{ "metadata": { "celltoolbar": "Slideshow", "name": "", "signature": "sha256:c3aeef5b2da2c8fbc29048a354e579b8a7d43080799d33436b3bc81b3ae95662" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Set some useful LaTeX commands for later in the document:\n", "$ \\newcommand{\\Int}[2] {\\displaystyle \\int\\limits_{#1}^{#2}} $\n", "$ \\newcommand{\\Prod}[2] {\\displaystyle \\prod\\limits_{#1}^{#2}} $\n", "$ \\newcommand{\\Sum}[2] {\\displaystyle \\sum\\limits_{#1}^{#2}} $ \n", "\n", "### \\Int{lower}{upper} : $ \\Int{lower}{upper},\\qquad $ \\Prod{lower}{upper} : $ \\Prod{lower}{upper},\\qquad $ \\Sum{lower}{upper} : $ \\Sum{lower}{upper} $ ###\n", "\n", "$ \\newcommand{subNsubR}[3] {{}_{#1} #2_{#3}} $\n", "$ \\newcommand{rust}[1] {{\\require{color}\\color{Bittersweet}#1}} $\n", "$ \\newcommand{sky}[1] {{\\require{color}\\color{SkyBlue}#1}} $\n", "\n", "### \\subNsubR{n}{K}{r} : $ \\subNsubR{n}{K}{r},\\qquad $ \\rust{q} : $ \\rust{q},\\qquad $ \\sky{q} : $ \\sky{q} $" ] }, { "cell_type": "code", "collapsed": false, "input": [ "'''\n", "debinningWithNewStatistics.ipynb\n", "This file is an ipython notebook designed to be converted to reveal.js\n", "slides via this command:\n", " ipython nbconvert debinningWithNewStatistics.ipynb --to=slides --post=serve [--config slides_config.py]\n", "This file also contains the main body of debinning work in the code blocks below.\n", "\n", "Copyright (C) 2015 Abram Krislock\n", "\n", "Talks given from ~= this version of the slides:\n", " \"Debinning: Data Smoothing with a New Probability Calculus\"\n", " - Fysisk institutt, Universitetet i Oslo, February 25, 2015\n", " - Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, March 13, 2015\n", "\n", "This program is free software: you can redistribute it and/or modify\n", "it under the terms of the GNU General Public License as published by\n", "the Free Software Foundation, either version 3 of the License, or\n", "(at your option) any later version.\n", "\n", "This program is distributed in the hope that it will be useful,\n", "but WITHOUT ANY WARRANTY; without even the implied warranty of\n", "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n", "GNU General Public License for more details.\n", "\n", "You should have received a copy of the GNU General Public License\n", "along with this program. If not, see http://www.gnu.org/licenses/gpl-3.0.txt.\n", "'''\n", "\n", "\n", "import sys\n", "sys.path[0] = '..'\n", "from __future__ import division\n", "import numpy as np\n", "from time import time\n", "import bisect\n", "import operator as op\n", "\n", "from utilities import settings\n", "import utilities.sampleFunctions as funcs\n", "import utilities.probCalc as pc\n", "import utilities.plotting as debinPlot\n", "import utilities.minimizers as miniz\n", "reload(funcs)\n", "reload(pc)\n", "reload(debinPlot)\n", "reload(miniz)\n", "\n", "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "from IPython.display import HTML" ], "language": "python", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "\"debinning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#
Data Smoothing with a New Probability Calculus
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##
Abram Krislock
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###
Fysisk institutt, Universitetet i Oslo.
\n", "\n", "###
[a.m.b.krislock@fys.uio.no](mailto:a.m.b.krislock@fys.uio.no \"Email Abram\")
" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Once Upon A Time..." ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We knew all the stuff!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "### \"At the end of the 19th century... it was generally accepted that all the important laws of physics had been discovered...\" ([Source](http://en.wikipedia.org/wiki/History_of_physics \"http://en.wikipedia.org/wiki/History_of_physics\"))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Then this stuff happened:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$${\\huge{\\rm He}^{++},~{\\rm e}^-,~\\gamma \\qquad\\qquad \\hbar \\qquad\\qquad g^{\\mu\\nu}}$$\n", "\n", "$${\\huge E^2 = (mc^2)^2 + (pc)^2}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$${\\Large \\cdots {\\rm SU}(3)_C \\times {\\rm SU}(2)_L \\times {\\rm U}(1)_Y}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Okay... But after that... Surely, we knew all the stuff!" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Well, actually...." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "### Then this stuff happened:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "![We know almost nothing.](stuffWeKnow.png \"We know almost nothing.\")" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let's face it." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "### Large Hadron Collider: A \"New Stuff\" Experiment" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "![New stuff experiment!](epicLHCHighFive.png \"New stuff experiment!\")" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Dark Matter @ Large Hadron Collider\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\\begin{align}\n", " {\\Huge \\widetilde{q_L}} & {\\Huge\\rightarrow} & {\\Huge \\rust{q}} \\\\\n", " & {\\Huge\\searrow} \\\\\n", " & & {\\Huge\\widetilde{\\chi}^0_2} & {\\Huge\\rightarrow} & {\\Huge h^0} & {\\Huge\\rightarrow} & {\\Huge \\rust{b}}\\\\\n", " & & & {\\Huge\\searrow} & & {\\Huge \\hookrightarrow} & {\\Huge \\rust{b}} \\\\\n", " & & & & {\\Huge \\color{Gray}{\\widetilde{\\chi}^0_1}}\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Calculate as one particle, the mass:\n", "\n", "$${\\huge m_{\\rust{q h^0}} \\qquad {\\rm using} \\qquad E^2 = (mc^2)^2 + (pc)^2}$$" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The $m_{\\rust{qh^0}}$ Maximum Measurement" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\"You" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Change the... bins? Seriously?!" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Change the bins! How bad could it be?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\"It" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Okay, that's bad, but how often...?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "funcs.randomGenerator.setSeed('seedOne')\n", "settings['simpleSortedOutput'] = True\n", "\n", "nPulls = 400\n", "basePars = (0.00006, 10., 200., 110., 1.5, 50., 140.)\n", "baseGuess = (140., -2., -0.1, 10.)\n", "\n", "def fitTwoHistograms(percentile):\n", " data = funcs.functionToData(funcs.easyEndpoint, nPulls, 0.5, (0,200), basePars)\n", " percentieth = data[data > np.percentile(data, percentile)]\n", "\n", " # The histograms are filled with the same data, only different binning.\n", " binContentsOne, binEdgesOne = np.histogram(percentieth, np.arange(3., 204., 10.))\n", " binContentsTwo, binEdgesTwo = np.histogram(percentieth, np.arange(0., 201., 5.))\n", " \n", " # The fit ranges are defined to be from the value of the 70th percentile data point\n", " # to \"the last non-zero bin\", blindly.\n", " fitBinsOne = np.flatnonzero(binContentsOne[binContentsOne.argmax():]) + binContentsOne.argmax()\n", " fitBinsTwo = np.flatnonzero(binContentsTwo[binContentsTwo.argmax():]) + binContentsTwo.argmax()\n", " \n", " ### FITTING METHOD: Binned Maximum Likelihood ###\n", " fitGuessOne = np.array([value * funcs.randomGenerator.normal(1., 0.1) for value in baseGuess])\n", " fitGuessTwo = fitGuessOne.copy()\n", "\n", " def chiSqOne(pars):\n", "# return funcs.chiSqSimple(binContentsOne, binEdgesOne, fitBinsOne, funcs.theKink, pars)\n", " return -2. * funcs.theKink_BinnedLikelihood(binContentsOne, binEdgesOne, fitBinsOne, pars)\n", " def chiSqTwo(pars):\n", "# return funcs.chiSqSimple(binContentsTwo, binEdgesTwo, fitBinsTwo, funcs.theKink, pars)\n", " return -2. * funcs.theKink_BinnedLikelihood(binContentsTwo, binEdgesTwo, fitBinsTwo, pars)\n", "\n", " fitOne = miniz.nelderMead(chiSqOne, fitGuessOne, xtol=0.01, ftol=0.05, disp=0)\n", " fitTwo = miniz.nelderMead(chiSqTwo, fitGuessTwo, xtol=0.01, ftol=0.05, disp=0)\n", " return (data, fitOne, fitTwo)\n", "\n", "xKinkOne = []\n", "xKinkTwo = []\n", "xKinkDiff = []\n", "percentile = 60\n", "nTrials = 1000\n", "\n", "for i in xrange(nTrials):\n", " data, fitOne, fitTwo = fitTwoHistograms(percentile)\n", " xKinkOne.append(fitOne[0])\n", " xKinkTwo.append(fitTwo[0])\n", " xKinkDiff.append(baseGuess[0] + fitTwo[0] - fitOne[0])" ], "language": "python", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "def plotHistoFitCompare():\n", " fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n", "# plt.hist(xKinkOne, range=(80,180), color='#66a61e', bins=np.arange(80, 181, 2), alpha=0.6, zorder=2)\n", "# plt.hist(xKinkTwo, range=(80,180), color='#0088ff', bins=np.arange(80, 181, 2), alpha=0.6, zorder=2)\n", " plt.hist(xKinkDiff, range=(80,180), color='#0088ff', bins=np.arange(80, 181, 2), alpha=0.8, zorder=1)\n", "\n", " axes.set_xticks(np.arange(80, 181, 10))\n", " axes.set_xticks(np.arange(80, 181, 2), minor=True)\n", " axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(80., 181., 10.)], fontsize=20)\n", "\n", " axes.set_yticks(np.arange(0, 250, 50))\n", " axes.set_yticks(np.arange(0, 250, 10), minor=True)\n", " axes.set_yticklabels([r'$%i$' % num for num in np.arange(0, 250, 50)], fontsize=20)\n", "\n", " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n", " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n", " axes.minorticks_on() \n", " axes.set_xlabel('True Kink (140) + Kink Fit Difference', labelpad=5, fontsize=22)\n", " axes.set_ylabel('Number of Counts (400 total)', labelpad=5, fontsize=22)\n", " \n", " axes.annotate(r'larger $x_{\\rm kink2}$', xy=(140.5,200), xycoords='data', xytext=(50,-5),\n", " textcoords='offset points', size=22,\n", " arrowprops=dict(arrowstyle='<-', color='#e7298a', linewidth=3))\n", " axes.annotate(r'larger $x_{\\rm kink1}$', xy=(139.5,200), xycoords='data', xytext=(-180,-5),\n", " textcoords='offset points', size=22,\n", " arrowprops=dict(arrowstyle='<-', color='#66a61e', linewidth=3))\n", " axes.annotate('', xy=(140.15,250), xycoords='data', xytext=(0,-100),\n", " textcoords='offset points', arrowprops=dict(arrowstyle='-'))\n", "\n", " print" ], "language": "python", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 45 }, { "cell_type": "code", "collapsed": false, "input": [ "plotHistoFitCompare()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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5T58+PoxRtWRmZjo8t1gspS4wDgAAgLKz2Wyy2WwV+po+WUe5urNarQ6PlJQU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\n7du3R82aNVGzZk34+vpi1apVyM/P14nVmHMkAGRlZWHFihXo0qULatW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"text": [ "" ] } ], "prompt_number": 46 }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "The debinning Project: Data Smoothing without Bins" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Histograms \"smooth\" the data in this way:\n", "\n", "![Let's try to find other shapes!](notTheOnlyShape.png \"Let's try to find other shapes!\")\n", "\n", "### Is there a more appropriate smoothing shape?" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Gaussian Smoothing: binfull Histogram" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### aka \"Kernel Density Estimation\":\n", "\n", "![Gaussian Smoothing](GaussianSmoothing.png \"Gaussian Smoothing\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Select a point from our data..." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Add a random deviate from a Gaussian distribution..." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### And repeat ad nauseam.\n", "### Put all results into a binfull Histogram (\"full\" of arbitrarily small bins)." ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "binfull Histogram Demo" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\"Linearly\n", "\n", "### Algorithm issues: Speed, choosing $\\sigma$, over/underflow, \"LinearExpanding\" - Kernel depends on \"time\"..." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 1) New Probability Calculus:\n", "\n", "### $\\qquad$ \"Can't I just calculate that thing?\"" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "## 2) The debinning Calculation:\n", "\n", "### $\\qquad$ \"Whoa, I can calculate something else!\"" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "## 3) The Future, and Shameless Advertising:\n", "\n", "### $\\qquad$ \"Yikes.... There is so much more!\"" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# New Probability Calculus:\n", "\n", "## \"Can't I just calculate that thing?\"" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Datum Probability" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "### What's the probability to get some datum, $x$?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ {\\large P(\\widetilde{x}\\in[x,x+dx]) = f(x) dx \\quad {\\rm and} \\quad \\Int{-\\infty}{\\infty} f(x) dx = 1~.