{ "cells": [ { "cell_type": "markdown", "id": "28b01bad", "metadata": {}, "source": [ "Title: Review of Bayesian Decision Theory\n", "Author: Thomas Breuel\n", "Institution: UniKL" ] }, { "cell_type": "markdown", "id": "837283e0", "metadata": {}, "source": [ "Bayesian Decision Making\n", "=======================" ] }, { "cell_type": "markdown", "id": "e9108540", "metadata": {}, "source": [ "(Joint Density)\n", "\n", "In decision problems, we have items with:\n", "\n", "- some measurable property/properties $x\\in R^n$\n", "- some class $\\omega\\in \\{0,...,C\\}$\n", "\n", "These are described by a _joint density_ $P(\\omega,x)$." ] }, { "cell_type": "markdown", "id": "523ad9c6", "metadata": {}, "source": [ "(Conditional Probabilities)\n", "\n", "The _class conditional density_ is $p(x|\\omega) = P(\\omega,x) / P(\\omega)$.\n", "\n", "The _posterior distribution_ is $P(\\omega|x) = P(\\omega,x) / p(x)$." ] }, { "cell_type": "markdown", "id": "37f449b9", "metadata": {}, "source": [ "(Bayes Rule)\n", "\n", "These two combine into _Bayes Rule_:\n", "\n", "$$p(x|\\omega) P(\\omega) = P(\\omega|x) p(x)$$\n", "\n", "or\n", "\n", "$$P(\\omega|x) = \\frac{p(x|\\omega) P(\\omega)}{p(x)}$$" ] }, { "cell_type": "markdown", "id": "0d6e0148", "metadata": {}, "source": [ "(Optimal Decision Rule)\n", "\n", "The _optimal decision rule_ under a zero-one loss function is \n", "\n", "$D(x) = \\arg\\max_\\omega P(\\omega|x)$" ] }, { "cell_type": "markdown", "id": "a635fc32", "metadata": {}, "source": [ "(Justification for Optimal Decision Rule)\n", "\n", "The reason for this is that the probability of error for each $x$ is\n", "\n", "$$P(\\hbox{error}|x) = 1 - \\max_\\omega P(\\omega|x)$$ \n", "\n", "and the total error is given by:\n", "\n", "$$P(\\hbox{error}) = \\int P(\\hbox{error}|x) p(x) dx $$" ] }, { "cell_type": "code", "execution_count": 1, "id": "613a623f", "metadata": { "collapsed": false }, "outputs": [], "source": [ "\n", "\n", "from scipy import stats\n", "from scipy.stats import norm" ] }, { "cell_type": "markdown", "id": "54fdf448", "metadata": {}, "source": [ "(probability density functions)\n", "\n", "We previously computed with distributions by sampling from them. Let's compute now directly with the probability density functions, like $p(x)$.\n", "\n", "Remember:\n", "\n", "$$ p(x) \\geq 0 $$\n", "\n", "$$ \\int p(x) dx = 1 $$" ] }, { "cell_type": "code", "execution_count": 3, "id": "c468ab8d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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lJcjJyYHX60VBQQGsVitKr//GFRYWYsGCBdi2bRvMZjOGDx+OV199FQDQ0tKC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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# normal density\n", "x = linspace(-8.0,8.0,1000)\n", "plot(norm.pdf(x))" ] }, { "cell_type": "code", "execution_count": 3, "id": "1cfc3ec6", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Oh+gIJQLSYnx2FCtrlJiycwrmDp6Lru278hMEuERgLKusj5COgLOlM80tMCGU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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Class Conditional Densities\n", "x = linspace(-8.0,8.0,1000)\n", "p_x_given_1 = norm.pdf(x,loc=-1.0)\n", "p_x_given_2 = norm.pdf(x,loc=1.0,scale=2.0)\n", "plot(p_x_given_1); plot(p_x_given_2)" ] }, { "cell_type": "code", "execution_count": 4, "id": "9016a5bb", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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QnAjaTg4ixUPC0UgiEFaxbx8MiKrkuwsVRPaN1DucTuHn7UdPj54cqzzWanlq\nKmzYoE9MQtwKSQTCKnJyYMCob0nsl4iLwXl+rYYHXtuxbORIKCqScYeE43Cev1hhUzk50C08h5HB\nI/UOpVNdr57AaIQJE2DdOp2CEqKDJBEIq9i5E6q8nS8RXK/lEEBaGmRm6hCQELdAEoG4bTU1cPSY\n4lBtttMlgqSgJHad3NWqhzFoiWDdOpnHWDgGSQTituXmQnRyKWZlZoDPAL3D6VQB3QPw8fC5pofx\ngAHg56ddGyHs3U0TQWZmJtHR0URGRrJkyZJr1h88eJBRo0bRrVs3XnvttQ7tK7qGnTshMEkrFnKG\nHsVt3RFyBztO7Lhm+T33wJdf6hCQEB1kMRGYzWaefvppMjMzMZlMfPLJJxw4cKDVNn379uXNN9/k\npz/9aYf3FV1DTg64hDpf/UCzlOAUskuzr1melgZr1+oQkBAdZDER5OTkEBERQVhYGEajkdmzZ5OR\nkdFqGz8/P5KSkjAajR3eV3QNOTlQ4e7EiSDk+ongrrtg/344fVqHoIToADdLK0tLSwkNvTKKZEhI\nCNnZ1/7C3+6+ixYtavk5NTWV1NTUdp1D6O/0aag8Z+Zs1S6Sg5L1DkcXif0SOVBxgPMN5/EyerUs\n79YNJk+G1avh8cd1DFB0CVlZWWTZqMu6xURwO+W9Hdn36kQgHMvOnTBk7CEqvP3p69VX73B04Wn0\nZKj/UHJP5XJn/ztbrZsxAz7+WBKBuH1tvyQvXrzYase2WDQUHBxMSUlJy/uSkhJCQkLadeDb2Vc4\njuxs8E1w3mKhZinBKWSfuPaJd+pUbQC6mhodghKinSwmgqSkJAoKCigqKqK+vp6VK1eSnp5+3W3b\nDrzVkX2F49q6FRr6beOOkDv0DkVXN6ow9vGB0aOlc5mwbxYTgZubG0uXLiUtLY0hQ4bw4IMPEhMT\nw7Jly1i2bBkAZWVlhIaG8vrrr/Piiy/Sv39/amtrb7iv6DoaG7WioaKmrYwJHaN3OLq6URNSgOnT\nYdWqTg5IiA4wqLZf5Ts7AIPhmqcJ4Ri+/RbmPn6Wk98L4+zzZ3FzsVjl1KUppfB91Ze9T+4lqEdQ\nq3VlZRATo83n7OmpU4Ciy7HmvVN6FotbtmULDBy7nZHBI506CYD2Rzk6dDRbi7des65fP0hKgs8/\n1yEwIdpBEoG4ZVu3gtugrYzp79zFQs3G9R/HpuLrT002d67WekgIeySJQNwSpbREcNpD6geajR0w\nls3HN1+CJxMQAAAag0lEQVR33cyZ2qxlZ892bkxCtIckAnFLjh8HM/Xsr/zW6VsMNRseOJyjlUep\nunjtzPU9e2pDTnz6qQ6BCXETkgjELdmyBWLG5xLZN5KeHj31DscuuLu6kxKcct16AtCKhz76qJOD\nEqIdJBGIW7JpE/jESrFQW2P7j71hPcGUKXDkCBw82MlBCXETkgjELdmwASp7bSQ1LFXvUOzKuAHj\n2HT8+onA3R0eewwud8ERwm5IIhAdVlwMVdWN7K7cLImgjZSQFPLL8znfcP666xcsgA8/hAsXOjkw\nISyQRCA6bONGSJjyLWG9wvD18tU7HLviZfQiISDhhr2MBw6EkSPh73/v5MCEsEASgeiwDRugR/wG\nxg8cr3codmncgHF8c/ybG67/wQ/gz3/WmuAKYQ8kEYgOUUp7Iviu+0buDrtb73Ds0oSBE1h/bP0N\n1997r9afYMuWTgxKCAskEYgOOXoUGtUl9pzdzrgB4/QOxy7d2f9O8svzOXfx3HXXu7rCz34GMo23\nsBeSCESHbNgAsfdkE+0bTa9uvfQOxy55Gj25I+QOsoqybrjNI49Abi7k53deXELciCQC0SFffgne\nsRukWOgmJg2axFfHvrrh+m7d4Mc/lqcCYR8kEYh2a2iAr7+GYve13BNxj97h2LWbJQLQKo3Xr9cm\nuBdCT5IIRLtt3QoDYys4cu7gNXPzitYS+iVQeaGS4nPFN9ymZ0/4+c+1lxB6kkQg2m3NGgib8CXj\nB47H3dVd73DsmovBhQmDJvDVUctPBU89Bfv2aUN2CKEXSQSi3dasgQvBa5kSMUXvUBzClIgprDmy\nxuI2Hh7w4ovw059CU1MnBSZEG5IIRLsUF0PZaTO7qr6URNBOUyOnsv7Yei42XrS43Zw5YDTKGERC\nP5IIRLusWQNJ6TsJ7BFIqE+o3uE4BF8vX+ID4tlYuNHidi4u8Ne/wv/7f9q8xkJ0NkkEol1WrQLv\nxH/J00AHpQ9OZ/Xh1TfdbuhQrRXRj34kQ0+IzieJQNzU2bOwfTvsb/qMGdEz9A7HoaRHpfP5oc9R\n7bi7v/ACHD4M773XCYEJcRVJBOKmVq+GkfceoKbhHCkhKXqH41CifKPwdvcmryzvptt26wYrV8Lz\nz4PJ1AnBCXHZTRNBZmYm0dHRREZGsuQG3SCfeeYZIiMjSUhIIC/vyi98WFgY8fHxJCYmMnLkSOtF\nLTrVP/4BvUd/xqyYWbgY5LtDR6VHpbPq4Kp2bTtkiNbb+Hvfg+pqGwcmRDNlQWNjowoPD1eFhYWq\nvr5eJSQkKJPJ1Gqbf/3rX2rKlClKKaV27NihUlJSWtaFhYWpM2fOWDqFukkIQmdVVUr16KFU/J+G\nqazCLL3DcUjZJ7LV4DcHq6ampnZt39Sk1JNPKpWWplRDg42DEw7LmvdOi1/vcnJyiIiIICwsDKPR\nyOzZs8nIyGi1zerVq3n00UcBSElJoaqqivLy8qsTjdWTl+g8n38OyZOPUXb+pPQmvkXJQck0NjW2\nq3gIwGCAP/5R+/eHP5TKY2F7bpZWlpaWEhp6palgSEgI2dnZN92mtLSUgIAADAYDEydOxNXVlYUL\nF7JgwYLrnmfRokUtP6emppKamnoLH0XYwscfg/+9/2B62HRcXVz1DschGQwGZsfOZsW+FQwPHN6u\nfdzctPqCCRPguefg9de1xCCcV1ZWFllZWTY5tsVEYGjnb96NvvVv2bKFoKAgKioqmDRpEtHR0Ywd\nO/aa7a5OBMJ+nDwJ23coQqZ9yJ9il+odjkObEzuHqR9P5ZWJr7S7nqVnT/jqK5g8GZ55Bt54Q+tz\nIJxT2y/JixcvttqxLf5aBQcHU1JS0vK+pKSEkJAQi9ucOHGC4OBgAIKCggDw8/NjxowZ5OTkWC1w\nYXsffwypD+6htqGGsQOuTeCi/WL9Y+np0ZNtJds6tF+vXrBuHezZA//2b3D+vI0CFE7NYiJISkqi\noKCAoqIi6uvrWblyJenp6a22SU9PZ/ny5QDs2LGDXr16ERAQwPnz56mpqQGgrq6OdevWERcXZ6OP\nIaxNKXj/fXBPXs68hHnSWsgKHop7iA/zP+zwfr16aU8G3t4wbhxc9b1LCKuw+Nft5ubG0qVLSUtL\nY8iQITz44IPExMSwbNkyll0eGGXq1KkMGjSIiIgIFi5cyJ///GcAysrKGDt2LMOGDSMlJYVp06Yx\nefJk238iYRU7d8L5iw1sqvxf5sXP0zucLuHRhEf5+/6/U1tf2+F9PTzggw+0p4KkJPjnP20QoHBa\nBqVzsx6DwSAti