{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Data Analysis and Machine Learning Applications for Physicists" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Material for a* [*University of Illinois*](http://illinois.edu) *course offered by the* [*Physics Department*](https://physics.illinois.edu). *This content is maintained on* [*GitHub*](https://github.com/illinois-mla) *and is distributed under a* [*BSD3 license*](https://opensource.org/licenses/BSD-3-Clause).\n", "\n", "[Table of contents](Contents.ipynb)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()\n", "import numpy as np\n", "import pandas as pd\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from sklearn import neighbors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Markov Chain Monte Carlo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Markov-chain Monte Carlo** (MCMC) is an algorithm to generate random samples from an un-normalized probability density. In other words, you want sample from $P(\\vec{z})$ but can only evaluate $f(\\vec{z})$ where the two are related by\n", "\n", "$$ \\Large\n", "P(\\vec{z}) = \\frac{f(\\vec{z})}{\\int d\\vec{z}\\,f(\\vec{z})} \\; .\n", "$$\n", "\n", "Note that $0 \\le P(\\vec{z}) \\le 1$ requires that $f(\\vec{z}) \\ge 0$ everywhere and that the integral has a non-zero finite value." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Examples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will start with some simple motivating examples before diving into the Bayesian applications and the theory of Markov chains.\n", "\n", "The function\n", "\n", "$$ \\Large\n", "f(z) = \\begin{cases}\n", "\\sqrt{1 - z^4} & |z| < 1 \\\\\n", "0 & |z| \\ge 1\n", "\\end{cases}\n", "$$\n", "\n", "is never negative and has a finite integral:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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pQzNLdGVDkZxZtaiaa1c3cPh0H/uPd3tdjicU5FmQSLhsffEoAcfhw7e2XP4HRCSrHrg9+b4r1l65gjwLXjnQxrmuYW69agHNOmVYJOeWNVeyeV0Tx84N8GZrp9fl5JyC/ArFEwmeeukYwYDD/Vp/U8QzD9zWguPA1heOFV2vXEF+hXYd6qC9d4Tbr15IQ3Wp1+WIFK1FDeXctL6Z0x2DRbfGp4L8Criuy7OvnMBx4J6blnldjkjR+2DqffjszuK6zK2C/AocON7DybZBrjdNNNdqbFzEa8uaK9m4sg57qpcjZ/su/wMFQkF+BZ595QSQvOaDiOSHe29aDsBzRdQrV5DP0YnzAxw43sP65bW0LKzyuhwRSVm3rIaWhZXsPtzB+e7iuAaLgnyOnns1+Wmv3rhIfnEch3tvWo4L/OTV4uiVK8jnoG9wjF2H2lnUUM6GljqvyxGRi2xa20h9VZQd+88zPDpx+R/wOQX5HLyw5xzxhMtd1y3GcRyvyxGRiwQCDndet4jYeIId+wp/FSEF+SwlEi7/8uYZIuEgt2xc4HU5IjKD269eRCjosO2NMwV/gpCCfJbeOtJJd/8YWzYuoDSSyQJLIuKFqvISNq9r4lzXMPZkr9flzCsF+Sxt230GQKv/iPhA+n36szfOeFzJ/FKQz0JbzzD7jnWzekk1S5t0qVqRfLd6cTVLGit443AHPQNjXpczbxTks/DSnuRBE/XGRfzBcRzu2rSYeMIt6IOeCvIMJVyXl/efpzQS5Pq1jV6XIyIZuml9E6FggJf3txXsQU8FeYbsyV66+8fYbJooCQe9LkdEMlQWDXPtmgbOdg5xom3A63LmhYI8Q+ndMk05FPGf9Pt2x97zHlcyPxTkGRiLxdllO2iojrJmaY3X5YjILG1sqaOyLMzOA21MxBNel5N1CvIM7H67g7FYnC0bFhDQmZwivhMKBrjpPc0Mjoyz72jhLdCsIM/Ajn3J3TENq4j4160bFwIU5OwVBfll9A2OceB4N6sWVWlhZREfW9ZcweKGct5s7Sy4C2kpyC9j99uduC7cuL7Z61JE5Ao4jsMN65uYiLu8daTT63KySkF+Ga/bdgCuN5o7LuJ315smAHbbDo8ryS4F+SUMjoxz6EQvLQsrqauKel2OiFyhRfVlLKgrY+/RLsZica/LyRoF+SW8+XYnCded/BQXEX9zHIfrTSOxiQR7j3Z5XU7WKMgvYXJYRafkixSMzenhlcOFM7yiIJ/ByNgE+493s6SxXLNVRArIsuYKGqqjvHWkk/GJwjg5SEE+gz1HupiIa1hFpNA4jsOmtY2MjMU5eKIwTg667BI3xpgA8ARwDTAGPGqtbZ2y/V7gC6lvdwOfttb6/hJjr6d2uzRbRaTwbDZN/OS1U+yyHVy9qsHrcq5YJj3yB4CotXYL8Hng8fQGY0wl8BfAL1prbwaOA75vlYl4gv3HumisibK4odzrckQky1YurqKqLMzeI10FcWnbTBadvA14DsBau9MYs3nKtluAvcDjxpiVwNetvfQEzdraMkKh3F4GtrGxclb333+0i5GxOO/bvIympqp5qsp7s22XYqA2mV4htsv165vZ9vpphiZcWhbN7X2eL+2SSZBXAX1Tvo8bY0LW2gmSve+7gGuBQeBFY8zL1trDMz1YT8/wldQ7a42NlXR0zO4axC/uPgXAqoWz/1m/mEu7FDq1yfQKtV3WLKpi2+vwwuunqAjP/nBhrtvlUh8amVTfD0x9hEAqxAG6gNesteettYPACyRD3df2He0mGHBYt0yXrBUpVO9pqcMB9hXAfPJMgnw7cB+AMeZmkkMpaa8DG40xDcaYEHAzcCDrVeZQ/1CME20DrF1aQ7Qkkx0WEfGjqrISli+o5O3TfYyM+fsiWpkE+VZg1BizA/gi8BljzGeNMR9KjYf/IfA88ArwA2vtvvkrd/7tP5acjrRxZZ3HlYjIfNu4sp54wuXQyR6vS7kil+1yWmsTwGMX3XxoyvbvAt/Ncl2e2XssuZt1VUu9x5WIyHy7amUdz+w4zr6j3Vy3xr9TjXVC0BQJ12Xf0W5qKkpY3KhphyKFbuWiKkojIfYe9fc0RAX5FCfODzA4Ms7GlfU4WtJNpOAFAwE2rKils2+Utp4Rr8uZMwX5FAeOp8bHWzQ+LlIsNq5MDqP6efaKgnwKe6oXgHXLaj2uRERyZf3y5Pvdnuz1uJK5U5CnJBIuraf7WFBXRlV5idfliEiONFRHqa+KYE/1kvDpOLmCPOVU+yCjsThrl1Z7XYqI5JDjOJhltQyOjHO2Y8jrcuZEQZ5yODWssnapzuYUKTYmdRa3X+eTK8hTJoN8iYJcpNikj4sd8uk4uYIccF2Xw6d7qa2MUF+tRZZFik1DdZTayghvn+715XxyBTlwvnuYgeFx1i6t0fxxkSLkOA5rllQzMDxOuw/nkyvI0fi4iMDqxcmJDq1n+i5zz/yjIAcOn0r+4dYu0YwVkWK1OvX+f/u0gtyX3j7dS3k0xEIt6yZStJY2VRAJB9Uj96Pu/lE6+0ZZs6SGgMbHRYpWMBBg5aIqznYOMTQ67nU5s1L0QX70bD9wYbdKRIrXytTancfO9XtcyewUfZCn/2AtCwt3kWURyczKhekg99capQryc/04wIoF+bEatoh4pyXdIz+rHrlvJBIux88PsKC+jNKI1ucUKXY1FRFqKyMcO9fvqxODijrIz3UPMxqLT+5OiYi0LKyibyhGz8CY16VkrKiDPL37tEJBLiIpLQuTw6x+OuBZ1EF+4nzygMaKhRofF5Gk9MSH4+f9c8CzqIP8ZPsAjgNLGyu8LkVE8sSy5mTH7lT7oMeVZK5ogzzhupxsH2RhfTkl4aDX5YhInqgoDVNXFeFEm3rkea+jd4SxWJxlTeqNi8g7LWuqpG8wRt9QzOtSMlK0QX6qLbnblN6NEhFJW5rq4J1q90evvGiDPL3btLRZPXIRead0B+9kmz/GyYs2yNMHMjS0IiIXW5bq4J30yTh5UQd5bWWEyrISr0sRkTzTUB2lNBL0zcyVogzy4dFxegbGWKzrj4vINBzHYVFDOe09I0zEE16Xc1lFGeRnO4cBWKQgF5EZLKovJ55wOd897HUpl1WcQd41BCjIRWRm6T32s51DHldyeZe95J8xJgA8AVwDjAGPWmtbp7nPj4CnrLV/NR+FZtOZjuQfRkMrIjKTRY3+CfJMeuQPAFFr7Rbg88Dj09znT4C6bBY2n852Jg9gqEcuIjNZ3JCcuXKmQIL8NuA5AGvtTmDz1I3GmF8BEsCzWa9unpzpHKKuKqJrkIvIjGoqSiiNhHzRI88kyaqAqctKx40xIWvthDFmI/Aw8CvAH2fyhLW1ZYRCub22SWPjhbM3B0fG6R2MsWld0ztuL0bF/vtPR20yvWJtlxULq7Ane6ipLSM8TW7lS7tkEuT9wNRqA9baidTXvwYsBn4GrABixpjj1trnZnqwnp7cHgFubKyko+PCpP7WM8nPpIbKyDtuLzYXt4uoTWZSzO3SWB3hYMJl/+F2Fl90ldRct8ulPjQyCfLtwP3Ak8aYm4G96Q3W2j9If22M+c/A+UuFeD5oS00lWlBX5nElIpLvmlM50dYz8q4gzyeZBPlW4G5jzA7AAT5hjPks0GqtfXpeq5sHbak9gubaUo8rEZF811ybCvI8n0t+2SC31iaAxy66+dA09/vPWappXrV1jwAXPmlFRGaS7vC15XhIeLaK7oSgtp5hSkIBaiojXpciInmuqbYUhwsdwHxVVEHuui5tPSM01ZYScByvyxGRPBcOBamriqpHnk/6hmKMxeKT414iIpfTXFdK72CM0djE5e/skaIK8vQBC42Pi0im0nnR3pO/wyvFFeSpP4RmrIhIpiZnrijI80P6E7VJQS4iGZqcuZLHUxCLKsg7+5JB3lijIBeRzDRURwHo6h/1uJKZFVWQd/WNEgw41FRo6qGIZKY+FeSdfQryvNDZP0ptZYRAQFMPRSQz0ZIQ5dEQXQpy741PJOgbjFFfFfW6FBHxmfrqKN39o7iu63Up0yqaIO8eSH6apse7REQy1VBdSmwiwcDwuNelTKtogjy9W1SvIBeRWUrvyefrAc/iC3INrYjILKU7gPk6Tl48Qd6vHrmIzE26A5ivM1eKJ8g1tCIic5Tvc8mLJ8hTf4C6SgW5iMyOhlbyRGffKNXlJYRDRfMri0iWlEdDRMJB9ci95LoufUMxLSYhInPiOA41FSX0DY55Xcq0iiLIR8bijE8kqC4v8boUEfGp6vISBobHiScSXpfyLkUR5H1DyU9RBbmIzFVVRQQX8vKkoKII8v6hGADVFQpyEZmbdEewbzDmcSXvVhRB3pcO8nKNkYvI3NSkOoLpPMknxRHkg+kgV49cROamKt0jH8q/A57FEeQaWhGRK5Teo+9Xj9wbOtgpIldKY+QeSzd8lYJcROYovUffqx65N/qGYkRKgkRLQl6XIiI+VVkWxgH68/CkoKIJcg2riMiVCAYCVJaFNWvFC/GEy8BwjBoFuYhcoeqKiILcC/2DY7hu8qwsEZErUV1ewmgszlgs7nUp71DwQd4zkJqxUqYeuYhcmeo8nUte8EE+MJzcDaooC3tciYj4XXlpMkeGRic8ruSdLjuNwxgTAJ4ArgHGgEetta1Ttn8G+Fjq2x9ba//LfBQ6V8OjyQvclJYEPa5ERPyuNJKMzJGx/AryTHrkDwBRa+0W4PPA4+kNxpiVwCPALcAW4APGmKvno9C5Gk59cqb/ACIic3UhyPNrjDyTdLsNeA7AWrvTGLN5yrZTwAettXEAY0wYuOQSGrW1ZYRCuesdDx1qB6C5qZLGxsqcPa8fqD3eTW0yPbVLUnNDOQCh1Dkp+dIumQR5FdA35fu4MSZkrZ2w1o4DncYYB/gL4A1r7eFLPVhPz/Dcq52DkVSPfHx0nI6OgZw+dz5rbKxUe1xEbTI9tcsF46khlfauQYCctsulPjQyGVrpB6Y+QsBaOzlAZIyJAn+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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plotf(zlim=1.2):\n", " z = np.linspace(-zlim, +zlim, 250)\n", " plt.plot(z, np.sqrt(np.maximum(0, 1 - z ** 4)))\n", " plt.xlim(-zlim, +zlim)\n", "\n", "plotf()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, the normalization integral cannot be evaluated analytically (it is related to the [complete elliptic integral of the first kind](https://en.wikipedia.org/wiki/Elliptic_integral#Complete_elliptic_integral_of_the_first_kind)), so this is a good candidate for MCMC sampling using the MLS `MCMC_sample` function (which wraps [emcee](http://dfm.io/emcee/)):" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from mls import MCMC_sample" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def logf(z):\n", " return 0.5 * np.log(1 - z ** 4) if np.abs(z) < 1 else -np.inf\n", "\n", "gen = np.random.RandomState(seed=123)\n", "samples = MCMC_sample(logf, z=[0], nsamples=20000, random_state=gen)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The notation `z=[0]` identifies `z` as the parameter we want to sample (starting the value 0). The result is a Pandas DataFrame of generated samples:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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z
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3-0.679219
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\n", "
