{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Machine Learning and Statistics for Physicists" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Material for a [UC Irvine](https://uci.edu/) course offered by the [Department of Physics and Astronomy](https://www.physics.uci.edu/).\n", "\n", "Content is maintained on [github](github.com/dkirkby/MachineLearningStatistics) and 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" ] }, { "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\n", "$$\n", "P(\\vec{z}) = \\frac{f(\\vec{z})}{\\int d\\vec{z}\\,f(\\vec{z})} \\; .\n", "$$\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", "$$\n", "f(z) = \\begin{cases}\n", "\\sqrt{1 - z^4} & |z| < 1 \\\\\n", "0 & |z| \\ge 1\n", "\\end{cases}\n", "$$\n", "is never negative and has a finite integral:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "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 at the value 0). The result is a Pandas DataFrame of generated samples:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
z
00.062330
10.047944
2-0.229985
30.061017
40.181863
\n", "
" ], "text/plain": [ " z\n", "0 0.062330\n", "1 0.047944\n", "2 -0.229985\n", "3 0.061017\n", "4 0.181863" ] }, "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", "$$\n", "\\langle g(\\vec{z})\\rangle_P \\equiv \\int d\\vec{z}\\, g(\\vec{z})\\, P(\\vec{z})\n", "\\simeq \\frac{1}{N} \\sum_{i=1}^N g(\\vec{z}_i) \\; ,\n", "$$\n", "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": [ "0.2729666505147651" ] }, "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": [ "0.5414157152385632" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(np.sin(np.pi * samples['z']) ** 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall that the reason we are using MCMC is because we do not know the value of the normalization constant:\n", "$$\n", "\\int d\\vec{z}\\,f(\\vec{z}) \\; .\n", "$$\n", "However, we can use MCMC samples to estimate its value as follows:\n", " - First, build an empirical estimate of the normalized probability density $P(\\vec{z})$ using any density estimation method.\n", " - Second, compare this density estimate (which is noisy, but normalized by construction) with the original un-normalized $f(\\vec{z})$: they should have the same shape and their ratio is the unknown normalization constant.\n", "\n", "For example, use KDE to estimate the density of our generated samples:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "fit = neighbors.KernelDensity(kernel='gaussian', bandwidth=0.01).fit(samples)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now take the ratio of the (normalized and noisy) KDE density estimate and the (un-normalized and smooth) $f(z)$ on a grid of $z$ values:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mean P(z)/f(z) = 1.761\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 the mean of $f(z) / P(z)$ estimates the normalization constant. 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": [ "Note that we cannot simply use $g(z) = 1$ in the importance sampled integral above to estimate the normalization constant since it gives exactly one! The unknown constant is the integral of $f(z)$, not $P(z)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we try a multidimensional example:\n", "$$\n", "f(\\vec{z}, \\vec{z}_0, r) =\n", "\\begin{cases}\n", "\\exp\\left(-|\\vec{z} - \\vec{z}_0|^2/2\\right) & |\\vec{z}| < r \\\\\n", "0 & |\\vec{z}| \\ge r\n", "\\end{cases}\n", "$$\n", "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 $\\vec{z}_0\\rightarrow 0$ 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 0.286831 -1.843221\n", "1 0.014914 -2.954994\n", "2 0.014914 -2.954994\n", "3 0.014914 -2.954994\n", "4 0.014914 -2.954994" ] }, "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", "$$\n", "P_X(x) = \\int dy\\, P(x, y) \\quad , \\quad P_Y(y) = \\int dx\\, P(x, y) \\; .\n", "$$\n", "For example, the expectation value of $g(x)$ with respect to $P_X$ is:\n", "$$\n", "\\langle g\\rangle \\equiv \\int dx\\, g(x) P_X(x) = \\int dx\\, g(x) \\int dy\\, P(x, y) = \\int dx dy\\, g(x)\\, P(x,y) \\; .\n", "$$\n", "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": [ "0.7418902711774612" ] }, "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.KernelDensity(kernel='gaussian', bandwidth=0.1).fit(samples.drop(columns='y'))\n", "fitY = neighbors.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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trZUXXvgf/uM/vn/J/r25LB6II/Zr8ljPgd6EHJWkdSleIZnCCJl5D7qEdOyfvoRtwzOYF/0/JP3V5xoRemd7QSUxESbGDI3teuMBZNDLTMq0sOdEDStdnm5fvaolw8jrLjmq9rWl8daufZ3du3fxwQf/5vHHn0Cv11+2LF5u7nj279/L2bNFLF58M4MGpVyyD28uiwfiiP2aPLXn0MWnIcmB9WMyZM4kZM7XOxbs2PoXr72tFTq0290cPVvP1NGJyLLvDSvMG52Iw+nh0Jk6rUvxG9daGu/LX76bv/zleX74w59gNHYcJF28LB5ATs44du7czsGD+y9bUMPby+KBCParUlUFpb4MOS4wL8E2ZORhnHIH7qI9uI5s0rqcgHLkbB0eRWX8iPiuN9ZA5pAYosKNfCZGx3Tb1ZbGA2hqamL27LmYTCGd37uwLN4FSUnJuFwuVq9+DIPh0mGv3l4WD0SwX5XaUgsuO3LcYK1L6TfG3EXo08bj+Ox1PHUlWpcTMPILawk3Gxg+yDeXLZRliamjEjl8po7mNmfXDxD4/vd/zL33fu2K9x07doQxYy6dIHDJkmXs2rUdh6NjCok33vgXN9wwn/HjJ172eG8viwci2K/qwoU9upiULrb0X5IkETL7AaSQMOyfvoSqXHnoltB9HkWh4EwdOcPjfLIb5oKZuYPwKCrbCyq1LsXvff3r37wssC9eFu/uu29nz57dPPLI9y57bH8siwfdDPb169ezaNEiFixYwJo1Vx9Iv3XrVubOneu14rSknA92OYCDHc4PiZz+FRTrWVwFokumrwrLmmizuxmX4ZvdMBekxIeROTiarQfLUcQ5ln5xYVm8NWve5OmnnyM09PK1kvtjWTzoRrBXV1fzzDPP8Morr7Bu3Tpee+01CgsLL9uutraW//7v//Z6gVpR6suQIiw+s2JSf9KnT+7oktm3FqVJDIPri/zCWvQ6iTHDfGs0zJXMmZBCbZOdg6esWpcieFmXwb5z507y8vKIjo4mNDSUhQsXsmHDhsu2+/GPf8zDDz/cL0VqQakvQxfre/Ov9wdJkjDNWAmyHvuuV7Qux6/ln64la0gMZpPvjySeeP7iqX/vLBYjowJMl8FeU1ODxWLpvJ2QkEB19aVHdS+//DKjR48mNzfX+xVqQPW4UJqqkIMk2AHksBiM45fiKTmEu+zaExcJV1ZZ10Z1g41cH++GuUAnyyyelkZxdYsY+hhgujysUBTlkik+VVW95PapU6fYtGkTf//736mq6t3wqbi43g/zsVi8P7mSs6aYVlUhOm044f2w/6vpj7b0hDLnFspObsVz4C2Sxk3t09SuWrfFm7rblm1HOg545k5JwxJ7eX+q1q7UjqXXj2Dj3lLe+qSI6yenYdD7xniKmhoZnU666u+g3kfq9Iau2qKqCjqd3KO/qS6DPSkpiX379nXetlqtJCQkdN7esGEDVquV2267DZfLRU1NDXfddRevvNL9t/R1da0oSs/fClosEVitLT1+XFdcRR3nEFrlGGz9sP8r6a+29JR+/M3Yt/6Fqn3b0A8d36t9+EpbvKEnbdmRX8bghHAkj8fn2n+tdnxpznB+/8Zh/vXBMW7K843pqWVZT1NTI2FhkZeFuxZXnvaXa7VFVVU8HjctLQ3odKZLXj9Zlq55QNxlsE+fPp3nnnuO+vp6zGYzmzZt4sknn+y8/5FHHuGRRx4BoKysjJUrV/Yo1H2R0lgJSMjRvjXPx0DQZ0xDOvAujv3r0KWNEwsydFOrzcXp8iYWTxuqdSk9ljM8nvEj4nl7WxFjhsUyJFH7d1sxMRYaGqy0tjZedp8sy5fMlOjPumqLLOswm8MJD+/ZNRFdBntiYiKrV69m5cqVuFwubr/9dnJycli1ahWPPPIIY8eO7WoXfkdprECKiA/KOVQkWYdx3GIcn76Ep+I4+pQrX20nXKrgTB2qis8Pc7yae2/K4om/7eHP7x7lP++ZjMmo7RwyOp2e+PgrH1gF6zvCnujWqfulS5eydOnSS7734osvXrZdamoqW7Zs8U5lGlIaK4LyaP0CQ8Y0nHvfwlmwUQR7Nx0srCUqzMjQZO2PdnsjItTIqiWjeerVfP61+TT33pSldUlCHwTOGQgvUVUFpbEqqINd0hsxjJqDp+QQSpOYT6Qrbo/CkaI6cjPikP2462rU0Fhuykvj00MV7D1Ro3U5Qh+IYP8CtaUOPC7kmEFal6Ipw6jrQZJwndymdSk+72RpI3anx2+GOV7L8pnDGJYcyd8/OEFdk13rcoReEsH+BR0nTgnqI3boGNeuG5yD69QOMYdMF/JP12LQy4z2sbnXe0Ovk/nGsjEoiso/Np0UFy75KRHsX3Ch6yFQFtfoC0PWLNT2Rjylh7UuxWepqsrB01bGDI3F5AeLVnRHQrSZW2alc/hMHftOiukG/JEI9i9QmqrBaEYK8c+TYN6kH5ILpjBcZ/ZoXYrPKqpopr7ZwaQsS9cb+5F5E1MZnBDOm1sLxcLXfkgE+xcozdXIUUli/DYgyXoMQyfgLj6I6hbzdl/J3hM16HUS4zICK9hlWeK22cOxNtr5JL9C63KEHhLB/gVKUzVyZELXGwYJffpkcNnxiPljLqOoKntP1JA9LI7QEN+f9KunxqbHMiI1ivc/KxZH7X5GBPtFVI8btbUWOSpR61J8hi5ldEd3zNm9Wpfic46fa6ChxUHemMD8fZEkiUV5aTS0ONh7XAx/9Cci2C+itlhBVZEjA/MPtTckWY8+bTzucwdRPS6ty/Ep2w5XEBaiZ/yIwOqGudjY4XEMig9jw54SMULGj4hgv4jS3DE7nzhiv5QhfTK4bKI75iKtNhcHTlmZNibJZ2ZE7A+yJLFg8mBKa1o5XdakdTlCNwXub2QvXFg9SBLBfgldyhgwhuIqEt0xF3x8oAy3R2XWuMC/kG3q6ERCTXq2HCjTuhShm0SwX6RjqGMokqn388MHIkl3vjum+CCq4ta6HM05XR427y9jbHocqZbA/10xGXTMyElm/0krTa0OrcsRukEE+0WUpmrkqEQx1PEK9MMmgLMdT+UprUvR3LbDlTS3u7hp6hCtSxkwc8an4FFUPjkkhj76AxHsF1Gaa8SJ06vQp2aDzoj73H6tS9FUu93FO9vPkjUkmswh0VqXM2ASY0MZMyyWT/Ir8ATIXOiBTAT7eWKo47VJehP61DEdo2OCeHTEv3cW02Zz8eW5I4Lund3c8Sk0tDjIP12rdSlCF0Swn6e01HQMdRTBflX6oRNQ2+pR6oq1LkUTNQ3tfLivlOvGJpOWFHxTTuRmxBMXaWLLgXKtSxG6IIL9PPX8iBhx1enV6YbkgiThPndA61I08cbWM+h1MrfOTte6FE3IssTscSkcL26gsq5N63KEaxDBfp7S1HFlnZjV8epkcyS6pJG4zx3UupQBd7Kkgf0nrSzKG0J0uEnrcjQzK3cQOlniY3HU7tNEsJ+nNFeDKQwpJPCHr/WFPm0CSn0pSnPwXGKuqCqvbikkJsLEginBMxLmSiLDjEzOSmDHkUrsTjH01VeJYD+vY/Iv0b/eFf3Q8QBBddS+70QNxVUt3DY7PWDmXO+LuRNSsTk8fHasWutShKsQwX6e0lSFHCX617siRyYgx6biLg6OfnaPovLO9rMMig8jb7TopgMYnhLJ4IRwNu8rQ1GCd4SULxPBDqgeF2prvThi7yb90Al4qk6h2Fu0LqXf7ThUTmVdO8tnDEOWg2t449VIksTiaWmU17ax66hY7NwXiWAHlGYrIIY6dpd+6ARQVTzF+VqX0u/e3VZEYoyZCZmBO4Njb0zKSmBYcgRrPy3C4RRr4voaEexcNNRRBHu3yHFpSBHxuIoCe8m8oopmThY3cMPEVOQguxipK7Ik8eW5I2hocfDG1kKtyxG+QAQ7oDSfX8BadMV0iyRJGIbn4Sk7imJr1rqcfrP1YDlmk57rxiZrXYpPGjk4mnmTUtlyoJxDheJqVF8igp3zY9jFUMce0WfkgargDtCFrh0uD3tP1jAjdxBmU+Ate+ctt80ezpDEcP787lHKra1alyOcJ4Kd8wtYi6P1HtHFpiLHpuI6vVPrUvrFwVNWHE4PcyYN1roUn2Yy6HjkthxMBh1/ePMwLe1i0XNfIIKdz6frFXrGkDkTxVqEp75U61K8bufRKuIiTYwZFqd1KT4vNjKEb9+WQ1Obk/95+4hY+NoHBH2wq25nx1BHEew9ph8xHWQ9rhOfal2KV7XbXRw/18DkrEQxxLGb0gdFct+iLE6VNvLPTSe1LifoBX2wKy1iqGNvySER6IdNxHVqB6orcFbWOXSmDo+iiiGOPZQ3OonF09L49FAl+08Gz5QTvkgEe+esjiLYe8OYPR+c7bhOBs5R+4FTVqLCjaQPitS6FL+zbMYw0hIj+MfGk7TaXFqXE7SCPtjFGPa+0SVmoEscgbNgI6ri/xequNweCorqGD/CIsau94JeJ3Pfoixa2l28t+uc1uUErW4F+/r161m0aBELFixgzZo1l93/4YcfsnTpUhYvXswPfvADnE7/OTOuNFcjmcKRTGFal+K3jLmLUFtqcRft1bqUPjtV1oTTpZA7XJw07a0hiRFMH5vE5v1l1DbZtC4nKHUZ7NXV1TzzzDO88sorrFu3jtdee43Cws+vNGtvb+fnP/85L730Eu+99x4Oh4O33367X4v2JqWpGklM/tUnurRc5OhknIc+8Ptl844U1aHXSWQNidG6FL92y8yOxUg27g68EVP+oMtg37lzJ3l5eURHRxMaGsrChQvZsGFD5/2hoaFs2bKF+Ph4bDYbdXV1REb6T9+kmK637yRJxpBzI0pdMZ7yo1qX0ydHiuoZOTgak1FMz9sXsZEhTB2VyPaCStrtoq99oHV5SV1NTQ0Wy+ejAxISEjh8+PAl2xgMBj755BMee+wxEhISmDFjRo+KiIvr/RWfFkvv155UXA5a2uqJGDSEmD7sx1v60hatKTELKD34Lsqh9ajj8vyyLdYGG+W1bSycNvSS+v2xLVcy0O340oIsdhypYn9hHbfOGeHVfQfKawL905Yug11RlEtWY1dV9Yqrs8+ePZvdu3fz9NNP89Of/pTf/e533S6irq61V/M6WywRWK29nzrWU9+xvJdNH4O7D/vxhr62xRfoxy3Fse3vtBfupz06U+tyeuzTQxUADE0I63wtAuF1AW3aEWGUyRoSzTufnmH66AR0snfGagTKawK9b4ssS9c8IO7yJ52UlITVau28bbVaSUj4vE+6sbGR7du3d95eunQpJ0/6xwUKStP5yb/EiBivMGTOQIpMoGHrv1BV/7v6sKCojpgIEynx4kS6t8yfPJj6Zgf7T1q73ljwmi6Dffr06ezatYv6+npsNhubNm1i1qxZnferqsqjjz5KRUXH0c6GDRuYMGFC/1XsRUpTJSAWsPYWSdZjmrgcZ8053EX7tC6nRzyKwrFzDWQPi73iO1Khd3Iz4kmIMfPhXnESdSB1GeyJiYmsXr2alStXsnz5cpYsWUJOTg6rVq2ioKCAmJgYnnzySb7xjW9w8803c/bsWR599NGBqL3PlMZqJHMUktGsdSkBQz88D0N8Ko59a1EV/1nsuKiiGZvDzdh0MczRm2RJ4oaJqZypaOZcVeBO8exrujUf6dKlS1m6dOkl33vxxRc7v543bx7z5s3zbmUDQG2qQo4WR+veJMkysXO/SvXrv8Z1bCvGbP/4vSgoqkeWJEYPFcMcve267GTWflLElv3l3L/Yf0bM+bOgvvK0YwFrEezeFpoxEd2gUTj3r0N1tGldTrccKaojPSWS0BCD1qUEnNAQPdPGJLL7eLWYZmCABG2wq/ZWVHuLCPZ+IEkSprwVqI42HAfXa11Ol5rbnJyraiF7WKzWpQSsuRNScbkVth2u0LqUoBC0wd45IkZ0xfQLXXwahswZuI582DnRmq86eq4eQPSv96PUhHBGpkbx8YHyXg1tFnomiIP9wuRfItj7i3HybaAzYN/+sk9PNVBQVEe42UBaUuBc9OKL5k5MpbbJLtZHHQBBHOxVIMlIEWLO7f4ih0ZjmnI7nvKjuH10CT2PolBwpo6c4XFiNsd+NmGkhfioEP69q9in/9EHguAN9sZKpF9/zL8AACAASURBVEgLkk4sVNyfDKPmIidmYN/5T5TWOq3LuUxhWRNtdjfjMuK1LiXg6XUyN+WlcbaymePFDVqXE9CCN9ibqkU3zACQZBnznK+DqmLb/Dyqx7dGReQX1qLXSYwRJ04HxIyxSUSFG3lvV7HWpQS0oAx2VVVEsA8gOTKBkFn3o1QXYt/2fz7zNlxVVQ6eriUrLQazSbxzGwgGvY6Fk4dwvLiBM+VNWpcTsIIz2NsawOMUwT6ADMOnYJywDPep7Ti2v+wTc8lU1bdT02BjvOiGGVDXjx9EWIie9TvPaV1KwArKYFcaz88RI4Y6DijjxOUYcxfhOv4xjm3/p3m455/uGJ2RK4J9QIUY9SycMoTDZ+o4UyGO2vtDcAZ756yOItgHkiRJGKfcgXHcElwnPsH+yV81XSf1YGEtQxLDiY0M0ayGYDVvUirhZgPrtp3VupSAFKTBXg2GEKTQaK1LCTqSJGGcfBvGSbfgPrUD+9YXNTlyb2pzcqasSYyG0UiIUc+ivDSOnq3nVGmj1uUEnOAM9sZK5KhEMT2rRiRJwjRhGcbJt+Eu/AzH7tcHvIa9x6tRgclZYr1brcyZkEJUmJF124q0LiXgBGewN1QgRw/SuoygZxy3BMPoG3Ad3oD73MEBfe7dx6oZnBBOiqX3yzIKfWMy6Fg0LY0TJY2cLBHj2r0p6IJdddpQ2+qRY1K0LiXoSZKEadoK5LghHf3t9tYBed6aRhtnKprJGy1WztLarNxBhJsNbNwjFuLwpqALdqWxY3Y5nQh2nyDpDITMWYXqbMNx4J0Bec7thyuRgKki2DVnMuiYOyGF/MJaKmr9Y4pnfxB8wd7QEexyjOiK8RW62MEYMmfhOrql32eC9CgK2w9XkJ0eJ0bD+Ii5E1PR6yQ+PliudSkBI+iC3dNQDjq9mPzLxxgn3QKyhLNgY78+T8GZehpbnczKFf/YfUVkqJEJIy3sOlKF06Xd8NdAEnTB3nHiNBlJDrqm+zQ5NBpDxnRcJ7f3a1/75v2lRIUbyc0Qc6/7ktm5g2h3uNl/yqp1KQEh6NJNaaxAjhb9677IMHYheJw4j3/cL/svrWnl6LkG5k1MRa8Lul99n5aZFoMlOoQdBZValxIQguq3W3XZUVtqRf+6j9LFpqBLzuw4au+HicI27inBZNBx/Xjxj93XyJLE1NGJHC9uoLnNqXU5fi+ogr1zjhgR7D7LkDkTtbkaT9Upr+63ocXB7mPVzMxJJkwsWO2TpmQloqqw72SN1qX4veAKdjEixufph00GQwiuk9u9ut+P9peiqCrzJw/26n4F70mxhDEoPow9x0Ww91WQBXs5yDrkSHEZua+SDCb0wybiPrfPa4ty2Bxuth6sYGJmApZos1f2KXifJElMHGnhdFkjrTbfWpDF3wRVsHsaKpCjkpBksaiCLzOkTwGnDU/ZUa/sb9vhSmwONwuniKN1X5ebEY+qdiwwLvReUAW70lghumH8gC5lDJjCcBXt6fO+PIrCh3tLGZkaxfBBUV6oTuhPQ5MjiAw1cPiMCPa+CJpgV91O1GarmPzLD0g6PYahE3CfO4Dq7tsIif0nrdQ121k4ZYiXqhP6kyxJjE2P40hRHR5F+1W2/FXQBHvHHDGqmPzLT+jTp4DLjrvsSK/3oaoqG/eUkBhjJneEmHfdX+RmxNNmd3OmvFnrUvxW8AR7Xcfscbo40c/qD3Qpo5BM4bj70B1zuqyJs5UtLJg8GFnMve83Rg+NRSdLHDpTq3Upfitogt1TXwY6A1KkmNHPH0iyvmN0THF+r7tjNu4pIdxsYPrYZC9XJ/Sn0BA9IwdHc7hQ9LP3VtAEu1JfhhyTIuaI8SOd3TGlBT1+bHV9O/mna7l+fAomg64fqhP6U87wOMpr26htsmldil/qVsqtX7+eRYsWsWDBAtasWXPZ/R999BHLli3j5ptv5pvf/CZNTb638rhSX4ocK7ph/IluUBZSSATuM7t7/NhNe0vR6SRumCDOqfijnOEdk7QViNExvdJlsFdXV/PMM8/wyiuvsG7dOl577TUKCws7729tbeWnP/0pL7zwAu+++y6ZmZk899xz/Vp0TyntTai2ZnSxqVqXIvSAJOs6umNK8lHdjm4/rtXmYkdBJXljkogKN/VjhUJ/SYoNJT4qhCNn67UuxS91Gew7d+4kLy+P6OhoQkNDWbhwIRs2bOi83+Vy8cQTT5CY2NF3nZmZSWWlb83QptSXASCLE6d+Rz98KriduEsOd/sxHx8ow+lWWCimD/BbkiSRnR7HseIG3B4x7LGnugz2mpoaLJbPF6VISEiguvrzVW5iYmKYP38+AHa7nRdeeIF58+b1Q6m9p9R3jIiRxRG739ElZSKZI7s9Osbl9rD5QDnZ6bFioWo/lz0sFofTw5ly3+va9XVdXluvKArSRUPFVFW95PYFLS0tfOtb3yIrK4tbbrmlR0XExfX+D9Biiehym5r2atxh0SQO8e3+1u60xV94sy21o6fTcmgLcVEGZOO1l7P7aE8xzW1Ovjw/02s1BMrr4m/tmBkRwvPrjnCmqpUZEy+9wMzf2nIt/dGWLoM9KSmJffv2dd62Wq0kJFw6iVZNTQ0PPPAAeXl5PP744z0uoq6uFUXp+fzbFksEVmtLl9u1VxQhRad0a1utdLct/sDbbXEPGo+6fwNVB7ZjGD71qtupqsqbW06TaglnUHSIV2oIlNfFX9uRkRLFniOVLLponh9/bcuV9LYtsixd84C4y66Y6dOns2vXLurr67HZbGzatIlZs2Z13u/xeHjwwQe56aab+NGPfnTFo3ktqYoHpaFc9K/7MV3iCKTQaFynd15zu4KiesqtbSycMtjnfg+F3slOj6WkppWm1u6fPBe6ccSemJjI6tWrWblyJS6Xi9tvv52cnBxWrVrFI488QlVVFceOHcPj8bBxY8dCxNnZ2fzyl7/s9+K7Q2muBo9bjIjxY5IsYxg5A+eh91Ba65DDr7xe6YbdxcREmJg6WlyEFiiyh8Xx1idFHDlbz3XiQrNu69b8tUuXLmXp0qWXfO/FF18EYOzYsZw4ccL7lXmJUnd+RIwYw+7XDKNm48x/D9eJTzFNuvwcTlFFMydKGlkxN0OsZxpABieGExlmpKCoTgR7DwT8X4BSXwqSjBwtfin8mRxhQTc4G9fxrVecYuCD3cWEmvTMzBWzdwYSWZIYOyyWI0X1YthjDwRBsJd1LK6hN2pditBHxpybUG1Nl/W1V9W3c+CklTkTUjCbxCIqgWbciHjaHW4Ky8Swx+4K+GD31JeK8esBQjdoFLJlGM5D76Mq7s7vb9xTgk4nM2+S6G4LRGOGxaLXSeQXitkeuyugg1112lBbasWImAAhSRKmCTejNtfgOr4VgKZWBzsKqpgxNomoMPGuLBCFGPWMSoslv7AWVe35sOhgFNDBfmEqAZ04cRowdEPGoRs0Cue+daiONj7aX4bHo7BwqlghKZCNHxlPTYON0ppWrUvxCwEd7B4xlUDAkSQJ07Q7UZ3ttG17mS0HypmYaSExJlTr0oR+NHGkBVmS2HO8RutS/EJAB7tSXwYGM9JVxj0L/kkXNwTjhJtRi3aTpZ7mprw0rUsS+llEqJFRQ2PYc7xadMd0Q8AHuy5OXIUYiOScxZQpCdwZvoe0CHfXDxD83pRRCdQ22TlZ3KB1KT4vYINdVVU8dWJETKDac6KWvzdPx6BTsX/8AqpY0T7gTcpMwGTQseGzc1qX4vMCN9hb68BlE8EegBRV5YPdJZjiBmGe8VU8lSdwHlindVlCPzOb9Ewdnci2/Ara7S6ty/FpARvsYkRM4Dp8po6K2jZuyhuCMXMm+pEzcB5Yj7vsiNalCf3s+vGDcLo8bDvsW4v5+JqADXYxIiZwffBZMXGRJiZndUwfHTLjq8gxg7Bv+TNKm+h/DWRDkyIZOzyeDbtLcLo8WpfjswI22JW6UqSIeCSjWetSBC8qLGvidFkTCyYP6ZzsS9KbCJn3LVS3E/vm51EV8QcfyO5ckElTm5NP8iu0LsVnBW6wN5SJbpgA9MHuYsJC9Mz6wmRfuphBhMy8B0/VKZz71mpUnTAQsofHMSothnXbz9Io5mm/ooAMdtXtRGmsEt0wAaayro3807XMnZCKyai77H7DiOkYsq7Hmf8e7pJ8DSoUBoIkSXx1YSYut8I/N50S49qvICCDXWmsBFURc7AHmA92l6DXy9ww8er/sE3T70KOG4zt4xdRWusGsDphICXFhnLLrGEcOGXlvV3FWpfjcwIz2M+PiJHjxBF7oKhvtrPrSBUzc5KJvMZkX5LeiHnet0DxYNv8/CWzQAqB5cYpQ5g6OpG1nxaxaW+p1uX4lIAMdk99Kej0yJFiibRAsWF3CQA3dmOyLzkqiZBZ96NUF+LY82Z/lyZoRJIk7l80iomZFl7dfJq/vXccu1P8I4cADXalrhQ5JgVJvrwfVvA/zW1OPj1UQd6YROKjujfKyTB8CobRc3Ed3oD73MF+rlDQikEv89CybJZMT2NHQSU/fWkvRRXNWpelucAM9voy0b8eQD7cV4rLrbCoh5N9mabdiRyfhm3riygt1n6qTtCaLEvcOms4j901Ho9H4Vf/2M/6HWdRlOA9qRpwwa7YmlFtTejEiJiA0G53seVAGROzEkiOC+vRYyWdoaO/XVWxffQ8qke8TQ9kmUNi+Nn9U5g8KoG3t53lv145ELTDIQMv2C+cOBVH7AFh8/4ybA4PS6b1bmpeOTKBkNn3o1iLcHz2qperE3xNaIiBb9w8hlVLR1Na3covX95HZV2b1mUNuMAL9rqOk2xiOTz/53B6+HBfGTnD4xiSGNHr/RjSJ2MYuxDX0Y9wFe7yYoWCr5o2Jonv3z0el1vhqVfzsTbatC5pQAVcsHvqSpFCo5HNkVqXIvTRloNltNpcLJk2tM/7Mk29A11yJvZPXsJTJ4bGBYOhSZH8vxXjcbo8PPvm4aAaMRNwwa7Ul4ij9QDQbnfz/q5istNjyUiN6vP+JFlPyA3fRDKFYtv0LKoj+N6eB6PUhHAeWp5NRV0bL288qXU5Ayaggl31uFEaKsQcMQFg454S2uxubps13Gv7lEOjMM9/GLWtHtuWP6OqYnGOYDB6aCzLrhvGZ0erOXg6OEZHBVSwK40VoHiQ48SK9f6suc3Jpr2lTMpKIC2p933rV6JLzMA07S48pYdxHnjXq/sWfNeiaWmkWsL456ZTQdElE1jBfr7vVHTF+Lf3dhXjdHu4Zeawftm/YfRc9COuw7n/Hdwlh/rlOQTfotfJrFyYRUOLgw+DYPqBgAp2T11Jx1QCUUlalyL0UnV9O1sOlHHd2OQej1vvLkmSCJl5T8dkYVv+jNJc0y/PI/iWjNQoJoy08MHuEprbnVqX068CKtiV+lLkmFQxlYAfe21LIXq9zG2z0vv1eSS9EfP8b4MkdZxMddn79fkE33DrrHQcTg8f7Qvso/aACXZVVVHqStGJbhi/dfRcPfmFtSyZlkZUuKnfn0+OtGC+4SGUhnLsH78oTqYGgUHxYUzItLBlfzk2R+D2tQdOsLc3otpbxIlTP+VRFF796DTxUSEsmDxw/5z1qdmY8lbgPrcf5/53Bux5Be0sykuj3eHm00OBu7Ret4J9/fr1LFq0iAULFrBmzZqrbvfYY4+xdq02y5J1njgVQx390if5FZTXtvHluRkY9APblWbIXoB+5AycB97BVbR3QJ9bGHjDkiPJSI1i68HygF19qctgr66u5plnnuGVV15h3bp1vPbaaxQWFl62zYMPPsjGjRv7rdCueOo7phIQXTH+p83uYt22s2QNiWbCSMuAP3/nydSE4di3vthxEl4IaNePG0R1g40TxQ1al9Ivugz2nTt3kpeXR3R0NKGhoSxcuJANGzZcss369eu54YYbuOmmm/qt0K4odaVI4XFIpv4ZSSH0n3e2n6XN7mLFDSOQJEmTGiSdAfOCbyOZwrBt/AOKTczpHcgmZSYQFqJna35gdsd0Gew1NTVYLJ8fRSUkJFBdXX3JNl/72te44447vF9dDyh1paIbxg9V1rXx8YFyZuUO6tNEX94gh0Zjnv9tVFsT9k/+GrBv0wUwGnRMz07mwCkrTW2BN/RR39UGiqJcchSlqqrXj6ri4sJ7/ViLJQLF5aClqYroMdOJtWgbDn1h8ePav6g7bVFVlefWFmAy6vja8hyiI/p/JEyXLLk0tX2Vug9fwly5DxLmBszrEijtAO+05Za5I/hwXykHz9Rxxw0jvVBV7/TH69JlsCclJbFv377O21arlYSEBK8WUVfX2qvVTiyWCKzWFjzWs6Aq2M2JWK0tXq1toFxoSyDoblv2HK/m4Ckrd80bgcvuxGr3jSMndehMdMk7sW78G+ZhOTQ4fOAfTh8F4+9XV0JkyBwczfs7zjJrbBKyBt2AvW2LLEvXPCDusitm+vTp7Nq1i/r6emw2G5s2bWLWrFk9LqQ/XTjZJU6c+o92u5t/fXSatKQI5k7wrdWuJEkmZPYDoCpY3/uT6JIJYLPGDaK2yc7JkkatS/GqLoM9MTGR1atXs3