+zQo48C0aso8P8vts3vWHGGuIrZDHV1UFsLly7x+L8WMj5iEg8lPgLu7uDj0+GC\n/x074KGH4O674dVXoU8fG8Uu7Jo1752SCMQ1KiogMhIS/zCZ+UmP8HD8w3qHZJ+amrRymoMHtVdB\ngVbDfuqU9u/p01Bfr5XpeHuDhwcX6s9Te74KP4/ecPGiliR8fKBvX/DzgwEDYOBA7RURAXFx2ro2\nqqu1ISn+8Q/4r/+Chx+WVkXORhKBsKlXXoGco4fZGjWW4z8+Tje3bnqHpL+mJm0goJ07ISdHe+3b\nB717Q3S09oqMhOBgCArSXv7+4OnZ6g5tbjIz8I2BZMzOIDEwERobobJSG9Dp9GkoKoLCQjh2DI4c\ngb17oUcPiI+HhAS44w4YMwZ8fQEtnB/8QBvG+pVXQFpeOw9JBMJmGhogPBzGvvgf9A/24OUJL+sd\nkj6U0r7lf/219vrmG63WduTIK6/4eK2NZwf97pvfUVxdzN/u+1v74igq0poN7d6tlQtt364lmjFj\nIDWVpomTWbHBn1/9CqKitIluRozo+EcWjkUSgbCZ99+H9z+pZt+EQex6YhdhvcL0Dqnz1NRAZqbW\nnXr9eq0Mf8IE7TV+PPTrZ5XTVNRVMHjpYA788AD9ut/CMc1m7UlhyxbYsEF7RURgnnQPqy7ew08+\nvYPBQ9x4/nktbCky6pokEQibMJu1Qc/u+uUSzvfYy0czP9I7JNsrLdWGV129GrZuhdGjIT0d0tJg\n0CCb3UV/uOaH9OrWi9+P//3tH6yhQXtKyMyEzEzU8eMcibmPPxTNYo//JJ75z27MmqUVH4muQxKB\nsIm//x1ee+MCx2cM5Kt5XxEX0EX7fZw6pX3YTz7Ryv2nTIH774d77rmlop5bcfTsUVLeTqHw2UJ6\nePSw7sFLSuCf/0R99hmNu/aw2fseVjbMpP+T9/LY095c7ucpHJwkAmF1DQ0QGwsTf/knit0z+XzO\n53qHZF2VlfDZZ9rNPzdX+9Y/Z45W7KPTV+WHPnuIoX5DeWHcC7Y7SXk5ZGRQ88FnuO7K5gumUZDy\nMGMXTWTs3W5SbOTAJBEIq3vrLVjxf7UcSovk8zmfkxSUpHdIt6+uTivv/+QTyMqCiRO1m/+992qt\neXRWcKaAUe+M4vCPDtPHsxM6A5SXc2H53zn3549xKykks+eDGB6ey6QXRuIfIBnB0UgiEFZVUwOD\nB8P0139LpZuJFQ+s0DukW2c2azf9Dz+EjAxISdFu/tOna+317cwTnz9BH88+vDLxlU49ryo4QvGS\n/8X904+5UGtmV9Rc+v3HXMY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OZM6cOWzYsIF58+Y55bUICQkhJCSE5ORkAB544AFyc3Pp\n16+f012LXbt2MXr0aPr27YubmxszZ85k+/btTnktmnXkbyIkJITg4GBOnDjRanl7roluicDZ+hko\npZg/fz5Dhgzhxz/+ccvy9PR0PvjgAwA++OCDlgSRnp7OihUrqK+vp7CwkIKCAkaOdMwpC9t66aWX\nKCkpobCwkBUrVjB+/Hg+/PBDp7wW/fr1IzQ0lMOHtd6y69evZ+jQodx3331Ody2io6PZsWMHFy5c\nQCnF+vXrGTJkiFNei2Yd/Zvo168fPXv2JDs7G6UUH374Ycs+FlmjguNWrVmzRg0ePFiFh4erl156\nSc9QbG7z5s3KYDCohIQENWzYMDVs2DC1du1adebMGTVhwoTrNg/7/e9/r8LDw1VUVJTKzMzUMXrb\nycrKamk15KzXYvfu3SopKUnFx8erGTNmqKqqKqe9FkuWLGlpPvrII4+o+vp6p7kWs2fPVoGBgcpo\nNKqQkBD17rvv3tJnb24+Gh4ern70ox+169y6T0wjhBBCXzI8pRBCODlJBEII4eQkEQghhJOTRCCE\nEE5OEoEQQjg5SQRCCOHk/j+drKG8gzxk8QAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Priors and Sample Distribution\n", "p_1 = 0.8\n", "p_2 = 0.2\n", "p_x = p_x_given_1 * p_1 + p_x_given_2 * p_2\n", "plot(p_x); plot(p_x_given_1*p_1); plot(p_x_given_2*p_2)" ] }, { "cell_type": "code", "execution_count": 5, "id": "c0e32be9", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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KerE8/TSwb5/w3F4pZV7LhEMnBwp6IikKexn42/ujuKwYN8pvSNrPli3AM89I2oVZ6dED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\ngMKeEELMAIU9IYSYAQp7QggxA/8fV9p/m+18YR8AAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Conditional Distributions\n", "p_1_given_x = p_x_given_1 * p_1 / p_x\n", "p_2_given_x = p_x_given_2 * p_2 / p_x\n", "plot(p_1_given_x); plot(p_2_given_x)" ] }, { "cell_type": "markdown", "id": "5b883541", "metadata": {}, "source": [ "(Density vs Conditional Distributions)\n", "\n", "A _density_ is a non-negative function $f:R^n\\rightarrow R$ such that $\\int f(x) dx = 1$.\n", "\n", "A _conditional distribution_ is a function $f:R^n\\rightarrow R^c$ such that $\\sum_i f_i(x) = 1$ for all $x$.\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "dd3160e8", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.117715838421\n" ] }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Error at each Point\n", "p_error_given_x = 1-maximum(p_1_given_x,p_2_given_x)\n", "plot(p_error_given_x)\n", "print sum(p_error_given_x*p_x)/sum(p_x)" ] }, { "cell_type": "markdown", "id": "b27fa5ce", "metadata": {}, "source": [ "# 2D Example" ] }, { "cell_type": "markdown", "id": "4c504ffd", "metadata": {}, "source": [ "Some preliminaries...\n", "\n" ] }, { "cell_type": "code", "execution_count": 19, "id": "ff5aa594", "metadata": { "collapsed": false }, "outputs": [], "source": [ "xs,ys = meshgrid(linspace(-4.0,4.0,200),linspace(-4.0,4.0,200))\n", "xys = c_[xs.ravel(),ys.ravel()]\n", "\n", "def mvpdf(x,mu=zeros(2),sigma=eye(2)):\n", " return ((2*pi)**len(mu)*det(sigma))**-.5 * exp(-0.5*dot(x-mu,dot(inv(sigma),x-mu)))" ] }, { "cell_type": "code", "execution_count": 20, "id": "20966aa1", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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X1knrYbn3ItdKDpHjmyOGWb17pM4kjmF+A/TeCq32j9wqmN979iXxjMuSyIeF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\nrmCfPBIjT5Z6f36LddTNGlA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hw4Ze53vwwQd7r5hrXa+1RrXtfFTbHg3GRuQ333yznDhx\nQl5//XVZXl6WZ599Vvbu3Tuuy/fhgw8+kPfee09ERN5//305evSo7Ny5U/bu3SuHDh0SEZFDhw7J\nXXfdtSb18+qxd+9eeeaZZ2R5eVlOnjwpJ06c6K1KGAfOnDnTCz///PO9Wf+1rtdao9p2Pqptjwjj\nnFn9/e9/373hhhu6W7Zs6f785z8f56X78K9//au7a9eu7q5du7pf+MIXenV5++23u7fffnt327Zt\n3T179nTfeeedkdfl3nvv7W7cuLE7Pz/fXVxc7P7mN78J6/Gzn/2su2XLlu6NN97YPXLkyNjq9fTT\nT3e/9a1vdXfu3Nm96aabul/72te6Z8+eHXu9JhXVtgdRbXt8qJ/oV1RUVEw56pedFRUVFVOOSuQV\nFRUVU45K5BUVFRVTjkrkFRUVFVOOSuQVFRUVU45K5BUVFRVTjv8DKDrP61exesoAAAAASUVORK5C\nYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# class conditional densities\n", "p_x_given_1 = array([mvpdf(x,mu=array([1,1.0])) for x in xys]).reshape(xs.shape)\n", "p_x_given_2 = array([mvpdf(x,sigma=diag([2.0,1])) for x in xys]).reshape(xs.shape)\n", "subplot(121); imshow(p_x_given_1,cmap=cm.gray)\n", "subplot(122); imshow(p_x_given_2,cmap=cm.gray)" ] }, { "cell_type": "code", "execution_count": 26, "id": "ba3eb05f", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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5FO2sCGmdayTA0/CRn+a0mC+pAI0UtOWDRAgaSXgEJ41PKrTILykDukfAHxfyNDzWCAHP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\nqKiASgQVFRUA8P8AmY12aNvpPfwAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Priors and Sample Distribution\n", "p_1 = 0.4\n", "p_2 = 0.6\n", "p_x = p_x_given_1 * p_1 + p_x_given_2 * p_2\n", "imshow(p_x,cmap=cm.gray)" ] }, { "cell_type": "code", "execution_count": 33, "id": "a0d002fd", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0.0, 0.1)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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gwQeD+MMfko8y82nRJxEoz/OtVuDmmoVf+N8pl449XqhgGiC9laSoJ5q9HWCN\nNEO6IsxgMBhXCjad5u3pgETMZNyaWYEWWdDIuRsLOrK9H2WGJAH//d92DB2qoF8/FXfdJeKuu+xY\nuLAIo0dL+O1vg7jtNhGXXebCP/4hQFWBZ5+14b77ghGR565dLHr0UNChg2ZgsGtX68vDrFl+vPWW\ngMGDQwUTAH70IxHbt3PYvj03lplsDVuONkQ72xZ+ySKKomXtMdtKblzJaSZWbyWxt2MYRo+0crkl\nJBbGvVmzFGyqyeTiZCxaIjc9ZoT/XcKHGpuNlMpm+nbZMh6iCNxzTxCqCjQ3Azt3cli48CyOHWPR\nt6+CuXNFrF7tw4svCqisdGDDBg4zZ0YWAm3Y0OIfSyzyWuPcc1VccomE6moW27ZxMK7pDgfw058G\n8b//m78Vs20hljBHG6IdXoEb7w1bNqPzfBseDVDB1O3tzAp7fD6fqeWbVQQzlRGmcfRYSUmJ5VKw\nyRBvxNwa0UZKhafTMhUNBALAH/5gRyDA4KqrJPzyl3Z89BGPOXNE/POfThw5wqKiQjuOAQMUfPSR\nF6dPswgEGKxbFymG69bxuOACTTCHDFHw1VcsgpEtmhHMnSti6VIbOnRQceBA6JJy9dUiNm3i8Oab\n+dOLl0nCK3DJ8IbwGaBWyHiEi3O+ufwABS6Yxt5KM3u7YDCYccu3bEAExWazwe12x703m80o2Xhj\nEw1VVfU0ajoi5mjptLZGA4myZIkAt1vF1VdL+PWv7diwgcN773nx//1/QaxY4USnTiqczpbHnz3L\noL6exQsv+PDggw48/LBdH9WlKMDGjS0RZlER0LOnJpqtMWGCDIdDc/zZskV7vM8HPP20DeefXwRB\nULFwobVTc9kWm3gwu2FrLeORzQgz32ZhAgUqmOGFPeH2dqR6MprlmxWiw1S9hqIoSbXHJEM6BZcY\nSkiSFBExh4ttqo4h3miALGTJ4PNprSSqChw/zuCrr1isWuVFhw5At24qxowJQhBC32PRIgE/+IGI\nK6+UsX69Bw0NDC680IWdO7VZmB07qujSpeU58e5jMgxw110ivv2WwaZNHF5+WcCoUUXYvp3FBx94\n8cgjQezZ07YIM9NClonrP1UiFk/GA4DexpLuz7IQIsz8ybvFiaIoesrMLAUbCATgdrtjtotYcf8x\nUUgUDWhesMlU/FqtilGSJDQ3N+sLSTaOjSxm5IaLGNXLshbB+Xw+/fdkXzyR43zxRQF9+yrYvJlD\nebmMt97XQTdbAAAgAElEQVTyhZilDxsmYcMGO5qbAbdb29t88UUBa9ZoIWW7dsDf/ubHihU8rr/e\niXHjZFxwQWjVLNnHvP326HM0CTfeKOJnP7Pj4EEWhw/LeOUVH8aM0dLB55yj/a6qikGfPm0fGE6J\nDcl4kJtDcjNM1jxVVfXrjVhapvNzpXuYOQzZq/T5fFAUJSSqlGUZTU1NkGUZpaWlGemtzGaESaJo\ncp5tFUsrLmJk1Fi8nr6Zwpi+ZRgGTqczajVka3/T5mbgz3+24dAhFt26KVi+3BcxWaSxkUH//jJe\nekn7G7/yioDJk+UIwbrpJgmffurFxo0cvN7Qz2r4cAU7d8YXGRYVAU6nCkUBXn+9RSwBoLRUM3T/\nxz+y17NciJBrnxQQpXuIdviNM03J5igkBUtSYkaBIPt3giDEvX9nlXRqopA9vebmZj0Fm01SWbRE\nKnzJqDGrl7MzDBPVTq21Yo7nntNSsWfOMFiyxA+zLfaqKh4zZ4qYP9+G5mbgL3+xRdjgEXr0UNGp\nk4pNm7S5mYShQ2Xs3ctCjjQKisDjAZqbtekl4e0lADBmjIwPPii4hJaliGeIdioLiHw+H9xudwqO\n3DrkvWCG91YSwlsoEkndWSUlm8hxGPf0wqPoTPnRpgujyUKio8asEIHGslMLd4Opr5fxpz/ZMGCA\n5sYzbJh5ZHD4MIcrrpAwaJCCxx6zo0cPBaNHR48ivv2WhSBohT+E0lKgSxcVBw+2vkxs28ahe3cF\nZ84w+OUv7Qi/JG66ScKhQ/GJbzbI9hisdL1PNMg1Fz5EO7yAKF4BJb83npfH48n6TXmqyXvBJHl6\nkoIltnfGBTYbLRSpEpp4XoOkYHmeDzGJt4JYJAuZQdqWlpFsC300jMUc4W4wv/qVDe3aKSgrkzFj\nht80leb3A99+y6F7dxUPPhjEsmXmI7wIZ84AogjccYcYkTbV9jHNlwmy8Msy8OSTNnzzDQunU0Vd\nHYPXXw/9Tl15pQRZBjZuzPslx1IkEgSYVeACbbfwy8ein7y/esM3tsl+Jcnrt2X/zgpRFTmOWJBC\nJpKCtdKeHpDc50gqTUmFb6ItI+l0L4qHRN6D7H/Ksh3vv+/ApZfK+M9/bLjmGp9pKq26mkV5uawP\ng5ZloF+/6NFldTWL3r0V3HqrhPff53HmTMvvhg2LvY957BiDq6924ssvWfzf//kxapSCjh1V/Pzn\ndtTUtHzGRUVatPraa4ntY1qtoKxQIAIaPgPUzMJPlmW9iNKI3++nKdlchGGYkNQs6a1MpoHdCnuY\nsV6DVMGSOZ3RCpnSZa+XTowVvq1VNFuRtl53L78soF07wOUCxo9X0KOH3TSVtneviD59JMiyjJUr\nefTooWL37uiiV12tGRx07KjissskLF/e8nlqnrLmy8QHH9hw8cUl+K//kqEoDK64QsakSTK+/ZbF\nQw8FMXeuE5KhwHbiRAmffkr3MTOZkk3V+4T3HBcVFelFa36/Hz6fL6RdD9AizHhSsqtXr8bAgQPR\nr18/PPHEE6aPuf/++9GvXz8MHz4cO3bs0H/++OOPY8iQIRg6dChuvfVW3a0tXRSEYJK0XXipfzZJ\np9CQ8+U4LuE5nVaHpNNJij2fzi0WwaBW7GOzAV9+yeKWW7RFySyVVltrQ0WFBL8/gH/+k8UFF/ix\nYweiVkIePtziCDR7toiXXxb0PcjhwxXs3h1qeRcIAI8+asdjjxXj5ZebcdVVEjp2VHHOOSqmT5fQ\n3AzMmyfC6VTx1FMtxVc33CDh2DEGDQ3p+YySgUayiWEsWjPuucuyjL/85S8477zzsHHjRmzevBkn\nT56M+jqyLOO+++7D6tWrsW/fPixbtgz79+8Pecy///1vHDp0CAcPHsTixYtxzz33AABqamrwwgsv\nYPv27fjyyy8hyzJef/31tJ53Qaw2fr9frwpLBVZKyRqPw5iCjbetIpsRZqLPJdNiwq0KC4FlywT0\n76/gm28YHDzIYfp0895IhmFQXc2jd28ZtbVuBAIcpk3T+imjuQ9pKVnt/0+eLMPnY7Btm7Y0dOqk\noqRE1dOrVVUMLrvMhSNHGKxZcxrjx8vYuJHD+PFaNc+wYQoYRhP1hQv9WLxYwNat2mtNmSKDYYAP\nP6RRZr5BbmAdDgfuv/9+vP7663C73Vi7di369++PYcOG4aGHHtL7kAmbN29G37590atXLwiCgJtv\nvhmrVq0Kecw777yD2bNnAwDGjx+Ps2fP4sSJE/p4Ra/Xq1f6lpWVpfc80/rqFqG4uFifeZgKobNK\nStZIuJ2f1dsqEoFUNJNpMamyKrTCTU88SJJmM3fjjSKKi1VUVoqIde936BCL3r0lrFwp4JprJIwe\nzeDLL3k4nebuQ4cOAT17agLKslqUaSz+IaO+li/ncemlLsycKeK11/xo3177/DZu5HD++dpCyHFA\nu3YqVq/mUVam4qmnArjzTqduoHDuuSpWrChswczFlGwi78WyLM477zyUlpZi/vz5OHXqFF544QX0\n798/Irt39OhRdO/eXf93eXk5jh49GtdjOnTogIcffhg9evRAt27d0K5dO1x66aVpPMsCEcxUmqYT\nrLDYhlf9sizbprYKK5xLNEg7jJkpfLLRba7w9ts8zjlHGwQdDAK33BLbeYcI5qpVPK67TkS3bur3\nFnqsqZVaTQ2LsjKfflNy440evPOOgIYG7bMdPFjBk0/a8OSTNrzzjg933SXC+PFt3twimABQUaHq\n7SnXXithwgQZjz2m3eRcfLGEL77gI9pOKPkHqZLleR7jx4/H3XffHfGYeL+HZt/zqqoqPPPMM6ip\nqcGxY8fQ3NyM1157LenjjkVBCGaqSZUPZCpmSRJBIRvxmRaCdKZkjY5EiZjC5xOKonnG/vSnQXz2\nGQeG0czOo9HYqBkINDayaGpiMHq0liIdMULB7t2hn5/W58njzBkWffo49ErITp1kTJoUwNKl2hDt\nQ4eAEycYrF3rxdChofugJ08yOH2awYABLT8fNkzG/v0t7/Xkk36sXcvj3Xd5VFZK8PkQMtA6FvkY\njWWKbJ+Tz+dDUVFRzMeUlZWhrq5O/3ddXR3Ky8tjPqa+vh5lZWXYunUrLrjgAnTs2BE8z+P666/H\nhg0bUnsSYRTUCpRPKVlVVfVJK/mYgvX7/SGORPm2mMXL6tUcBAG47DIZ69bxuPhiGbHuG6qqWPTp\no+C99xy45hpRf+ywYbJpe0hNjTY0muNaKiEdDgfuuEPG0qVuiCKHTz/l4XIpYJjIRvZNm3iMHRt6\nTBMnyvjuOwZNTdq/i4uBxYt9ePBBOyoqFCgKsHp1YaZlzRr88wEzcY5HMMeMGYODBw+ipqYGwWAQ\ny5cvR2VlZchjKisrsWTJEgDAxo0b0a5dO3Tp0gUDBgzAxo0b9QrdNWvWYPDgwak9sTAKTjCB1KRT\ns5nGNA61Zlk2qapfq6Vkwy3uMuXra0VUFfi//7Pj4YeDkGWgro7BD38Ye0DloUPa0Oj33nPg2mtb\nUrdatWvk191Y8GPk4os1157nnivCyJEqTpzgwPOh7kOyLGPjRhbjx4f63/btq8DhQIhF3vjxCn70\nIxGPPOJA9+4qVq7MrVYgSuLEY1zA8zzmz5+PK664AoMHD8aMGTMwaNAgLFq0CIsWLQIATJ8+Hb17\n90bfvn0xb948LFiwAAAwYsQIzJo1C2PGjMGwYcMAAHfddVdaz6kgbvOMCyIRiGQWyVQusIkcC2ka\nJqbGPM+jidzGZ4lUpmSJqYQgCCgpKUl7ha/ZZ2+lG4jPPuPQ2AhcfbWEd97RxGfKlNgm2YcOsWjf\nXkVjI4exY2UA2vkNHy7jV7+KLJY6fJjRW0qMsCxw++0iFiwQ8OKLfuzb58CJEzy6d+f0EVJerxeb\nNwv4+c+b4PUG9ZatXr14iCKwYQOHiy9uSR8/8kgQl1/uwrnnKti6lUMgAFMfXEpqyLbdHxly0RrT\npk3DtGnTQn42b968kH/Pnz/f9LmPPPIIHnnkkQSPtu0UVISZKlKVkk2E8MgrVZWiVhEIYoJP+rrS\n/UW3alRp5KmnbHj44SA4DvjHP2woK1NjpmMBLSV78iSDK6/0hzy2okLF2bMMTp8OfTxx+TGjd28F\nDQ0Mxo2T0bu3gurqlhdkGAZ+P4P9+3lMnCjoRt6yLMNm84DnVXz6KROSvuV54IUXfNizR0szf/FF\n9vuhCXSvNPWEu6zlAwUnmJn0cE3VsZAULICQKlgriF0qjsHr9eom+A6HI0VHltts2cLi8GEWN94o\noaFBa92YMKH1uZRVVSz27mVx1VW+kJ+zrDZ9ZNeuUJGKJZivvy5gyBAZb78toKJCDRFMANi1S8DA\ngTJcrtBJGG53EXr3VrB7twCPp6V9JRgMolcvCb/+tR8eD/D++wWR4Moa2Ywws70upYuCEEyzlGyq\nXi/Z12ntWIzN+m63O+VfgGyKLnGekSQpayb4VuVPf7LjgQeCEARg1SoBXbsqGDUqdjpWVYGvv2bh\n9TIYM0aM+L3ZPubhw+aC+fXXLHbtYvGznwXx0ksCKioUVFeHXntbtggYNy6yYpdhGPTtq6JzZxUH\nDhTp7StkS+GWW86iqEjFa6/xrc5hLKSILN/Ix79dQQimEStUuMZDPM36Vogw24okSfr+a1tbRqyU\nLUgle/aw2L6dxe23a6L3+us8HA5g0KDY4nLqlDY55NprJdPULTEgIIgicPQogx49Is9/wQIBd9wh\nYvp0GceOMRCEyAhzyxYB48ebR729eino2lXBhg2ciQ+pCzfdFEBjI4Ndu4Km7kP5Sj6KCBC9HiDf\nKDjBTBXpTMka5zuWlpa2Gnll0zw90eeTlhHSO0peI5tk+/3D+fOfbfjxj4NwOoHaWgZ797I4fpzF\nkCGtF/wAwHXXmYvY8OFKiJH6kSMMunZVEd6R9N13DN5+WxNMngdmzRKxcyeHw4dbnquqwNattqiC\nWVGhwuk036dkWRbTpqngeWDVqmJT9yEyKCFTApqPQpbNc8rHzxMoQMG0UkrWjEAgEPd8x1y7IMML\nl0jvaDaiilRUS6eDqioGn3zC4Y47tOjyr38VcPnlEnheMzePxYYNLFQVIa47Rvr3V3D0KIvvB71E\n3b/8+98FXH21qL/fzJkiPv6Yx+HDrO7Qc/Agi6IiFeeea35MvXopCASAL77gYZZ1Pf98GYoCrFnD\nR53DGAgEdOFMZA4jJfOEf5cCgUBe9YYTCkIw07WHmcrUbngKNtH5jqk4hnQ+n0TNQGThUjLk2wL6\n9NM2zJ0rorgYWLaMx4IFNjQ3o9XoEtDEZ+jQ6MYGggAMHKhgzx7tAWSsl5FAAPjb3wTce2/LHmiP\nHirGjpUhScDp09rfa+NGDuPGRe8JrahQcOwYi3btVHz9deQBtWunGbvv28fB72/5OZm+QtK3drsd\nLMvqY6S8Xi/8fj9EUWx1/9OKZLvVI1Pk4/BooEAE04jV/GRVVdXFxMwvtTVyYR+TtIzEEzUngtWi\nw2Spr2fw7rsC5s4N4te/tuF3v7OjpETF1q18q/uXAPDllxwuuSS6bR4Quo9pVvDzz39q7xUu0HPm\naK5BpPBn0ybWtLCIUF6u4sQJBmPHylHbR0aMUCAIwLp10dtLSGuCw+HQJw5xHKdPpyDp20LY/7Qy\n4eJMBZMSQqr8ZIlxut1uzzu/VDJuzOPxwO12R42arbTQZfMG5LnnbLjpJhH33efE1q0cbrpJxC23\nSGhuZlBcHPuYqqoYeL3AtGmxW0+GDVN0wayuZlBRYRwPB8yfr+2fhjN1qgRJAtav156rRZjRBZPn\nNdEcMEAr/DHjootEyDLwn/9Ev0E0LsTE2UoQhJD0rdF9yOfztSl9a8X0fC4Tjy1eLpI/q3OcWMVP\nlkSWgUAgqRRspot24n0+GTcmiiJKS0ujWtzRRUrj228ZLF0q4NNPOZxzjoKVK3348EMe110nobjY\nPK1p5O23taHP/frFjkSHD5f11hLj4GgA+PxzzX3n0ksjo1RB0J777rs8vvuOwcmTLAYMEGP+/Xr1\nUtC5sxI1wqyslBAMav2YbbkESfrWZrPpwwcEQdALy0j1ba6mb5Mlm+lfr9ebsvnDVqIgBDPVe5iE\ntr4OsYBTVRVOpzOp/kMrpmRJ1MxxHIqLi9MWNadzUkqm+cUvbJAk4Ec/EvHccwEcOcLg1CkGY8bI\nOHuWwdq1PHy+6M9/4w0e7dqpcLtjv8+QIQoOHGDh8wG1taGC+Ze/2PDjH4tR90CnTZOwaxeHdetY\njBkjozUL44oKBcEgA59P88ENp3t3LRJtbgYOHEj+GjG2rxQVFcHlcunuQ16vVy84y2b6tlAiWY/H\nQ1Oy+UKqIsy2QPbzBEHIiLF4a6RqzBjBaLTgcrkKYnFIFp8PWL5cwBNP+HHPPdqsyVWrBFRWSqip\nYXDuuSrGjNGiOzMOH2bwzTcMBg5sPYpyOjXLu3XrOBQXtwjsoUMMtmxhcfPN0dOs48ZppupLlwoY\nPz72XimgRZjV1SwmTIi+j9mli4qOHVX85z+pt8kzug8VFRXpWRxj+0o+V99mM8KkKdkcx7gPkqrX\nS3SPhBQpGEdW5YKJQmvvD8RntBDt+fm4WCXCiy8KsNmA2bNb9h9XreJxzTUS9u7lMGiQjJkzRbzy\nivkN1sqVAgYPVlpNxxKGDVPw2WdcSMHPwoU2zJkjIlYWraJCm625fj0fp2CqqKlhcMEFsj5QOpyB\nAxV4PEzMfcxUYEzfGodnE/chSZIgSZKevi30azJZaNFPnpCNlCwZ8kws4EhkaYXoK1URZlNTU5uq\nfCnAK68IGDasRYCqqxkcPaoJzb59mmHBlVdK2LOHRU1N5DWzahWPzp1V9O0bn2COGKHNxiQFP6dP\nA2++KWDu3OjRJQB066bC59OGVJeXt/5emp0ei/PPl6MW/kyYIOHbbxns2MHh7Nm4Dj8lhLsPcRwH\nlmUhyzJ8Pp/evpLq9G0+pmTNPh8qmHlCKot+4kEURTQ0NEAQhIj9vHyIMBVFQTAYhCAIGa/yzfa5\np4KjRxkcOsSisrIlunznHR5XXy2B44B9+1gMHqzAbgduvFHC0qWhUWZ1NYP6egZeLxO3YA4bpuDg\nwZb9y5desmHqVAldu8b+LFkW6NZNgc0GbN/eegq1Vy8FNTUshg1TUFfHRkxKATT3IbsdGDxYxscf\nR95oZUpgSARK2les4D6ULJkWZ5qSzSNS7aTf2mJNWiqam5tDUrBWo62iQ84vEAiA5/k2n1+2RC+b\nYmt872XLBBQVqZg0qSXCXLlSwDXXaAK6dy+n90TefruIV18VIBuyoatWaeJaVcWiT5/4zmfoUBkn\nTzLo1UtBMAgsXiyYtpKY0bEj0L69irVrWxfMkhLA6VRx5oxWvLR5c+Rz+vbV0rydOqlpT8vGi1n6\n1ug+lEz7SqFABTNPSKVoRfuikBRsPC0VuRhhqqqK5uZmBIPBjDkS5SOqCixZIsDnYzBsmCaKR44w\nqKlhMGmSDK9Xi0D79NF+N3Sogs6dVXz6aYvwrFwp4KqrJBw9qglgPJSWAhyntYq8/TaPvn0V/f1b\nw+nUppB8/nl84tarl4rqaiZqWrZnTxV+v+Yg9MEHXMjNQCaJ9R0Kdx8i7SttcR/K5NzNTGF2TrSt\nJE9Id0qWpGB5no+rpSLbd6eJfh6yLKOhoQEsy4ZY3OUqwWBQj5Tl71frTP1NNm1iIYoqRo2SQe6p\n3n2Xx5VXShAE4KuvWPTtq8B4vzVzphZlAkBNDYMjRxiUlyvo1k1FvDPFVVX77+xZYMECc6OCWLhc\nKpqbgbq61v/2vXtradkLLpCxYUOkyPI80KOHgt27OXTurGL79uwtSfEKGdn/JNW3VnYfyqY1Ho0w\n84B0GRcYU7CkB6y1izVVbkGZ+lKSlhiSpsr28SfzXFVVdbEkGYBAIACfzwdVVTPS7P7qqwL691dD\nKk6N6Viyf2nkhhtErFnD4/RpLR171VUSamrYuPcvAeDMGW0/8vPPeTQ2MrjiivjDOq+Xgd/P4MIL\nZaxf37q5dq9eCg4f1vo29+xhTXtJBwxQ0LGjghEjZMukZRMhXe5DuYJZhElTsjlOOvcwja42xikc\nibyGlTG2xIS3jOTKORhRVRWSJEGWZRQXF4dUS5I0Urqb3T0e4J13BEgSdME8epTBgQMspkzR/r1v\nHxfh6dq+PXDFFRJWrBCwcqWAa6+VcOiQ+dSRaBw+zKKsTMVnn3G4995gVKMCM06dYnD6NIPJk2Ws\nXy+0etNUUaFFmEVF2jzPbdsio9J+/VR07arC5QJWr44UzFxK+bfmPhTevpIusl2NS6tk84RUX0Th\nrjaZTlGm2xqP7MfKspwXLSMkpcwwjD4Jw4jR7NvY7B4eLSTbq/fuuzaMHStj924OY8cq3/+Mx7Rp\nkj6fUmspiYz+Zs4U8eKLAmpqGEycqBXT9OyZmGD27Kng9GkGt9wSu5XEiCQBx48zOHGCwcSJEtav\nt7dqaUf2MAF8n5Y1E0ytUra2lkVdHYt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TSDnd8zjTecf/2mst6Vi/X4v2iHBMny5FPL6x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16mnUrq1ToYKOLIffzR45IvPUU/F88ombevVyvs7ZsxU++sjCpk2uiAM8JqZOVVm2TGHNGndE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\nJv/FF96/37Pj9uxZeP/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y9KhKZGQwe/feoHBhxf3ZZldnyRovMtO2bWEqVVK4c0d8zvXq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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# sample distribution in 3D\n", "from mpl_toolkits.mplot3d import Axes3D\n", "subplots(1,1,figsize=(8,8))\n", "ax = gcf().add_subplot(111,projection='3d')\n", "ax.plot_wireframe(xs[::10,::10],ys[::10,::10],p_x[::10,::10])\n", "ax.set_zlim3d(0.0,0.1)" ] }, { "cell_type": "code", "execution_count": 32, "id": "fbd7c6f7", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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FT31EUYlgjeCpAc2zRcuKkgEyMi1+lCSA0shrrQ6oXa22jbZrgrbYx/PIwzzabkOS+DKf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\nEkFFRQVVIqioqKBKBBUVFUT0f8zHgaoUkx9nAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# conditional distributions\n", "p_1_given_x = p_x_given_1 * p_1 / p_x\n", "p_2_given_x = p_x_given_2 * p_2 / p_x\n", "imshow(p_1_given_x,cmap=cm.gray)" ] }, { "cell_type": "code", "execution_count": 31, "id": "af89fbe7", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0.0, 1.0)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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/fn4cDolwWGHSpFrceKOaMi36yy8Ss2Y504qbYcDjj7to3tygXj2TTz5xYBjW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u/kSw5wh1BjE0Ya1Wq3d42tCEHTHCwhNPeKhWLW9DzDP2zevZGfRwh8PMs89G4vFI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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# conditional