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Simple example of a bootstrap computation of model errors
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Computing Model Errors with Bootstrap\n",
"\n",
"This is a quick example of computing model parameter errors with a bootstrap approach.\n",
"For simplicity, we'll do a straight-line fit, with errors on slope and intercept"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Generate the Data\n",
"\n",
"First we'll generate some data"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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XJo+BPiS99tB7HYQcxWClJSBpshnoQ9QthPuZjmjPWdJWDPQh6RbW/dbGDXRJWzHQh6CX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\npJL4f1Wdh6PoNtQiAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106db3eb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Here we'll randomly generate 20 points along a line\n",
"rand = np.random.RandomState(42)\n",
"N = 20\n",
"\n",
"x = 10 * rand.rand(N)\n",
"y = 2 * x + 5 + rand.randn(20)\n",
"\n",
"plt.errorbar(x, y, 1, fmt='o');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simple Linear Regression\n",
"\n",
"There are many ways to do linear regression in Python; for simplicity we'll use ``np.polyfit`` to fit a polynomial of degree 1:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"slope = 1.94834652666\n",
"intercept = 4.963605003\n"
]
}
],
"source": [
"# simple straight-line fit\n",
"slope, intercept = np.polyfit(x, y, deg=1)\n",
"\n",
"print(\"slope =\", slope)\n",
"print(\"intercept =\", intercept)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimating errors with bootstrap\n",
"\n",
"We can estimate the errors on the slope and intercept using a bootstrap approach: essentially we resample the data *with replacement* repeatedly and determine the distribution of the fitted parameters.\n",
"Resampling can be done efficiently using Numpy's fancy indexing:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"slope = 1.95 +/- 0.07\n",
"intercept = 4.96 +/- 0.42\n"
]
}
],
"source": [
"# We'll do 1000 bootstrap samples\n",
"Nbootstrap = 1000\n",
"\n",
"# create a 2D array to hold all the results\n",
"fits = np.zeros((Nbootstrap, 2))\n",
"\n",
"for i in range(Nbootstrap):\n",
" # generate N integers between 0 and N\n",
" sample = rand.randint(0, N, N)\n",
" \n",
" # these integers are used to resample the data\n",
" fits[i] = np.polyfit(x[sample], y[sample], 1)\n",
"\n",
"# compute the standard deviation along axis 0\n",
"slope_err, intercept_err = fits.std(axis=0)\n",
"\n",
"print(\"slope = {0:.2f} +/- {1:.2f}\".format(slope, slope_err))\n",
"print(\"intercept = {0:.2f} +/- {1:.2f}\".format(intercept, intercept_err))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This approach also lets us get an idea of the covariance between the error terms:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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O77r37OwiCwtGLBaV9nYnJlMLZvM6Ho+bZLKJ1erCYjGSz2eIxaIUCjr0+uNU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\nICIiolESRERENEqCiIiIRucAJXrSNcrf668AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106db3c18>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Scatter the individual realizations to get an idea of correlations\n",
"plt.scatter(fits[:, 0], fits[:, 1], alpha=0.2)\n",
"plt.scatter([slope], [intercept], s=100, marker='x', c='red')\n",
"plt.xlabel('slope')\n",
"plt.ylabel('intercept');"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.5",
"language": "",
"name": "python3.5"
},
"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
}
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