" ], "text/plain": [ " z\n", "0 -0.170898\n", "1 -0.254509\n", "2 -0.299468\n", "3 -0.679219\n", "4 -0.845475" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "samples[:5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The generated samples are (approximately) drawn from the normalized $P(z)$ corresponding to the $f(z)$ provided:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(samples['z'], range=(-1,1), bins=25);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What are MCMC samples good for? They allow us to estimate the expectation value of an arbitrary $g(z)$ using [importance sampling](https://en.wikipedia.org/wiki/Importance_sampling):\n", "\n", "$$ \\Large\n", "\\langle g(\\vec{z})\\rangle_P \\equiv \\int d\\vec{z}\\, g(\\vec{z})\\, P(\\vec{z})\n", "\\simeq \\frac{1}{N} \\sum_{i=1}^N g(\\vec{z}_i) \\; ,\n", "$$\n", "\n", "where $\\vec{z}_1, \\vec{z}_2, \\ldots$ are the MCMC samples.\n", "\n", "For example, to estimate the expectation value of $g(z) = z^2$ (aka the variance) with the samples generated above:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.27477733502973284" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(samples['z'] ** 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expectation values of more complex functions are equally easy, for example, $g(z) = \\sin(\\pi z)^2$," ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5414969519493271" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(np.sin(np.pi * samples['z']) ** 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also build an empirical estimate of the normalized probability density $P(\\vec{z})$ using any density estimation method, for example:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "fit = neighbors.kde.KernelDensity(kernel='gaussian', bandwidth=0.01).fit(samples)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mean P(z)/f(z) = 1.757\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plotfit(zlim=1.2, Pmin=0.1):\n", " z = np.linspace(-zlim, +zlim, 250)\n", " f = np.sqrt(np.maximum(0, 1 - z ** 4))\n", " P = np.exp(fit.score_samples(z.reshape(-1, 1)))\n", " plt.plot(z, f, label='$f(z)$')\n", " plt.fill_between(z, P, alpha=0.5, label='$P(z)$')\n", " ratio = f / P\n", " sel = P > Pmin\n", " plt.plot(z[sel], ratio[sel], '.', label='$P(z)/f(z)$')\n", " mean_ratio = np.mean(ratio[sel])\n", " print('mean P(z)/f(z) = {:.3f}'.format(mean_ratio))\n", " plt.axhline(mean_ratio, ls='--', c='k')\n", " plt.xlim(-zlim, +zlim)\n", " plt.legend(loc='upper left', ncol=3)\n", "\n", "plotfit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The estimated $P(z)$ does not look great, but since it is just a scaled version of the smooth un-normalized $f(z)$, their ratio at each $z$ is an estimate of the integral:\n", "\n", "$$ \\Large\n", "\\frac{f(z)}{P(z)} = \\int dz\\,f(z) \\; .\n", "$$\n", "\n", "Therefore the mean of $f(z) / P(z)$ provides an estimate of the normalization integral. In practice, we restrict this mean to $z$ values where $P(z)$ is above some minimum to avoid regions where the empirical density estimate is poorly determined.\n", "\n", "In the example above, the true value of the integral rounds to 1.748 so our numerical accuracy is roughly 1%." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we try a multidimensional example:\n", "\n", "$$ \\Large\n", "f(\\vec{z}, \\vec{z}_0, r) =\n", "\\begin{cases}\n", "\\exp\\left(-|\\vec{z} - \\vec{z}_0|^2/2\\right) & |\\vec{z}| < r \\\\\n", "0 & |\\vec{z}| \\ge r\n", "\\end{cases}\n", "$$\n", "\n", "This function describes an un-normalized Gaussian PDF centered at $\\vec{z}_0$ and clipped outside $|\\vec{z}| < r$. The normalization integral has no analytic solution except in the limits $\\vec{z}_0\\rightarrow \\vec{z}$ or $r\\rightarrow\\infty$.\n", "\n", "To generate MCMC samples in 2D:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def logf(x, y, x0, y0, r):\n", " z = np.array([x, y])\n", " z0 = np.array([x0, y0])\n", " return -0.5 * np.sum((z - z0) ** 2) if np.sum(z ** 2) < r ** 2 else -np.inf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The variables to sample are assigned initial values in square brackets and all other arguments are treated as fixed hyperparameters:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "samples = MCMC_sample(logf, x=[0], y=[0], x0=1, y0=-2, r=3, nsamples=10000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The generated samples now have two columns:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " x y\n", "0 -1.093375 -1.042815\n", "1 -1.100172 -1.049932\n", "2 -1.009046 -1.006879\n", "3 -1.009046 -1.006879\n", "4 -1.009046 -1.006879" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "samples[:5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A scatter plot shows a 2D Gaussian distribution clipped to a circle and offset from its center, as expected:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(samples['x'], samples['y'], s=10)\n", "plt.scatter(1, -2, marker='+', s=500, lw=5, c='white')\n", "plt.gca().add_artist(plt.Circle((0, 0), 3, lw=4, ec='red', fc='none'))\n", "plt.gca().set_aspect(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With multidimensional samples, we can estimate expectation values of marginal PDFs just as easily as the full joint PDF. In our 2D example, the marginal PDFs are:\n", "\n", "$$ \\Large\n", "P_X(x) = \\int dy\\, P(x, y) \\quad , \\quad P_Y(y) = \\int dx\\, P(x, y) \\; .\n", "$$\n", "\n", "For example, the expectation value of $g(x)$ with respect to $P_X$ is:\n", "\n", "$$ \\Large\n", "\\langle g\\rangle \\equiv \\int dx\\, g(x) P_X(x) = \\int dx\\, g(x) \\int dy\\, P(x, y) = \\int dx dy\\, g(x)\\, P(x,y) \\; .\n", "$$\n", "\n", "In other words, the expectation value with respect to a marginal PDF is equal to the expectation with respect to the full joint PDF.\n", "\n", "For example, the expectation value of $g(x) = x$ (aka the mean) with respect to $P_X(x)$ is:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.8078391639675472" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(samples['x'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also estimate the density of a marginal PDF by simply dropping the columns that are integrated out before plugging into a density estimator. For example:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "fitX = neighbors.kde.KernelDensity(kernel='gaussian', bandwidth=0.1).fit(samples.drop(columns='y'))\n", "fitY = neighbors.kde.KernelDensity(kernel='gaussian', bandwidth=0.1).fit(samples.drop(columns='x'))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plotfitXY(r=3):\n", " xy = np.linspace(-r, +r, 250)\n", " Px = np.exp(fitX.score_samples(xy.reshape(-1, 1)))\n", " Py = np.exp(fitY.score_samples(xy.reshape(-1, 1)))\n", " plt.plot(xy, Px, label='$P_X(x)$')\n", " plt.plot(xy, Py, label='$P_Y(y)$')\n", " plt.legend()\n", " \n", "plotfitXY()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayesian Inference with MCMC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We introduced MCMC above as a general purpose algorithm for sampling any un-normalized PDF, without any reference to Bayesian (or frequentist) statistics. We also never specified whether $\\vec{z}$ was something observed (data) or latent (parameters and hyperparameters), because it doesn't matter to MCMC.\n", "\n", "However, MCMC is an excellent tool for performing numerical inferences using the generalized Bayes' rule we met earlier:\n", "\n", "$$ \\Large\n", "P(\\Theta_M\\mid D, M) = \\frac{P(D\\mid \\Theta_M, M)\\,P(\\Theta_M\\mid M)}{P(D\\mid M)}\n", "$$\n", "\n", "In particular, the normalizing denominator (aka the \"evidence\"):\n", "\n", "$$ \\Large\n", "P(D\\mid M) = \\int d\\Theta_M' P(D\\mid \\Theta_M', M)\\, P(\\Theta_M'\\mid M)\n", "$$\n", "\n", "is often not practical to calculate, so we can only calculate the un-normalized numerator\n", "\n", "$$ \\Large\n", "P(D\\mid \\Theta_M, M)\\,P(\\Theta_M\\mid M) \\; ,\n", "$$\n", "\n", "which combines the *likelihood of the data* and the *prior probability of the model*.\n", "\n", "If we treat the observed data $D$ and hyperparameters $M$ as fixed, then the appropriate function to plug into an MCMC is:\n", "\n", "$$ \\Large\n", "\\log f(\\Theta) = \\log P(D\\mid \\Theta_M, M) + \\log P(\\Theta_M\\mid M) \\; .