distribution in 3D\n", "from mpl_toolkits.mplot3d import Axes3D\n", "subplots(1,1,figsize=(8,8))\n", "ax = gcf().add_subplot(111,projection='3d')\n", "ax.plot_wireframe(xs[::10,::10],ys[::10,::10],p_1_given_x[::10,::10])\n", "ax.set_zlim3d(0.0,1.0)" ] }, { "cell_type": "markdown", "id": "0101bcec", "metadata": {}, "source": [ "# Bayesian Decision Theory" ] }, { "cell_type": "markdown", "id": "23afb221", "metadata": {}, "source": [ "(zero-one loss)\n", "\n", "Above, we used a _zero-one loss_. That is, we used a cost of 1 for an error and\n", "a cost of 0 when there was no error.\n", "\n", "In the general case, we have a 2D table of costs, saying how much of a penalty\n", "we pay if the decision is one thing and the state of nature is another thing.\n", "\n", " state 0 state 1\n", "\n", " action 0 0 1\n", "\n", " action 1 1 0" ] }, { "cell_type": "markdown", "id": "d084a425", "metadata": {}, "source": [ "(other losses)\n", "\n", "These costs need not be at all like this. In fact, costs frequently are\n", "asymmetric.\n", "\n", " state 0 state 1\n", "\n", " action 0 0 10\n", "\n", " action 1 1000 0\n", "\n", "\n", "We call this matrix the _loss matrix_ and write the elements\n", "as $\\lambda_{ij}$, or a function $\\Lambda(\\alpha,\\omega)$, which\n", "is the cost of taking action $\\alpha$ when the state of nature\n", "is $\\omega$." ] }, { "cell_type": "markdown", "id": "ffd8560b", "metadata": {}, "source": [ "(relationship to game theory)\n", "\n", "We will see these kinds of matrices much more later on when we talk about\n", "_game theory_.\n", "\n", "- In Bayesian decision theory, nature picks a state at random and we take an action in response.\n", "- In game theory, we need to make a decision and then someone else is going to make a decision in response." ] }, { "cell_type": "markdown", "id": "957f4e43", "metadata": {}, "source": [ "(risk = expected loss)\n", "\n", "In general, we want to minimize expected loss. \n", "We call expected loss the _risk_ of a decision.\n", "\n", "Just like there are conditional probabilities, there\n", "are conditional risks.\n", "\n", "$$R(\\alpha_1|x) = \\lambda_{11} P(\\omega_1|x) + \\lambda_{12} P(\\omega_2|x)$$" ] }, { "cell_type": "markdown", "id": "c36396da", "metadata": {}, "source": [ "(minimizing expected loss)\n", "\n", "We want to minimize overall risk, and for that we minimize risk at each point $x$.\n", "To do that, we choose action $\\alpha_1$ if the risk of that action is lower than\n", "action $\\alpha_2$ and vice versa.\n", "\n", "\\begin{eqnarray}\n", "R(\\alpha_1|x) & \\leq & R(\\alpha_2|x) \\\\\\\n", "\\lambda_{11} P(\\omega_1|x) + \\lambda_{12} P(\\omega_2|x) & \\leq & \n", "\\lambda_{21} P(\\omega_1|x) + \\lambda_{22} P(\\omega_2|x)\\\\\\\n", "(\\lambda_{12}-\\lambda_{22}) P(\\omega_2|x) & \\leq &\n", "(\\lambda_{21}-\\lambda_{11}) P(\\omega_1|x) \\\\\\\n", "\\end{eqnarray}" ] }, { "cell_type": "markdown", "id": "24bf6c0f", "metadata": {}, "source": [ "(likelihood ratio vs risk)\n", "\n", "With _Bayes Rule_, we can transform this into a decision rule based on the likelihood ratio:\n", "\n", "\\begin{equation}\n", "\\frac{p(x|\\omega_1)}{p(x|\\omega_2)} \\geq\n", "\\frac{\\lambda_{12}-\\lambda_{22}}{\\lambda_{21}-\\lambda_{11}} \n", "\\frac{P(\\omega_2)}{P(\\omega_1)}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": null, "id": "a6f54fb7", "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }