "nbconvert_exporter": "python", | |
| "file_extension": ".py" | |
| }, | |
| "gist": { | |
| "id": "ed434f786826c6c3666e73b924a06b80", | |
| "data": { | |
| "description": "Visual understanding of law of large numbers and central limit theorem with dices", | |
| "public": true | |
| } | |
| }, | |
| "_draft": { | |
| "nbviewer_url": "https://gist.github.com/ed434f786826c6c3666e73b924a06b80" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 4 | |
| } |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment