Created
February 5, 2017 20:59
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Bad bootstrapping of a residuals
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Bootstrapping the residuals of a linear model" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"import probscale\n", | |
"import numpy\n", | |
"from matplotlib import pyplot\n", | |
"\n", | |
"%matplotlib inline" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### bootstrapping the data seems to work properly:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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WEeePjT/kdv0DKqKz9LZ8jJD7JhIltpzmW1NTQ3t7O+Xlawe/EGJr5Pox6m+A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\nhAS6EEIUif8L0RxTqEImqQAAAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10ac4e400>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"data = numpy.array([\n", | |
" 3.113, 3.606, 4.046, 4.046, 4.710, 6.140, 6.978,\n", | |
" 2.000, 4.200, 4.620, 5.570, 5.660, 5.860, 6.650,\n", | |
"])\n", | |
"\n", | |
"fig = probscale.probplot(data, ci_estimator='fit', bestfit=True, plottype='pp')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"# pretty much the same as the _bs_resid function:\n", | |
"# https://github.com/phobson/mpl-probscale/blob/bs-resids/probscale/algo.py#L64\n", | |
"\n", | |
"\n", | |
"x, y = probscale.plot_pos(data)\n", | |
"\n", | |
"niter = 10000\n", | |
"xhat = numpy.linspace(x.min(), x.max(), num=len(x))\n", | |
"fitlogs = False\n", | |
"alpha = 0.05\n", | |
"\n", | |
"index = probscale.algo._make_boot_index(len(x), niter)\n", | |
"yhat, results = probscale.algo._fit_simple(x, y, xhat, fitlogs=fitlogs)\n", | |
"resid = y - yhat\n", | |
"bs_y = y + resid[index]\n", | |
"\n", | |
"percentiles = 100 * numpy.array([alpha*0.5, 1 - alpha*0.5])\n", | |
"yhat_lo, yhat_hi = numpy.percentile(bs_y, percentiles, axis=0)\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Expected this to have similar shape as the figure above" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.collections.PolyCollection at 0x10e1ada20>" | |
] | |
}, | |
"execution_count": 5, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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BI0fz6e8Q6T2Ef/YoaV87Q9e/Z7FNsHZ3l6nzOOhq9hOQ2ZZCmGrd/UQZhubM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\nCyFEDZMQF0KIGiYhLoQQNez/A7dpwqLn00iTAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10ac4e3c8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig, ax = pyplot.subplots()\n", | |
"ax.plot(x, y, '.', zorder=10)\n", | |
"ax.plot(xhat, yhat, '-', zorder=5)\n", | |
"ax.fill_between(xhat, yhat_lo, yhat_hi, alpha=0.25, zorder=0)" | |
] | |
} | |
], | |
"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": "3.5.2" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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