\n", "$$\n", "\n", "The machinery described above then enables us to generate samples $\\Theta_1, \\Theta_2, \\ldots$ drawn from the *posterior* distribution, and therefore make interesting statements about probabilities involving model parameters.\n", "\n", "The likelihood function depends on the data and model, so could be anything, but we often assume Gaussian errors in the data, which leads to the multivariate Gaussian PDF we met earlier ($d$ is the number of data features):\n", "\n", "$$ \\Large\n", "P(\\vec{x}\\mid \\Theta_M, M) =\n", "\\left(2\\pi\\right)^{-d/2}\\,\\left| C\\right|^{-1/2}\\,\n", "\\exp\\left[ -\\frac{1}{2} \\left(\\vec{x} - \\vec{\\mu}\\right)^T C^{-1} \\left(\\vec{x} - \\vec{\\mu}\\right) \\right]\n", "$$\n", "\n", "In the most general case, $\\vec{\\mu}$ and $C$ are functions of everything: the data $D$, the parameters $\\Theta_M$ and the hyperparameters $M$.\n", "\n", "When we have $N$ independent observations, $\\vec{x}_1, \\vec{x}_2, \\ldots$, their combined likelihood is the product of each sample's likelihood:\n", "\n", "$$ \\Large\n", "P(\\vec{x}_1, \\vec{x}_2, \\ldots\\mid \\Theta_M, M) = \\prod_{i=1}^N\\, P(\\vec{x}_i\\mid \\Theta_M, M)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, consider fitting a straight line $y = m x + b$, with parameters $m$ and $b$, to data with two features $x$ and $y$. The relevant log-likelihood function is:\n", "\n", "$$ \\Large\n", "\\log{\\cal L}(m, b; D) = -\\frac{N}{2}\\log(2\\pi\\sigma_y^2)\n", "-\\frac{1}{2\\sigma_y^2} \\sum_{i=1}^N\\, (y_i - m x_i - b)^2 \\; ,\n", "$$\n", "\n", "where the error in $y$, $\\sigma_y$, is a fixed hyperparameter. Note that the first term is the Gaussian PDF normalization factor.\n", "\n", "First generate some data on a straight line with measurement errors in $y$ (so our assumed model is correct):" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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bZ3nNhvmeJPXUUxDxys6dlF1+MSWTrsW33f3D73Qv69qzvIrnVBREMslx8G3b6j4uKqL2nl9T89encbp/9odfX3UpXtpjUTDGHJOJICKdXihE97EXUP61MdDcDLjfeRAacuznXtZlZ3mVrNCeMYU7jTG9gD8Cf7LWfprmTCKdUyBA5Ev98IVC+GpqcHr18jqRyBfssShYa082xuwDXArMMcb8B3gYeNZa25zIzowx3YBHgd5ALXCZtXZzq9dMBYZGsz1orX0okX2IQPYMggaWLyN//ivsvG4yAHU/+wXk5+uOZMla7RpTsNZ+iNtT+DNwKHANsNoY87UE93cVsMpaOyy6vZviFxpjTgYOsNYej1sYfmSMqUhwHyLZwXEo+fEkiqbegX/9u25bQYEKgmS19owpTDDGvAbMBfzAUGvtScDJwG8T3N9Q4KXo49nAyFbLlwDjo4+d6P4S6o2IeMpxyPvPh+5jn4/au39FzbOzCR8w0NtcIu3UnjGF4cDN1tr58Y3W2k+MMVfvaiVjzATg2lbNG4GWD13XAp/7rJ21tgFoMMYEgUdwLx/V7S5cRUURgUDyUwBUVpYmvW46KVdisibXpZfC88/DmjVAKT1OOTGpzfijnz5K18+VNcerFeVKXKqztWdM4Vu7WfbUbpZNB6bHtxljngZafoJSoLr1etHLRU8C8621d+wpX1XVzj29ZJcqK0vZvLk26fXTRbkSk025Cg8/ioIPP6L2v9vouffeSecKR+9oTsfPlU3HK55yJa4j2XZVTDJ9n8Ii4Mzo49HAgviF0YHoecAMa+1tGc4mkrDAyjcp/e5ECIUAaPjWOGqefJZI/y97nEwkOZme5uIB4BFjzEKgCbgEwBhzJ27v4ERgf+BKY8yV0XXGWWs/yHBOkXbp9offU/jEX2g47wKaTxkJebofVHJbRouCtXYncEEb7S3fPL4MuDeTmUQS5V+9ivChhwFQd/PtNFx4Mc1DT/I4lUhq6G2NSAKKb7mJHqecSOCNpQA4PXuqIEinollSRRLQeObZBP71Fk6vnl5HEUkL9RSky5o0bTGTpi3e7WsC/3qLsgvPxbdlCwChIcdS89TzhAfovgPpnFQURHYjuGQR+fNfoWD2C5816o5k6cR0+UikleDC12k+YSjk5VE/YSLNRwwmdNzxXscSyQj1FETidPvdbyg/7ywKH5nhNgQCKgjSpainIOI4sUtCDeeeT/D1+W5PwUPZMsurdD3qKUiX1m/jB5SPOY3AWysAcPr0YftjfyNsDvI4mYg3VBSkSyvZuZ3g8mXk//1lr6OIZAVdPpIuJ3/eHJqPcr9ldu1+R7DttaWEBx3scSqR7KCegnQp+bOep+zi8yn+2a2xNhUEkc+oKEjnF4m4g8lA06gzaLhoLPXjrvA4lEh2UlGQTs3//nrKzxpFweN/dhuCQWp/+QDhgw/xNphIllJRkE7NKSjEv+YdgiuWex1FJCdooFk6neArc4ns/SXCgw4m0rcfVQuXEenbz+tYIjlBPQXpVPyr/kX5RedRev21sXEEFQSR9lNPQXJfJAKNjVBQQPiww9kx6QYazxijietEkqCeguS0vE//C8OHU3zbT2JtOyfdQPiwwz1MJZK7VBQkp0XKK2DTJvI2bnR7DCLSISoKknOCr71K/pzZ7pPCQli6lNqHHoa89p/Om6rrqdnRyNbtDUx5bAWbquvTE1Ykx6goSE7xbdlC2bcuouS670NTk9tYUZHwdmbMWkMo7A5Er9tQzYxZa1IZUyRnaaBZsp/j4KupximvwOnVi9q77ndnMc3PT3qT731cs9vnIl2VioJkt7o6ysZeAD4fNTNngc9H4wUXdXizA/qWsW5D9eeei4guH0m2KynBKSvH6V6Gb0ddyjY7fswgAn73I6sH9i9n/JhBKdu2SC5TT0GyTnDRAgLvrKb+yqsA2P7gH9wB5RTqXd6NsuICACaPHZzSbYvkMhUFyS7NzZT+73fI2/hfGs75Ok7v3ikvCCKyayoK4j3HIe+Tj93pKIJBan/9W5zCQrcgiEhGqSiItxyH7pecT+Cdt6la9A+cklKaj9OX1ot4RUVBvOXzEfrKUe6NZzvroaTU60QiXZqKgmRccOliCp55iro77gKfj50//JFbFDSBnYjnMloUjDHdgEeB3kAtcJm1dnMbrysCFgOTrbUvZTKjpF/RfXcRfHUeDReNJXTkYPD7vY4kIlGZvk/hKmCVtXYY8Efgpl287jeAk7FUkl6Og/+dt2NPa39xD9Wz/u4WBBHJKpkuCkOBlnf+s4GRrV9gjLkOt5fwzwzmkjQq/d+rqRg1HP+76wCI7LMvoaOHeJxKRNqStstHxpgJwLWtmjcCLZPM1AJlrdY5FRhorZ1ojDmxPfupqCgiEEj+8kNlZXYObOZyrgm3zwFg+k2j3IZvnA/VW+nRtxek6edK5nj5o3c0p/NY5/L/oxeUK3Gpzpa2omCtnQ5Mj28zxjwNtPwEpUB1q9UmAPsYY+YDBwGDjTGfWmvf2tV+qqp2Jp2xsrKUzZtrk14/XXI9134frOashU+w+dIjoKgITjwVTjjFHUhOw8+V7PEKR2dJTdexzvX/x0xTrsR1JNuuikmmP320CDgTWAaMBhbEL7TWXtLy2BjzMPDX3RUEyU5fsW9w5Lo3qHl1Hk1jznYb9ckikZyQ6TGFB4BDjDELgW8DPwUwxtxpjNFF5lzlOAQXL4w9fXb4Jdw24d7PCoKI5IyM9hSstTuBC9pov76NtsszkUk6rmjKbRTfexc1D/+ZpjPPoim/kPf6a9ZRkVykm9ckOY4TuyTUeMHFBN5eTWjQwR6HEpGO0vcpSMICK5ZTfuap5P37AwDCBwxk+6NPENlvf4+TiUhHqacgCfN/+G+Cby4nf94cGiZM9DpO0qZerYn3RFpTUZCYSdMWA238sXQc8l+eDRecA0DjuV9n20BD+NDDMh1RRNJMl49kjwr/9DBl37oIpkxxG3w+FQSRTko9BWlbJOLOXAo0nnc+wSWLKBw71uNQIpJu6inIF/jfXk35yJPIn+dOV+GUlFL7wO9h4ECPk4lIuqkoyBf5fATWvkNg2VKvk4hIhunykQCQ/+IL9KgJs62skvDBh7Bt6UoiX97H61gikmHqKQjB+a9QdvklXPzS72JtKggiXZN6Cl1VOOwOJgeDNA8/mZ1XX8PTPn2iSKSrU0+hC8r74H3KzziFbg/8ym3w+dhxy+38t7K/t8FExHMqCl2QU1GB/5OP8X/4Ycq3vam6npodjWzd3sCUx1awqbo+5fsQkfRRUegi8l+eTXCpe8eyU17BtgVvUHf3/Snfz4xZawhFv7xm3YZqZsxak/J9iEj6aEyhC8h7/z26X3YxYXMQVfOXgM+H06NnWvb13sc1u30uItlNPYXOKhzGV+d+TV9k/wHU3XEX2x98OO3fgDagb9lun4tIdlNR6IR8W7ZQPmYkJT/4XqytYdwVhM1Bad/3+DGDCPjdwnNg/3LGj9GX7YjkEl0+6oScHj0gz+/+a26GYDBj++5d3o2y4gIAJo8dnLH9ikhqqCh0EvlzX8a3ZQuNF42FvDyqn3wOioq8jiUiOUZFoRPw1dVS+t2JEInQeNY5UFKigiAiSdGYQq6KRMjb+CkQncX017+j+pnZbkFIgu4vEBFQUchNTU2Uf/UMyi481x0zAJpGnk744EOS3qTuLxAR0OWj3JSfT+igg/Ftr8a3cwdOWXmHN6n7C0QEVBRyRvCVuQSXLmbnj38CQN2UuyCQuv++AX3LWLeh+nPPRaTr0eWjXBCJUPzzWyn69X3kffhvty2FBQF0f4GIuNRTyFaRCP731hMeeCDk5VF7/zSIRIjss29adqf7C0QEVBSyVvfLLia4ZDFVi/5BpM9ehA851OtIItIFqChkqaZTR0EwH4f0zlUkIhJPYwpZIvjaq5RecRmEQgA0XDae7TP+hNOnj8fJRKQrUVHIEoVPPk7BC88SXLbUbUjzbKYiIm3J6OUjY0w34FGgN1ALXGat3dzqNZcDVwF+4Flr7W2ZzJgxjkNg2RuEjj0OgLpbfkb9FRMJHfEVj4OJSFeW6Z7CVcAqa+0w4I/ATfELjTEDoq8ZAQwB8o0xmZviM4NKrvs+FWePIvCG2zNwevZUQRARz2W6KAwFXoo+ng2MbLV8JLAceAR4DVhkrW3OXLzMafjGJTSOPotIv35eRxERiUnb5SNjzATg2lbNG4GW+RNqgda3zfYCTgJOALoBi4wxx1hrq9mFiooiAgF/0jkrK0uTXjchr70GP/4xPPMMVFbCmJEwZiQFXueK44/evLa7fbcn18M3n56yTO3lxfFqD+VKjHIlLtXZ0lYUrLXTgenxbcaYp4GWn6AUaP3Hfisw31pbC9QaY94BDgSW7Wo/VVU7k85YWVnK5s21Sa+fiG4LllC8ZAm1Tz5L4/nfyJpc8cLRCfF2tW+vcu2JciVGuRKTrbmgY9l2VUwyffloEXBm9PFoYEEby0cYYwqNMcXAwcD6DOZLHcchf/YsiEQAqJ8wkap5C/dYEEREvJTpovAAcIgxZiHwbeCnAMaYO40xQ6y1q3B7F4twC8Zt1tptGc6YEkX33UXZZRdT+MgMtyEQIHzoYd6GEhHZg4x+JNVauxO4oI326+Me3wfcl8lcKROJQJ5bZxsuuRT/2ndoGjnK41AiIu2nm9dSJLB8GRUnn0DgrRUARPrsRe3v/kCk/5c9TiYi0n4qCiniq6/Hb9cSXLLY6ygiIknThHjJchwKnnmKppNPxSmvoHnYcLYtXUlk3/28TiYikjQVhSQVPPUE3a++kvrLJ1B3570AOV8Qpl59gtcRRMRjKgqJaG52v/HM56PxnPOoX76MnVd9z+tUIiIpozGFdvK/8zYVI4dR8NfH3IZgkLopd6ftm9BERLygotBOTvfu5G3YQGD9u15HERFJG10+2hXHoeDZpwkdeBDhgw8h0q8/25b9E6dXL6+TiYikjXoKuxBYsZzu3x5HyU0/irWpIIhIZ6eeQrzmZvdfURGho46h7v9upXHM2V6nEhHJGPUUovL+8yEVpw2n+Ge3xNrqv/d9IvsP8C6UiEiGqShERXr3gaZGfA2N4DhexxER8UTXvXzkOPDkk+TvDNE0egwUFlL199ehuNjrZCIinumyRSFv46dw6aWU9Kpk22mnuzelqSCISBfXZYtCZK+94ZFHqPnyAW5BEBGRrlsUALjwQsJZ+jV7IiJe0ECziIjEqCiIiEiMioKIiMSoKIiISIyKgoiIxKgoiIhIjIqCiIjEqCiIiEiMz9HkbyIiEqWegoiIxKgoiIhIjIqCiIjEqCiIiEiMioKIiMSoKIiISIyKgoiIxHSZL9kxxnwNuMBae0kby64EJgIh4HZr7QvGmF7An4FuwCfAOGvtzhTm6QY8CvQGaoHLrLWb45afAUyOPvUBQ4FDo3meB96NLnvAWvt4pnJFX/Mc0BNoBuqttaONMQcADwMOsBr4jrU2kuFcU3GPUwB40Fr7kDGmB7AumglgprX2/hTkyQOmAUcAjcAV1tr1ccszfk61M9e1wEXRpy9aa39qjPEBH/HZObXEWntDhnP9EjgR9/8W4BwgiIfHyxhzJHBf3MuPA84FlpGGc2oX+Y4FfmGtHdGq/WzgJ7jn14zoub7H35H26BI9BWPM/cAdtPHzGmP2Aq7BPSFPB+4wxhTgHvA/W2uHAStxf8FT6SpgVXT7fwRuil9orX3JWjsiejK8gHtirAEGA/e0LEtlQWhPrqgDgKHR/Y+Ott0D3BRdz4f7S52xXMaYk4EDrLXH4xaGHxljKnCP11/ijleqfnnPBQqj+5sM3B2Xxatzak+59gfGAicAxwOjjDGHAwOAFXHHKKUFYU+5ogYDp8dlqMHj42WtfSvud/A3wNPW2pdI3zn1OcaY64HfA4Wt2oPAvcAoYDjw7eg5157f3T3qEkUBWIx7wNoyBFhkrW2MnojrgcNx/7C8FH3NbGBkijO1a/vGmH7ApcBPo01HAWOMMa8bY6YbY0ozmcsY0wcoB543xiw0xpwVl+u1Xa2X7lzAEmB89LED+HF7MkcBg40xrxlj/maM2TvVeay1S4Gj45Z5dU7tKdcG4AxrbTjaiwsCDbjHqK83Ij/WAAAEKklEQVQx5lVjzIvGGJPJXNF36wOBB40xi4wx41uvgzfHqyVfMe7v3zXRpnSdU629B5zXRvsgYL21tspa2wQsBIaRouPVqS4fGWMmANe2ah5nrX3cGDNiF6t1B2rintcCZa3aW9pSmWtjO7f/A+Bea21j9Pky4PfW2jeNMTcCNwPXZTBXPu67qfuBHsAiY8wywGetdXazXlpzWWsbgIbou6hHcC8f1Rlj1gJvWmvnGmPGAr8Czk82W5zW503YGBOw1obaWJbycyqZXNbaZmBL9HLRVGCltXZd9F3mHdbavxljhuJegjgmU7mAYtz/l3twi/mrxpjleHy84tomAH+z1m6JPk/XOfU51tqnjDH7tiNzSs+vTlUUrLXTgekJrrYdiH+3XQpUx7XXx7WlLJcx5um4/ba5/eg7qLOAG+OaZ1prW147E/eEzGSuT4HfRn9pNhljVgIGiB8/8Op4VQBPAvOttXdEm18BWq5DzwRuTTZXK63Pm7y4PyRpP6eSzIUxphCYgftH4+po83Lca9NYaxcaY/oaY+KLfLpz7QTubxkvMMa8gnuN3/PjFTWWz//RT9c51V57Or/i2xLWVS4f7c4yYJgxptAYU4bbNVsNLALOjL5mNLAgxfttz/YPBdZaa+vj2l42xgyJPj4VeDPDuUYCTwAYY0qiGdcAK+N6Yxk/XtFBtnm4g263xS36PfD16ONUHq9YHmPMccCquGVenVO7zRXtITwL/NNaO9FaG44uuhn4fvQ1RwD/SXFB2G0u4EBgoTHGH+3pDQVW4PHxiraVAQXW2g1xzek6p9prDTDQGNPDGJMPnIR7+TQlx6tT9RQSYYz5Ae51ueein3xYgFskb7TWNhhjbgceiX6KZAvwhU8tddAD0e0vBJpatm+MuRN40lq7DPcd+Put1rsK+LUxpgn3Xfu3M5xrtjHmdGPMUtzewY+ttVuMMT8EHoqepGtw37FnLBfuoO7+wJXR/zOAcbiDhzOMMVcDO4ArUpRnJnCaMWYx7sD6uCw4p3abC/fSzHCgwBjT8gGBG4ApwKPGmDG4PYbLM5krerweA5bijgP90Vr7ttfHy1r7HG7B+nerddJ1Tu2WMeYSoMRa+2A048u459cMa+3Hxpg2f0cSpamzRUQkRpePREQkRkVBRERiVBRERCRGRUFERGJUFEREJEZFQUREYlQUREQkpsvevCaSLsaYa3DveB2Be1PdH4CvWGvrvMwl0h7qKYik3q9w7/a+CndKhMtVECRX6I5mkTQwxuyHO9/RNGvtJK/ziLSXegoi6bEP7kykg6MT0YnkBBUFkRSLzh77EHA27rTPu/qCJ5Gso6Igknp3ArOstf8AvgP8JHo5SSTraUxBRERi1FMQEZEYFQUREYlRURARkRgVBRERiVFREBGRGBUFERGJUVEQEZGY/wf1u5rmFOMcggAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gen = np.random.RandomState(seed=123)\n", "N, m_true, b_true, sigy_true = 10, 0.5, -0.2, 0.1\n", "x_data = gen.uniform(-1, +1, size=N)\n", "y_data = m_true * x_data + b_true + gen.normal(scale=sigy_true, size=N)\n", "\n", "plt.errorbar(x_data, y_data, sigy_true, fmt='o', markersize=5)\n", "plt.plot([-1, +1], [-m_true+b_true,+m_true+b_true], 'r:')\n", "plt.xlabel('x'); plt.ylabel('y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, define the log-likelihood function:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def loglike(x, y, m, b, sigy):\n", " N = len(x)\n", " norm = 0.5 * N * np.log(2 * np.pi * sigy ** 2)\n", " return -0.5 * np.sum((y - m * x - b) ** 2) / sigy ** 2 - norm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, generate some MCMC samples of the posterior \n", "\n", "$$ \\Large\n", "P(m, b\\mid D, M)\n", "$$\n", "\n", "assuming uniform priors \n", "\n", "$$ \\Large\n", "P(b,m\\mid \\sigma_y) = 1\n", "$$\n", "\n", "as follows:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "samples = MCMC_sample(loglike, m=[m_true], b=[b_true],\n", " x=x_data, y=y_data, sigy=sigy_true, nsamples=10000, random_state=gen)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.jointplot('m', 'b', samples, xlim=(0.2,0.8), ylim=(-0.3,0.0), stat_func=None);" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " m b\n", "count 10000.000000 10000.000000\n", "mean 0.519848 -0.162424\n", "std 0.071418 0.033693\n", "min 0.246512 -0.274527\n", "50% 0.519207 -0.162753\n", "max 0.780647 -0.045919" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "samples.describe(percentiles=[])" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** We always require a starting point to generate MCMC samples. In this example, we used the true parameter values as starting points:\n", "```\n", "m=[m_true], b=[b_true]\n", "```\n", "What happens if you chose different starting points? Try changing the starting values by $\\pm 0.1$ and see how this affects the resulting means and standard deviations for $m$ and $b$." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "solution2": "hidden" }, "outputs": [], "source": [ "samples = MCMC_sample(loglike, m=[m_true+0.1], b=[b_true+0.1],\n", " x=x_data, y=y_data, sigy=sigy_true, nsamples=10000, random_state=gen)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "solution2": "hidden" }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " m b\n", "count 10000.000000 10000.000000\n", "mean 0.526590 -0.158687\n", "std 0.075981 0.030783\n", "min 0.278667 -0.273902\n", "50% 0.522548 -0.158949\n", "max 0.808847 -0.058641" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "samples.describe(percentiles=[])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "solution2": "hidden" }, "outputs": [], "source": [ "samples = MCMC_sample(loglike, m=[m_true-0.1], b=[b_true-0.1],\n", " x=x_data, y=y_data, sigy=sigy_true, nsamples=10000, random_state=gen)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "solution2": "hidden" }, "outputs": [ { "data": { "text/html": [ "
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max0.767536-0.054175
\n", "
" ], "text/plain": [ " m b\n", "count 10000.000000 10000.000000\n", "mean 0.523581 -0.165276\n", "std 0.071686 0.032710\n", "min 0.259379 -0.262730\n", "50% 0.523113 -0.167189\n", "max 0.767536 -0.054175" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "samples.describe(percentiles=[])" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "The changes are small compared with the offsets ($\\pm 0.1$) and the standard deviations in each parameter." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "# Add your solution here..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `MCMC_sample` function can apply independent (i.e., factorized) priors on each parameter:\n", "\n", "$$ \\Large\n", "P(\\Theta\\mid M) = \\prod_j P(\\theta_j\\mid M)\n", "$$\n", "\n", "Define the two most commonly used independent priors:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "def TopHat(lo, hi):\n", " \"\"\"Return un-normalized log(prior) for x in [lo,hi]\"\"\"\n", " return lambda x: 0 if (lo <= x <= hi) else -np.inf" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "def Gauss(mu, sigma):\n", " \"\"\"Return un-normalized log(prior) for x ~ N(mu,sigma)\"\"\"\n", " return lambda x: -0.5 * ((x - mu) / sigma) ** 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To apply a prior, we replace `z=[value]` with `z=[value,logprior]`. For example, suppose we believe that $0.4 \\le m \\le 0.7$:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "samples = MCMC_sample(loglike, m=[m_true,TopHat(0.4,0.7)], b=[b_true],\n", " x=x_data, y=y_data, sigy=sigy_true, nsamples=10000, random_state=gen)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.jointplot('m', 'b', samples, xlim=(0.2,0.8), ylim=(-0.3,0.0), stat_func=None);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also add a prior on $b$. For example, suppose a previous measurement found $b = -0.20 \\pm 0.02$ (in which case, the new data is not adding much information about $b$):" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "samples = MCMC_sample(loglike, m=[m_true,TopHat(0.4,0.7)], b=[b_true,Gauss(-0.20,0.02)],\n", " x=x_data, y=y_data, sigy=sigy_true, nsamples=10000, random_state=gen)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.jointplot('m', 'b', samples, xlim=(0.2,0.8), ylim=(-0.3,0.0), stat_func=None);" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** Suppose we know that all $y_i$ values have the same error $\\sigma_y$ but we do not know its value.\n", " - Generate samples of $(m, b, \\sigma_y)$ using `m=[m_true], b=[b_true], sigy=[sigy_true]`.\n", " - Look at the samples with an `sns.pairplot`.\n", " - Which panel shows the marginalized posterior $P(\\sigma_y\\mid D)$? Do you understand its peculiar shape?\n", " - Add a prior on $\\sigma_y$ to fix this peculiar shape." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "solution2": "hidden" }, "outputs": [], "source": [ "samples = MCMC_sample(loglike, m=[m_true], b=[b_true], sigy=[sigy_true],\n", " x=x_data, y=y_data, nsamples=10000, random_state=gen)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "solution2": "hidden" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.pairplot(samples);" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "solution2": "hidden" }, "outputs": [], "source": [ "samples = MCMC_sample(loglike, m=[m_true], b=[b_true], sigy=[sigy_true, TopHat(0.01,1)],\n", " x=x_data, y=y_data, nsamples=10000, random_state=gen)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "solution2": "hidden" }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.pairplot(samples);" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "# Add your solution here..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a more in-depth case study of the many subtleties in fitting a straight line, read this 55-page [article by Hogg, Bovy and Lang](https://arxiv.org/abs/1008.4686)." ] } ], "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": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 2 }