LlSpYvX86SJUvIyclh1apVFBQUDESNXVLqSkFvQor07jsJof+8/WkRze1OVi7MRJa1OWF6LXJkAqYpd2ArOoRbDIEMWBNGWjCbdGw/XKl1KV7VZVcMwNKlS1m6dOkl33vxxRcv2+6//uu/vFNVDyn1pcixqUhSwFxvFdBOljSw5UAZcyekMizZdxdEMYyei3pmB47P/oV+SA6SIUTrkgQvMxl0TBmVyK4jVXxlwUjMpm5Fos/z+yRUVQVPXQk6ccWpX2izu3jx38ewxJi5dXb/zgfTV5IsE3/jKtS2BjHFbwCbMTYZp1th74nAmQzO/4O9qQacNmTLUK1LEbqgqir/98EJmlqdfOPmMX5xdBSSmol+5EychzfiaQzMMc/BLn1QJMlxoWw7HDivr98Hu6f2LAA6i28f/Qmw9WA5+05auWVWuk93wXyRaeodYDDh2LFGnEgNQJIkMSMnmTPlzVTWBcaSif4f7DVnQWdEjhmkdSnCNRw8beWfH55ibHocN071r24z2RyJadKteMqP4j67r+sHCH5n+piO4Y7bCwLjJKrfB7tSew45foiYg92HFZY18b/vHGVoUgQPLR+jyXjhvjKMnoMcNxjHrn+huhxalyN4WVS4ibHpsew8UoVH8f/pm/062FXFg6f2HDpL/yyhJvTd6bJGfv/GIWIjTHznjlxCjL7fr34lkqzDdN1K1LZ6nAfXa12O0A9m5CTT1Ork6Nl6rUvpM78OdldtObidIth91MFTVp56NZ+IMCPfWzGOyFCj1iX1iT5pRMdaqYc/QGms0rocwctyM+IJNxsCYky7Xwe7o7Jj+mAxIsa3KIrKht0l/PHtAlIt4Tz+lQnER5m1LssrTFO/BDoj9p3/FCdSA4xeJ5M3JpGDp2tp8fM1Uf082M+AIUQsXu1DWtqdPPm33bz+cSETRlh47M7xRPj5kfrF5NAoTJNvxVN2BNexzVqXI3jZjLHJeBSVz45Vd72xD/PPDs/zHJVn0MUPFVec+oiTJQ38+d2jtNrcfGXBSOaMT9FsfvX+ZBhzA+6yIzh2vYouLg1d0gitSxK8ZEhiBGmJEWw7VMm8ial++/vrt4moetw4qs+KbhgfoCgq724/y2/+dRCTUc/vvjOLuRP894+iK5IkY75+FVJ4HO0bf4+noVzrkgQvun78IMqsrZwq9d+Jwfw22JWGMvC4xYVJGmtsdfDUqwdZt/0seaMT+c97JpGeEqV1Wf1OCgkndNH3kGQ9tnd/jaemSOuSBC+ZNiaJcLOBTXtLtS6l1/w22JF16GOS0CVrN0F+sDtSVMcTf9tDUWUz9y8axdeWjPaLaQK8RY5MIPTmH4LBRPu7v8J55ENxQjUAGA06rh8/iPzTtdQ0tGtdTq/4bbDrYgcz5Jv/gxwarXUpQUdRVN7ceoanXz9EZJiR/7xnMjNykgO26+Va5KgkQm95Al3qGBw712Db+HuUtsBcIDmYzBmfiixLfLSvTOtSesVvg13Qhs3h5tm3DvP+Z8XMyh3ET1ZOYlB8cC8gLpsjMS/8Lqbpd+MpP0rbaz/Aeeh9VI9b69KEXoqJMDFlVALbCippt/vf6yiCXei2+mY7v/7nfo4U1fOVBSO596YsjAYxlQN0TCRlzJ5P2B2/QjdoFI7dr9P+1k9wlx/TujShlxZMHoLD6WHzfv/raxfBLnRLc7uTp17Np7bJzne/lONzy9n5CjkygdAbv4t54XdRPW5s7/0G20d/Qmn1/8vUg01aUgTjMuLZsKeUNrtL63J6RAS70CWbw80zrx2irtnOd+/IJXtYnNYl+Tx92jjC7vglxonLcRcfpO31H+LIF90z/mb5zGHYHG7e/6xY61J6RAS7cE1Ol4dn3zxMmbWVby7PZuRgcbK6uyS9EdPE5YTd8Sv0KaNx7nmdtjd/hOvcATF6xk8MSYxg2pgkPtxbSrUfjZARwS5clduj8L/vHOVUaSMPLBlFbka81iX5JTnSgnnhdzDfuBpJkrFvehbbe7/BU1eidWlCN9wxZzh6ncw/N53ym3/IItiFK1JUlZfeP0F+YS1fWTCSvNFiPp6+0g/JJfT2JzFN/wqeuhLa33oC25b/RWn0/9kEA1l0uInbrx/O0bP1bD3oH1cZB8/VJEK3qarKqx+dZtfRKm6ZOYw54kSp10iyHmP2PAwjpuHMfw/n0Y9wn9mNfsR0TBOWIUcmaF2icAVzxqeQf7qWV7cUMjQ50ueXdhRH7MIlVFXl7W1FfLS/jAWTB7Nk+lCtSwpIkikM09QvEXbnUxiyF+A+s4e2136A/dO/obTUal2e8AWSJPG1JaOJDDXy3FuHqW2yaV3SNYlgFzqpqsobH5/h3zs7Lj760tyMoLyadCDJ5khCpt1J2J2/xTB6Lq5TO2l77fs49r6F6vGvIXaBLjLMyHduz8HpUvjNKwexNvpuuItgF4COaQJe+fA0G/aUMHdCCitvzPTLtUn9lRwaTch1XyFsxW/Qp0/BeXA97W/9J+6q01qXJlwkNSGc760YR7vdzZP/t4+TJb45fYQIdoGmVgfPvJ7P5gNlLJwymLvnjxShrhE5PBbz3G9gvul7qG4ntnd/hf2zV1Hd/r2iTyAZlhzJj++ZRLjZwFOv5vPxwXKfGy0jgj2IuT0Km/eX8eO/7OZUWRP33pTFl+eOEN0vPkA/eCxhd/wSw6jrcR3eQPvan+KxntW6LOG8pNhQfrxyEqOHxvKPjSd5Yf0xbA7fufhMjIoJMqqqUl7bxs4jVew8UkVzm5PMwdGsvDGT5LjgnszL10iGEEJm3oN+6ATsn/6N9nVPYhh1PcYJN4tZTX1AaIie79yRw/u7inl7WxHnKpt5aHk2QxIjtC5NBHugarO7qG92UNdsp6HZTl2zg4raNgrLm2i1udDJEjnD47h+fArZw2LFUboP0w8eS9jtv8Cx9y1cxz/BdXIbhqxZGDKmISeki6UhNSRLEkumD2Xk4Gj+/O5RfvHyfu68IYPrNV4WUgR7AGhuc3K8uIHjxfWUWduorm+n7QtTjepkifhoM7nD48hIjWLcCAtRYYGzyHSgk0xhhMxYiTHnRhz73+kI+KObkcJi0admo0sZjW5QljiS18jIwdH89L7J/OXfx/nHplMcL2nk3huzCA3RJmJFsPspu9PN/pNWdhRUcqKkY23GUJOetKQIpoxKJCHGTFxkCDGRJmIjQogKMyLL4qjc38mRCZjnrEK97m7cxfm4z+7HdXYfrpOfdtwfk4Ju0Ch0KaPRJ2cimUT32kCJCDXynTty2Li7hLc+KaK4qpkHl2VrcjGTpPrA6dy6ulYUpedlWCwRWK0t/VDRwOtOW1xuhWPn6tl7oob9J604XB4Sos1My04iZ3gcaYkRPhHewfa6aE1VFJS6Ytzlx/FUHMNTeQo8TpAk5ITh6IeMI2HcdTQSHRBdbv7wmhSWNfG/7x6hqdXJvEmpLJ0+lNAQw2Xb9bYtsiwRFxd+1fu7Fezr16/n+eefx+12c88993D33Xdfcv/x48f50Y9+RFtbG5MmTeJnP/sZen333wyIYO9oS3V1M+0ON+12F212N212F202NxW1bZyraqGwvBGbw4PZpGdSpoUZOclkpET53B9roL0u/tYW1ePCU1OEp/wY7tLDKOdH00gRFvRDctGnjEFOykAO0f4kX2/4y2vSanPx+seF7DhcSZjZwMIpg5menUxMhKlzG82Cvbq6mjvvvJO1a9diNBpZsWIFTz/9NBkZGZ3bLFmyhF/84heMGzeOxx9/nOzsbO66665uFxlIwa4oKg6XB6fLg8Pl6Qhom4vWiz7abG5a7S5a25202juCvN3hod3m4ko/BVmSGBQfRvqgSCaMjGdUWiwGve+eMPPF16W3AqEtSlsD5voTNBz9DE/5MTh/RasclYScmIEuNhU5ehByzCCk8Nh+Oxmrqgqqow21vRnV1oRqa0Z1toOiAOr5zwqoKqra8bnjQ/n8syQREW+hTQlBCo1CNkchhUYjGUxdPb1miqtaeHNrIUfPNSBJMGZoLKOHxjJycDRTcgZRW9va4312FexdHlbv3LmTvLw8oqM7TsosXLiQDRs28PDDDwNQXl6O3W5n3LhxANx66608++yzPQr23lBUlX3Hq6m2tpx//dWOUFRBRf38d6LjG52BqagX3VZVLvw/ueTx5792upXOgHa6Lv7ag8Ot4HSe/3xRkLs9Xf+DCgvRE2Y2EG42EBlqJDkulPjoUGRUQkMMHfeHGAgz6wkNMRAfFYJJLEEn9JIcFkPk0AU4Bk9DdTvxWM/iqT6Np6oQT+lh3Ke2X7SxDskchWSORNIbQWcAnR5J1oMkgSSDLHd8lnRI8vnvXfyBiuq0g8uG6rSh2lvPB3kLqJ7eN0SSQIW6Kx3+GEI6At5oRtKbvu01jwAAB4tJREFUwGDqqP8LtV1Sr6w7/7XU8c/skrZd5TEXbdf5mAs/l6u8cx4EPDJZommUgRMlDRRVVnBqh5MTqkS7fRHZ6Ym9/5lcRZfBXlNTg8Vi6bydkJDA4cOHr3q/xWKhurq6R0Vc6z/P1RSWNvKzv3zW48f1lCxLhBh1hBh1mAx6TEYdJqOOMLOB2Ehzx/cvfBh0hJj0HZ8vbBdiICLMSESokcgwI+FmAzqd7x5te4vF4p9v868kUNrS2Y7kOGBS5/c97c04a8tw1ZbhaqzG09aEp60R1e1Edbs7wtnj7jhiVpSOo2lFQVU854+sFVTl88+SJCGZQpFNZnRGM7qYeHSpw9GFRaMLi/r8c3gMckhYR0CeD1TpopCUZPnS4KXjqF9pb8HT1oi7tQHP+Y8LXysOG6rLgeJsQW1zXFbb5/V6Lm3L+c+oSr/9/E1A7vkPzkdeBCOwWDKu/qBe6jLYlfMv1AWqql5yu6v7u6M3XTFRITr++qP5VFQ3c+F8oSRJSADS51933kbq+Md6vjZJ6rhPOv9F59dwfn8SRoOM3osh7LQ5qbdd+dLwQHjLf4Foi++5djskMA+GwYNhcMffQn8Ml/Oc/+ikApfMo6VctOXVWSxR1LfLEBELF/3PlfHOpfQXwr8j6C90BX0h/Ds/1M//MVx9j1f8riTJxGeM6Jc+9i5fv6SkJPbt29d522q1kpCQcMn9Vqu183Ztbe0l9/enhNhQJE8f3toJgiB8wefdMl/4fr88V/8MfOjyH9z06dPZtWsX9fX12Gw2Nm3axKxZszrvT0lJwWQysX//fgDeeeedS+4XBEEQBlaXwZ6YmMjq1atZuXIly5cvZ8mSJeTk5LBq1SoKCgoAeOqpp/j1r3/NjTfeSHt7OytXruz3wgVBEIQrExco+QjRFt8UKG0JlHaAaAt03cce+MMzBEEQgowIdkEQhAAjgl0QBCHA+MTsjn2ZuMoXJr3yFtEW3xQobQmUdoBoS1eP8YmTp4IgCIL3iK4YQRCEACOCXRAEIcCIYBcEQQgwItgFQRACjAh2QRCEACOCXRAEIcCIYBcEQQgwItgFQRACjAh2QRCEAOP3wb5v3z5uvfVWli5dyoMPPkhTU5PWJfXa/v37uf3221m2bBn33HMP5eXlWpfUJ7///e957rnntC6jV9avX8+iRYtYsGABa9as0bqcPmltbWXJkiWUlZVpXUqf/PGPf2Tx4sUsXryY3/zmN1qX0yd/+MMfWLRoEYsXL+all17y/hOofm7evHnq6dOnVVVV1d/+9rfq7373O40r6r05c+aox48fV1VVVd944w31wQcf1Lii3mlublZ/+MMfqjk5Oeqzzz6rdTk9VlVVpc6ZM0dtaGhQ29ra1KVLl3b+jvmb/Px8dcmSJeqYMWPU0tJSrcvptR07dqhf/vKXVYfDoTqdTnXlypXqpk2btC6rV3bv3q2uWLFCdblcqs1mU+fMmaOeOXPGq8/h90fs77//PhkZGbhcLqqrq4mMjNS6pF5xOp185zvfISsrC4DMzEwqKys1rqp3Nm/ezNChQ7nvvvu0LqVXdu7cSV5eHtHR0YSGhrJw4UI2bNigdVm98vrrr/PEE08M2DrE/cVisfCDH/wAo9GIwWBg+PDhVFRUaF1Wr0yZMoWXX34ZvV5PXV0dHo+H0NBQrz6H3we7wWDg5MmTzJ49m927d7N48WKtS+oVo9HIsmXLgP/f3h27pBbGYRz/wkmhraVOWw42uERUSw26hCBCKDTUItGQZCAI5RAROAgJQRFCQ/QP+A8IkqsutUgEEUGDICW4SXgqu4MgyO126+Tlvef4+4DDOcM5z7s8/nwHX2i322SzWRYXFxWnMicUCrGxsYGmaaqjmPL09MTo6Gj3emxsjMfHR4WJzEun08zNzamO8WOTk5NMT08D8PDwQD6fx+fzKU5lnsPh4OTkhGAwyPz8PLqu9/X5lin2fD6P1+vt+aytrQGd6bZUKhGLxUgkEmqDfsFnazEMg+3tbV5fX4lGo2qD/sVn67Cydrvdc3r8+/v7PztNXnzP3d0d6+vrJJNJXC6X6jg/Eo/HKZfL1Go1crlcX5/9X/wf+1cEAgECgUDPvVarxcXFRXeyXVpaIpPJqIj3LR+tBaDZbLK5ucnIyAinp6c4HA4F6b7uT+uwuvHxcS4vL7vX9Xrd8lsZdnB1dUU8Hmd3d9eyv8wB7u/vMQwDj8fD8PAwfr+f29vbvr7DMhP7R4aGhkilUlxfXwOdCXJmZkZxKvN2dnaYmJjg+PgYp9OpOs7AWlhYoFwu02g0eH5+plAo4PV6VccaaLVaja2tLQ4PDy1d6gDVapW9vT0Mw8AwDIrFIrOzs319h2Um9o9omsbR0RH7+/u8vb2h6zrpdFp1LFNubm4oFou43W7C4TDQ2ds9OztTnGzw6LpOIpEgEonw8vLC8vIyU1NTqmMNtPPzc1qtFgcHB917KysrrK6uKkxljs/no1KpEAqF0DQNv9/f9y8rOUFJCCFsxtJbMUIIIX4nxS6EEDYjxS6EEDYjxS6EEDYjxS6EEDYjxS6EEDYjxS6EEDYjxS6EEDbzCymXwb3RtHPyAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "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", "$$\n", "P(\\Theta_M\\mid D, M) = \\frac{P(D\\mid \\Theta_M, M)\\,P(\\Theta_M\\mid M)}{P(D\\mid M)}\n", "$$\n", "In particular, the normalizing denominator (aka the \"evidence\"):\n", "$$\n", "P(D\\mid M) = \\int d\\Theta_M' P(D\\mid \\Theta_M', M)\\, P(\\Theta_M'\\mid M)\n", "$$\n", "is often not practical to calculate, so we can only calculate the un-normalized numerator\n", "$$\n", "P(D\\mid \\Theta_M, M)\\,P(\\Theta_M\\mid M) \\; ,\n", "$$\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", "$$\n", "\\log f(\\Theta) = \\log P(D\\mid \\Theta_M, M) + \\log P(\\Theta_M\\mid M) \\; .\n", "$$\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", "$$\n", "P(\\vec{x}\\mid \\Theta_M, M) =\n", "\\left(2\\pi\\right)^{-d/2}\\,\\left| C\\right|^{-1/2}\\,\n", "\\exp\\left[ -\\frac{1}{2} \\left(\\vec{x} - \\vec{\\mu}\\right)^T C^{-1} \\left(\\vec{x} - \\vec{\\mu}\\right) \\right]\n", "$$\n", "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", "$$\n", "P(\\vec{x}_1, \\vec{x}_2, \\ldots\\mid \\Theta_M, M) = \\prod_{i=1}^N\\, P(\\vec{x}_i\\mid \\Theta_M, M)\n", "$$" ] }, { "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", "$$\n", "\\log{\\cal L}(m, b; D) = -\\frac{N}{2}\\log(2\\pi\\sigma_y^2)\n", "-\\frac{1}{2\\sigma_y^2} \\sum_{i=1}^N\\, (y_i - m x_i - b)^2 \\; ,\n", "$$\n", "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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\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 $P(m, b\\mid D, M)$ assuming uniform priors $P(b,m\\mid \\sigma_y) = 1$:" ] }, { "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 0.531518 -0.163364\n", "std 0.074150 0.032178\n", "min 0.277887 -0.271737\n", "50% 0.533564 -0.162615\n", "max 0.799155 -0.039917" ] }, "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 0.526889 -0.164017\n", "std 0.071437 0.033185\n", "min 0.287060 -0.263188\n", "50% 0.524377 -0.164970\n", "max 0.800168 -0.051169" ] }, "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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" ], "text/plain": [ " m b\n", "count 10000.000000 10000.000000\n", "mean 0.526197 -0.163166\n", "std 0.073906 0.032095\n", "min 0.287884 -0.272038\n", "50% 0.525020 -0.163915\n", "max 0.811648 -0.042163" ] }, "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", "$$\n", "P(\\Theta\\mid M) = \\prod_j P(\\theta_j\\mid M)\n", "$$\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", "text/plain": [ "
" ] }, "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": "shown", "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": "shown" }, "outputs": [], "source": [ "gen = np.random.RandomState(seed=123)\n", "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": "shown" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.pairplot(samples);" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "solution2": "shown" }, "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": "shown" }, "outputs": [ { "data": { "image/png": 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\n", 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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": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 2 }