Skip to content

Instantly share code, notes, and snippets.

Show Gist options
  • Star 0 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save stharrold/c829d721470c363f27bf to your computer and use it in GitHub Desktop.
Save stharrold/c829d721470c363f27bf to your computer and use it in GitHub Desktop.
20160115T103000Z_StackExchange_CrossValidated_CLT-vs-ncombos.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Relationship of CLT for estimator of sample and number of possible combinations for subsample\n",
"\n",
"What is the relationship between the Central Limit Theorem for an estimator of a parent sample and the number of possible combinations of a subsample used to calculate that estimator?\n",
"\n",
"If you draw a fixed number of subsamples (`num_subsamples`) from a parent sample with replacement, the variance of an estimator calculated from those subsamples does not seem decrease for subsample sizes (`size_sub`) $ \\gtrapprox $ half the parent sample size (`size_parent/2`). The number of possible combinations of subsamples (`ncombos`) peaks at `size_sub = size_parent/2`, but only for sampling _without_ replacement. Is there a relationship between the variance of an estimator from the subsamples and `ncombos`?"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/samuel_harrold/anaconda3/lib/python3.5/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
" warnings.warn(self.msg_depr % (key, alt_key))\n"
]
}
],
"source": [
"# Requires Python 3x.\n",
"# Import standard packages.\n",
"import os\n",
"import subprocess\n",
"# Import installed packages.\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import scipy\n",
"import seaborn as sns\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Generate samples.\n",
"np.random.seed(seed=3)\n",
"size_parent = 29\n",
"sample_parent = np.random.normal(loc=0.0, scale=1.0, size=size_parent)\n",
"sizes_stds = list()\n",
"sizes_means = list()\n",
"sizes_ncomboswrepl = list()\n",
"sizes_ncombosworepl = list()\n",
"percentiles = [16, 50, 84]\n",
"num_subsamples = 1000\n",
"for size_sub in range(1, size_parent+1):\n",
" means = list()\n",
" stds = list()\n",
" for _ in range(num_subsamples):\n",
" sample_sub = np.random.choice(sample_parent, size=size_sub, replace=True)\n",
" means.append(np.mean(sample_sub))\n",
" stds.append(np.std(sample_sub))\n",
" sizes_means.append((size_sub, *np.percentile(means, q=percentiles)))\n",
" sizes_stds.append((size_sub, *np.percentile(stds, q=percentiles)))\n",
" sizes_ncomboswrepl.append((size_sub, scipy.misc.comb(size_parent, size_sub, repetition=True)))\n",
" sizes_ncombosworepl.append((size_sub, scipy.misc.comb(size_parent, size_sub, repetition=False)))\n",
"sizes_means = np.asarray(sizes_means)\n",
"sizes_stds = np.asarray(sizes_stds)\n",
"sizes_ncomboswrepl = np.asarray(sizes_ncomboswrepl)\n",
"sizes_ncombosworepl = np.asarray(sizes_ncombosworepl)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/samuel_harrold/anaconda3/lib/python3.5/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
" warnings.warn(self.msg_depr % (key, alt_key))\n",
"/home/samuel_harrold/anaconda3/lib/python3.5/site-packages/matplotlib/__init__.py:892: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
" warnings.warn(self.msg_depr % (key, alt_key))\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Size of parent sample = 29\n",
"Num. subsamples used for estimate = 1000\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAh0AAAF/CAYAAADttHsrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ndBAREZFT/D/3y991bqirZgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f660dfe3f98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Make plot.\n",
"sns.set()\n",
"print(\"Size of parent sample =\", size_parent)\n",
"print(\"Num. subsamples used for estimate =\", num_subsamples)\n",
"fig = plt.figure()\n",
"ax0 = fig.add_subplot(111)\n",
"ax0.set_title(\n",
" \"Est. mean, stddev. of parent sample; num. possible\\n\" +\n",
" \"combos of subsample vs subsample size\")\n",
"ax0.plot(\n",
" sizes_means[:, 0], sizes_means[:, 2],\n",
" marker='.', color=sns.color_palette()[0], label='est mean (dark=actual, shade=16-84th pctls)')\n",
"ax0.fill_between(\n",
" sizes_means[:, 0], y1=sizes_means[:, 1], y2=sizes_means[:, 3],\n",
" alpha=0.5, color=sns.color_palette()[0])\n",
"ax0.axhline(y=np.mean(sample_parent), color=sns.color_palette(palette='dark')[0])\n",
"ax0.plot(\n",
" sizes_stds[:, 0], sizes_stds[:, 2],\n",
" marker='.', color=sns.color_palette()[1], label='est stddev (dark=actual, shade=16-84th pctls)')\n",
"ax0.fill_between(\n",
" sizes_stds[:, 0], y1=sizes_stds[:, 1], y2=sizes_stds[:, 3],\n",
" alpha=0.5, color=sns.color_palette()[1])\n",
"ax0.axhline(y=np.std(sample_parent), color=sns.color_palette(palette='dark')[1])\n",
"ax0.set_xlabel(\"Size of subsample\")\n",
"ax0.set_ylabel(\n",
" \"Est. mean, stddev. of parent sample\")\n",
"ylim0 = (-1.0, 1.5)\n",
"ax0.set_ylim(ylim0)\n",
"nticks = 6\n",
"ax0.set_yticks(np.linspace(start=ylim0[0], stop=ylim0[1], num=nticks, endpoint=True))\n",
"ax0.legend(loc='upper left')\n",
"ax1 = ax0.twinx()\n",
"ax1.plot(\n",
" sizes_ncomboswrepl[:, 0], np.log10(sizes_ncomboswrepl[:, 1]),\n",
" marker='.', color=sns.color_palette()[2], label='log10 num combos w repl')\n",
"ax1.plot(\n",
" sizes_ncombosworepl[:, 0], np.log10(sizes_ncombosworepl[:, 1]),\n",
" marker='.', color=sns.color_palette()[3], label='log10 num combos w/o repl')\n",
"ax1.set_ylabel(\"Log10 number of possible combinations\")\n",
"ylim1 = (0, 20)\n",
"ax1.set_ylim(ylim1)\n",
"ax1.set_yticks(np.linspace(start=ylim1[0], stop=ylim1[1], num=nticks, endpoint=True))\n",
"ax1.legend(loc='upper right')\n",
"plt.savefig(os.path.join(os.path.expanduser(r'~'), 'estimate_vs_subsample_size.jpg'))\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"jupyter nbconvert --to html --template full /home/samuel_harrold/sandbox/ipynbs/20160115T103000Z_StackExchange_CrossValidated_CLT-vs-ncombos.ipynb --output /home/samuel_harrold/sandbox/ipynbs/20160115T103000Z_StackExchange_CrossValidated_CLT-vs-ncombos-full.html\n",
"\n"
]
}
],
"source": [
"# Export ipynb to html\n",
"path_ipynb = os.path.join(\n",
" os.path.expanduser(r'~'),\n",
" r'sandbox/ipynbs/20160115T103000Z_StackExchange_CrossValidated_CLT-vs-ncombos.ipynb')\n",
"template = 'full'\n",
"path_html = os.path.splitext(path_ipynb)[0]+'-'+template+'.html'\n",
"cmd = ['jupyter', 'nbconvert', '--to', 'html', '--template', template, path_ipynb, '--output', path_html]\n",
"print(' '.join(cmd))\n",
"subprocess.run(args=cmd, check=True)\n",
"print()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.1"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment