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bootstrap.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "bootstrap.ipynb",
"provenance": [],
"collapsed_sections": [],
"authorship_tag": "ABX9TyOJsBkBPxuAPxtrvbr2WUt5",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
},
"widgets": {
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"children": [
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],
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"readout": true,
"readout_format": "d",
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"msg_id": "",
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 360x360 with 1 Axes>",
"image/png": 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AlqRGDGBJasQAlqRGDGBJasQAlqRGHAcsLWC7n9jF+RddMum2FWNL2bZl85Ar0iADWFrAjtSSSW+sAdi7deOQq9Gx7IKQpEYMYElqxC6IRWiqCXfASXekYTKAF6GpJtwBJ93R1L+g/dBu7hnAkn7GVL+g/dBu7tkHLEmNeAUsLVJTjRH2c4DhMYClRWqqMcJ+DjA8dkFIUiMGsCQ1YgBLUiMGsCQ1YgBLUiMGsCQ1YgBLUiMGsCQ10uRGjCRPAz8BXgCOVNXaJEuBzwGrgaeBy6vquRb1SdIwtLwCfntVramqtd369cD9VXUOcH+3LkkL1nzqglgH3N4t3w68q2EtktS7VgFcwF8leSjJhq5tWVUd7Ja/Dyyb7MAkG5LsSLJjfHx8GLVKUi9aTcbz1qran+SfAfcm+c7gxqqqJDXZgVW1CdgEsHbt2kn3kaRR0OQKuKr2d8+HgLuAc4FnkiwH6J4PtahNkoZl6AGc5OeSvPLoMvCrwKPAduCqbrergLuHXZskDVOLLohlwF1Jjv78LVX1pSTfAO5Mcg2wF7i8QW2SNDRDD+Cqegp4wyTtPwAuHHY9ktTKfBqGJkmLigEsSY0YwJLUiAEsSY0YwJLUiAEsSY0YwJLUiAEsSY0YwJLUiAEsSY0YwJLUSKv5gDUEl165ngPjh49r3/PkU6xqUI+kn2UAL2AHxg+z6rIbj2vfedPVwy9G0nHsgpCkRgxgSWrEAJakRgxgSWrED+EkvWhTjbhZMbaUbVs2N6hoNBjAkmZk9xO7OP+iSybdtufJp7jw+luPa79v4/opjzGcDWBJM3Sklkw6rBGmHto43TF7t26cq9JGln3AktSIASxJjdgFMSL8kENaeAzgETHVbcX2o0mjyy4ISWrEAJakRgxgSWrEPuARd6LB8c77K81fBvCIm83geEnzgwEsqYmp/npbTEMrDeB5xq8R0mIx1V9vi2lopQE8z/g1QtLi4SgISWrEAJakRgxgSWrEAJakRgxgSWrEAJakRhyG1qOpxvTue/q7rFx99qTHON5XWjwM4B5NN6bX24elk7fQvpjAAJY0MhbaFxPYByxJjXgFPEML7U8fab5aTFOsGsAzNNWfPvdtXL9o/rFIw7CYpliddwGc5GLgj4BTgE9V1ccblzStxfSPRZqvprtqns9/pc6rAE5yCvDfgYuAfcA3kmyvqsfbViZpPpvuQmg2H9ANq8txXgUwcC6wp6qeAkhyB7AOmNMAdnyutHjMZuL3YY22SFXN6Qu+GEneA1xcVb/Vrb8P+OWqum5gnw3Ahm71XwC7hl7o3HoV8GzrIubQQjqfhXQu4Pm09GxVXXxs43y7Aj6hqtoEbGpdx1xJsqOq1rauY64spPNZSOcCns98NN/GAe8HzhpYX9m1SdKCM98C+BvAOUnOTvJS4Apge+OaJKkX86oLoqqOJLkO+DITw9Buq6rHGpfVtwXTndJZSOezkM4FPJ95Z159CCdJi8l864KQpEXDAJakRgzgIUrysiRfT/L3SR5L8rtd+6eTfDfJw91jTetaZyrJKUm+leSL3frZSR5MsifJ57oPU0fGJOczyu/N00m+3dW9o2tbmuTeJLu75zNa1zkTU5zLx5LsH3hv3tm6zpNlAA/X88AFVfUGYA1wcZLzum0frqo13ePhdiWetA8AOwfWfw+4uapeCzwHXNOkqtk79nxgdN8bgLd3dR8dL3s9cH9VnQPc362PimPPBSb+rR19b+5pVtksGcBDVBP+oVt9SfcY2U9Bk6wE/jXwqW49wAXA57tdbgfe1aa6k3fs+SxQ65h4X2DE3p+FyAAesu5P3IeBQ8C9VfVgt2ljkkeS3JzktIYlnow/BP4r8NNu/eeBH1bVkW59H3Bmi8Jm6djzOWoU3xuY+OX+V0ke6m7hB1hWVQe75e8Dy9qUdtImOxeA67r35rZR6U4ZZAAPWVW9UFVrmLjL79wkrwduAH4ReDOwFPhIwxJnJMklwKGqeqh1LXNhmvMZufdmwFur6k3AO4Brk/yrwY01MQZ1VP4Cm+xcbgFew0R33kHgEw3rmxUDuJGq+iHwABOTDx3suieeB/6MiVnh5ru3AP8mydPAHUx0PfwRcHqSozf4jNKt5MedT5L/OaLvDQBVtb97PgTcxUTtzyRZDtA9H2pX4cxNdi5V9Ux3QfNT4JOM0HtzlAE8REnGkpzeLb+ciXmPvzPwHyJM9Mk92q7KmamqG6pqZVWtZuKW8a9U1W8w8UvlPd1uVwF3NyrxpExxPv9+FN8bgCQ/l+SVR5eBX2Wi9u1MvC8wIu/PVOdy9L3pvJsReW8GzatbkReB5cDt3cTzS4A7q+qLSb6SZAwI8DDwH1oW+SJ9BLgjyU3At4BbG9fzYn1mRN+bZcBdE783OBXYUlVfSvIN4M4k1wB7gcsb1jhTU53Ln3fDAgt4Gnh/uxJnx1uRJakRuyAkqREDWJIaMYAlqREDWJIaMYAlqREDWJIaMYAlqZH/B5LzZca0nN8KAAAAAElFTkSuQmCC\n"
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"_model_module_version": "1.2.0",
"_model_name": "LayoutModel",
"_view_count": null,
"_view_module": "@jupyter-widgets/base",
"_view_module_version": "1.2.0",
"_view_name": "LayoutView",
"align_content": null,
"align_items": null,
"align_self": null,
"border": null,
"bottom": null,
"display": null,
"flex": null,
"flex_flow": null,
"grid_area": null,
"grid_auto_columns": null,
"grid_auto_flow": null,
"grid_auto_rows": null,
"grid_column": null,
"grid_gap": null,
"grid_row": null,
"grid_template_areas": null,
"grid_template_columns": null,
"grid_template_rows": null,
"height": null,
"justify_content": null,
"justify_items": null,
"left": null,
"margin": null,
"max_height": null,
"max_width": null,
"min_height": null,
"min_width": null,
"object_fit": null,
"object_position": null,
"order": null,
"overflow": null,
"overflow_x": null,
"overflow_y": null,
"padding": null,
"right": null,
"top": null,
"visibility": null,
"width": null
}
}
}
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/coppeliaMLA/a384bfb2680fc1847d88f493e58ae4e1/bootstrap.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"source": [
"# Bootstrapping"
],
"metadata": {
"id": "vLJfnE42jITC"
}
},
{
"cell_type": "markdown",
"source": [
""
],
"metadata": {
"id": "Uq_S7rNyqvXP"
}
},
{
"cell_type": "markdown",
"source": [
"Here's a data set that gives the ages of a random sample of 25 people from a population. This gives us the empirical distribution function. "
],
"metadata": {
"id": "3ypXwu7eZIui"
}
},
{
"cell_type": "code",
"source": [
"from ipywidgets import interact\n",
"import ipywidgets as widgets\n",
"import seaborn as sns\n",
"import numpy as np\n",
"age = [23, 34, 44, 34, 22, 65, 32, 45, 65, 73, 93, 43, 54, 37, 23, 24, 68, 28, 32, 54, 23, 32, 67, 52, 43]\n",
"_ = sns.displot(age)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 369
},
"id": "lbZ5C8_oZfao",
"outputId": "2f52b7d6-c14b-4406-d0fb-e97cd47b3b31"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"The following code allows you to vary the bootstrap sample size and see how it affects the distribution of the estimator for the population mean. "
],
"metadata": {
"id": "-garmH06ZwHD"
}
},
{
"cell_type": "code",
"source": [
"@interact(n=(10,5000,100))\n",
"def boot_size(n=10):\n",
" bootstrapped_means = []\n",
" for i in range(n):\n",
" bootstrap_sample = np.random.choice(age, replace=True, size = len(age))\n",
" bootstrapped_means.append(np.mean(bootstrap_sample))\n",
" _ = sns.displot(bootstrapped_means)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 401,
"referenced_widgets": [
"80d8593cbe1445e3b80ebd68b1f1b599",
"522db9791be944b7b8c01aa0c0426277",
"0e1980db124d4ef999aff8bcc37d9687",
"c4c0f0b7a2ce4763b63320d1fef862aa",
"f20bf8721d4e458e8f0d7f213b15b0fc",
"830bf91f683b4e71b2fb3dde673070f8",
"0946f9eb6fca427ca5bf8b19d4758e28"
]
},
"id": "6n-Ou4-2W7nx",
"outputId": "eb160390-361a-42c4-dd2a-a77dddba395e"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"interactive(children=(IntSlider(value=10, description='n', max=5000, min=10, step=100), Output()), _dom_classe…"
],
"application/vnd.jupyter.widget-view+json": {
"version_major": 2,
"version_minor": 0,
"model_id": "80d8593cbe1445e3b80ebd68b1f1b599"
}
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"You can alter the code to explore the distribution of the estimator for any sample statistic. \n",
"\n",
"Try\n",
"\n",
"1. The standard deviation\n",
"2. The coefficient of variation (variance/abs(mean))\n",
"\n",
"And explain the results\n",
"\n",
"Why would bootstrap estimates of the median, min and max be more problematic? Try this out"
],
"metadata": {
"id": "Mpatiwn4alG2"
}
}
]
}
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