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@kain88-de
Created June 5, 2015 11:19
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Fitting with Bayes MCMC
{
"cells": [
{
"cell_type": "code",
"execution_count": 89,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from __future__ import print_function\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from scipy import constants\n",
"import seaborn as sns\n",
"sns.set_style(\"darkgrid\")\n",
"import scipy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Table of Contents\n",
"* [Generate test data](#Generate-test-data)\n",
"* [Fit the test data to a sin function using bayes interference](#Fit-the-test-data-to-a-sin-function-using-bayes-interference)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Generate test data"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"alpha = 1.4\n",
"f = lambda x : np.sin(alpha * x)"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {
"code_folding": [],
"collapsed": false
},
"outputs": [],
"source": [
"x = np.linspace(0, np.pi, 8)\n",
"x_fine = np.linspace(-.5,np.pi +.5,1000)\n",
"y = np.sin(1.4*x)"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {
"code_folding": [],
"collapsed": false
},
"outputs": [
{
"data": {
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BoK/uZhMbFcJLz00lMd7aa34hmvPCinHERoV8NSGohqce6im/0z6oTeWutf4U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\nkJS7EEL4ICl3IYTwQf8fxu1aLPE1Cc8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fa8d9ea3a50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#plot\n",
"sns.plt.plot(x,y, 'o', zorder=2)\n",
"sns.plt.plot(x_fine, f(x_fine), zorder=1)\n",
"plt.ylim(-1.1, 1.1)\n",
"plt.xlim(min(x_fine), x_fine.max());\n",
"plt.title('original curve with points');"
]
},
{
"cell_type": "markdown",
"metadata": {
"code_folding": []
},
"source": [
"For each dot here generate an ensemble of possible measurments. They will be distributed with a simple gaussian first in this example."
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sigma = .01\n",
"measurements = np.array([np.random.normal(mu, scale=sigma, size=15) for mu in y])"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {
"code_folding": [
0
],
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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mZpqU+xhtzd3UV18jIyeenIJEs+MIMeNSnn8Be3wC9vgEUp9/gXVbfbOJyWTa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\nQgQhKXchhAhCUu5CCBGEpNyFECII/V/v8/JjhnhVuwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fa8dba8b1d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#measurements comparison with original curve\n",
"plt.plot(x, measurements, 'o', c='indianred')\n",
"plt.plot(x_fine, f(x_fine))\n",
"plt.title('Measurements');\n",
"plt.xlim(min(x_fine), max(x_fine));"
]
},
{
"cell_type": "markdown",
"metadata": {
"code_folding": [
0
]
},
"source": [
"# Fit the test data to a sin function using bayes interference"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import pymc as pm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are several unkowns in this example now. First the two variables $\\alpha$ and $\\phi$ from the original sin curve and then $\\sigma$ the standard deviation of the error for each measurement."
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"alpha = pm.Normal('alpha', 3, 1)\n",
"tau = pm.Normal('tau', 5, 10)"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"obs = [pm.CommonDeterministics.Lambda('obs_{}'.format(i), \n",
" lambda alpha=alpha : np.sin(alpha*xx))\n",
" for i, xx in enumerate(x)]"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"noises = [pm.Normal('noise_{}'.format(i), o, tau,\n",
" value=m, observed=True) for i, (m, o) in \n",
" enumerate(zip(measurements, obs))]"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"var_list = [tau, alpha]\n",
"var_list.extend(obs)\n",
"var_list.extend(noises)"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"model = pm.Model(var_list)"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"map_ = pm.MAP(model)\n",
"map_.fit()"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 100000 of 100000 complete in 15.0 sec"
]
}
],
"source": [
"mcmc = pm.MCMC(model)\n",
"mcmc.sample(100000, 90000)"
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting alpha\n"
]
},
{
"data": {
"image/png": 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8AKzB1dKllOoLVIcTePmKZnqTgGLQGvKOz3QwBTnBx5hKJjM/inx8KLMhG377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\nGYseg/0qVX8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fa8e8443d90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.Matplot.plot(mcmc.trace(\"alpha\"))"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting tau\n"
]
},
{
"data": {
"image/png": 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91EZOyrkSERFXUz6P+6mNnOIKrowxLYEFwB+stU8FbT8auAeoAqZZa+9OSylF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\nbIHeoJNH96Vbx1b1nnG8qH3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GzMJ38R8PPOU/9n1gcsMUuy5jzEBgIPC2f9NY4Cr/46yp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\nIiIiIglScyUiIiKSIDVXIiIiIgn6f2RXJAMOD8pAAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fa8ebec8d10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.Matplot.plot(mcmc.trace(\"tau\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" ##Look at plot of estmated values"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy.stats.mstats import mquantiles"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"alpha_ = mcmc.trace('alpha')[:]\n",
"alpha_mean = np.mean(alpha_)\n",
"alpha_qs = mquantiles(alpha_, [.025, .975])"
]
},
{
"cell_type": "code",
"execution_count": 107,
"metadata": {
"code_folding": [
0
],
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa8d9b41090>"
]
},
"execution_count": 107,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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c5mbq173nU11U3ubEgSIaalvc7p+1OMXlOhajnTgjA9TeZuNMzmUCAg1Myojv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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fa8d9cadc50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#plot CI for alpha value\n",
"plt.fill_between(x_fine, np.sin(alpha_qs[0]*x_fine),\n",
" y2=np.sin(alpha_qs[1]*x_fine),\n",
" color='#7A68A6')\n",
"plt.plot(x_fine,np.sin(alpha_qs[0]*x_fine), color='#7A68A6',\n",
" label='95% CI')\n",
"plt.plot(x_fine, np.sin(1.4*x_fine), label='input', zorder=1,\n",
" c='indianred')\n",
"plt.plot(x, measurements, 'o',zorder=-1,\n",
" color='blue')\n",
"plt.ylim(-1.4, 1.4)\n",
"plt.legend(loc='lower right')"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"betas = 1 / mcmc.trace('tau')[:]\n",
"betas_mean = np.mean(betas)\n",
"betas_qs = mquantiles(betas, [.025,.975])"
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {
"code_folding": [],
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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v2YQhLo6I+QvOvj9zzCiOn+mssNsdGAxdW7ykv+rLuTgr6wmP5WJRIAsel3+4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xGTQEGDQEGjVEhRoZGmYk2N+vV7t6mMZPoD0rk7aDB0hPSGIXoRTm1jBvYq+dQuih3szF27Zt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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fa8d9bab990>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# widest and narrowst error distribution\n",
"def plot_error_distri(idx):\n",
" mu = np.sin(1.4*x[idx])\n",
" m = measurements[idx]\n",
"\n",
" xx = np.linspace(mu-1, mu+1,100)\n",
" plt.plot(xx, scipy.stats.norm.pdf(xx, mu, betas.max()), label='max')\n",
" plt.plot(xx, scipy.stats.norm.pdf(xx, mu, betas.min()), label='min')\n",
" plt.plot(xx, scipy.stats.norm.pdf(xx, mu, betas.mean()), label='mean')\n",
" plt.plot(xx, scipy.stats.norm.pdf(xx, mu, .2), label='Input')\n",
"\n",
" plt.plot(m, np.ones(len(m))*.1, 'o')\n",
" plt.xlim(mu-1, mu+1)\n",
" plt.legend();\n",
" plt.title('idx = {}'.format(idx))\n",
"\n",
"plt.figure(figsize=(10,10))\n",
" \n",
"for i in range(len(measurements)):\n",
" plt.subplot(4,2,i+1)\n",
" plot_error_distri(i)\n",
" \n",
"plt.tight_layout();"
]
}
],
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"kernelspec": {
"display_name": "Python 2",
"language": "python",
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
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},
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