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@davidrichards
Created November 11, 2016 01:24
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Bayesian Correlation\n",
"\n",
"A well-used, but sometimes seldom-explained distribution is the [MVNormal][mvnormal] distribution. This distribution combines parent variables into a normal distribution. There are several examples I've found. This [one][singer] from Phillip Singer is a good start. He takes the idea of Pearson's R and estimates it. The benefit of this approach, however, is that we can inspect the posterior distribution on R to check our confidence in that value. \n",
"\n",
"This is a simplified version of his example.\n",
"\n",
"[mvnormal]: https://pymc-devs.github.io/pymc/distributions.html#multivariate-continuous-distributions\n",
"[singer]: http://www.philippsinger.info/?p=581"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import pymc as pm\n",
"from numpy.linalg import inv, det\n",
"from numpy import log, pi, dot\n",
"import numpy as np\n",
"from scipy.special import gammaln\n",
" \n",
"def _model(data):\n",
" # priors might be adapted here to be less flat\n",
" mu = pm.Normal('mu', 0, 0.000001, size=2)\n",
" sigma = pm.Uniform('sigma', 0, 1000, size=2)\n",
" rho = pm.Uniform('r', -1, 1)\n",
" \n",
" @pm.deterministic\n",
" def precision(sigma=sigma,rho=rho):\n",
" ss1 = float(sigma[0] * sigma[0])\n",
" ss2 = float(sigma[1] * sigma[1])\n",
" rss = float(rho * sigma[0] * sigma[1])\n",
" return inv(np.mat([[ss1, rss], [rss, ss2]])) # Important, it takes an inverse covariance matrix.\n",
" \n",
" mult_n = pm.MvNormal('mult_n', mu=mu, tau=precision, value=data.T, observed=True)\n",
" \n",
" return locals()\n",
" \n",
"def analyze(data, plot=True):\n",
" model = pm.MCMC(_model(data))\n",
" model.sample(50000,25000)\n",
" \n",
" print\n",
" if plot:\n",
" pm.Matplot.plot(model.rho)\n",
" \n",
" return model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The model is defined with a few priors:\n",
"\n",
"* mu: mean of both data series, estimated to be very near 0 (note, size=2).\n",
"* sigma: standard deviation of both data series, estimated to be somewhere between 0 and 1,000 (also size=2).\n",
"* rho: an estimate of Pearson's R, the correlation between the two data series, some value between -1 and 1.\n",
"\n",
"There is a deterministic variable for the precision. This combines the standard deviation and the R estimate into an [inverse covariance matrix][inverse]. An inverse covariance matrix for Bayesian statistics is used to measure the amount of information we have in the prior distributions. We calculate it by building a matrix (2x2 in this case):\n",
"\n",
"| mean squared of the first distribution | covariance |\n",
"|----------------------------------------|-----------------------------------------|\n",
"| covariance | mean squared of the second distribution |\n",
"\n",
"We then take the **inverse** of this matrix and provide it to the model.\n",
"\n",
"Finally, we build our multivariate normal distribution. It is a distribution that is able to take ths covariance data and convert it into a combined distribution that expresses how best to fit the parameters to the data. In our case, we observe this combined variable, so the model's purpose is to predict it's parameters, the means, standard deviations, and most importantly rho, our estimate of Pearson's R.\n",
"\n",
"[inverse]: http://stats.stackexchange.com/questions/73463/what-does-the-inverse-of-covariance-matrix-say-about-data-intuitively"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 50000 of 50000 complete in 20.2 sec\n",
"Plotting r\n",
"-0.288266714163\n"
]
},
{
"data": {
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NmBB/eyw76cM3bNCL4CYydar18XZu5ry6mUqWYa5zZ/1oZNNt0SLxjZc58YbB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\nMjqLyEwR2SIia0XkHhHJidm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sX6+fx36+n3/2du0jv4bRnXaavu5O1tlyuh7ZV18BBxyQ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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x110e9de10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"x = np.array([525., 300., 450., 300., 400., 500., 550., 125., 300., 400., 500., 550.])\n",
"y = np.array([250., 225., 275., 350., 325., 375., 450., 400., 500., 550., 600., 525.])\n",
"data = np.array([x, y])\n",
"model = analyze(data)\n",
"print(np.mean(model.rho))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This plot only shows our rho variable, our estimate of Pearson's R. It comes out near 0. That means these data are not very correlated. But notice how wide this distribution is. The dashed lines show us the highest density interval (HDI, similar to a confidence interval). It stretches between about -0.45 and 0.7. That means we really don't know much about the correlation of these two data sets.\n",
"\n",
"Let's take a look at more-clearly correlated data sets."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 50000 of 50000 complete in 19.7 sec\n",
"Plotting r\n",
"0.916951819685\n"
]
},
{
"data": {
"image/png": 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390RGX4T1cg4cfDAsWOA+PUDr1nDYYd62cdLSy5RbCWjLo2rK/vGPfyRPBFx7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\nfQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x111c16950>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"x = np.array([525., 300., 450., 300., 400., 500., 550., 125., 300., 400., 500., 550.])\n",
"y = np.array([500., 225., 400., 350., 425., 450., 450., 100., 300., 425., 500., 525.])\n",
"data = np.array([x, y])\n",
"model = analyze(data)\n",
"print(np.mean(model.rho))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we see there is a very strong correlation. About 0.9. More-importantly, our HDI is between 0.8 and 1.0. That means we wouldn't ever expect a correlation less than 0.8 for data like these."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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