} $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "#### $f(x)$ is the Probability Distribution Function (PDF). \n", "#### Its anti-derivative is the Cumulative Distribution Function (CDF):\n", "\n", "$$ F(x) = \\Int{-\\infty}{x} f(x') dx' = P(\\tilde{x} \\le x)$$\n", "$$ 1 - F(x) = \\Int{x}{\\infty} f(x') dx' = P(\\tilde{x} > x) $$" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Sample Probability" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "### Probability to get a sample of data points, $\\{x_i\\}_{i=1}^n$?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\\begin{align} \n", " dP(\\{x_1\\}) &= \\phantom{3!} \\phantom{\\times!!} f(x_1) dx_1 \\\\\n", " dP(\\{x_1, x_2\\}) &= \\rust{2}\\phantom{!} \\rust{\\times} f(x_1) dx_1 f(x_2) dx_2 \\\\\n", " dP(\\{x_1, x_2, x_3\\}) &= \\rust{3!} \\rust{\\times} f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Order doesn't matter... WLOG, sort:\n", "\\begin{align}\n", " \\{x_1, x_2\\} &\\equiv \\{x_2, x_1\\} \\\\\n", " \\{x_1, x_2, x_3\\} &\\equiv \\{x_2, x_3, x_1\\} \\equiv \\cdots \\\\\n", " \\phantom{dP(\\{x_1, x_2, x_3\\})} &\\phantom{= 3! \\times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3}\n", "\\end{align}\n", "\n", "$$ \\Rightarrow\\ {\\rm WLOG}\\ x_j < x_k\\ {\\rm for}\\ j < k\\ {\\rm for\\ all}\\ x_j, x_k \\in \\{x_i\\}_{i=1}^n$$ " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\\begin{align}\n", " \\therefore dP(\\{x_i\\}_{i=1}^n) &= \\rust{n!} \\Prod{i = 1}{n} f(x_i) dx_i \\\\\n", " \\phantom{dP(\\{x_1, x_2, x_3\\})} &\\phantom{= 3! \\times f(x_1) dx_1 f(x_2) dx_2 f(x_3) dx_3}\n", "\\end{align}" ] }, { "cell_type": "heading", "level": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Probability Calculus: Integration" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "### The data is all sorted... Careful with those integration limits!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ \\Int{\\{x_1, x_2\\}}{} dP(\\{x_1, x_2\\}) = 2 \\Int{-\\infty}{\\infty} f(x_2) \\left[ \\Int{-\\infty}{x_2} f(x_1) dx_1 \\right] dx_2, $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$\\Int{\\{x_1, x_2, x_3\\}}{} dP(\\{x_1, x_2, x_3\\}) = 3!\\Int{-\\infty}{\\infty} f(x_3) \\left[ \\Int{-\\infty}{x_3} f(x_2) \\left( \\Int{-\\infty}{x_2} f(x_1) dx_1 \\right) dx_2 \\right] dx_3$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$\\vdots$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Limits of inner integrals are *also* integration variables...\n", "### Thus, integrals are \"chained\" together... Chain Integrals." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Probability Calculus: Being $r$th of $n$ ##" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\\begin{align}\n", " \\subNsubR{n}{f}{r} (x_r)\\ dx_r &\\equiv\\ \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_{i=1}^n) \\\\\n", " \\quad = n!\\ f(x_r)\\ dx_r\n", " &\\phantom\\times\\ \\Int{-\\infty}{\\infty} f(x_n) \\Int{-\\infty}{x_n} f(x_{n-1}) \\cdots \\Int{-\\infty}{x_{r+2}} f(x_{r+1}) \\Prod{i=r+1}{n} dx_i \\\\\n", " &\\times\\ \\Int{-\\infty}{\\infty} f(x_1) \\Int{x_1}{\\infty} f(x_2) \\cdots \\Int{x_{r-2}}{\\infty} f(x_{r-1}) \\Prod{i'=1}{r-1} dx_{i'}\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### $\\subNsubR{n}{f}{r}$ Theorem:\n", "\n", "$$ {\\Large \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r}\\ f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Probability Calculus: Being $r$th of $n$ ##" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### $n$ identical siblings: Race! $\\quad$ ... Outcomes? $n!$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Only care about $r$th place. $\\quad$ ... $n!$ is overcounting.\n", "### $\\quad$ ... $(r-1)$ faster... who cares what order...\n", "### $\\quad$ ... $(n-r)$ slower... who cares what order...\n", "\n", "### $$ \\Rightarrow \\subNsubR{n}{K}{r} \\equiv \\frac{n!}{(n-r)!(r-1)!} $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ {\\Large \\therefore \\quad \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r}\\ f(x_r)\\ F^{r-1}(x_r)\\ \\left(1 - F(x_r)\\right)^{n-r} } $$\n", "\n", "$ {\\Large ({\\rm HW}-1)}$\n", "$${\\large {\\rm Prove\\ the}\\ \\subNsubR{n}{f}{r}\\ {\\rm Theorem\\ by\\ computing\\ the\\ chain\\ integral.} }$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Proof:\n", "\n", "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = \\Int{\\{x_{i \\neq r}\\}_n}{} dP(\\{x_i\\}_n) = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\Int{-\\infty}{x_2} f(x_1) \\Prod{i=1}{r-1} dx_i $$\n", "\n", "$$ \\times\\ f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\Int{x_{n-1}}{\\infty} f(x_n) \\Prod{j=r+1}{n} dx_j $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\Int{-\\infty}{x_3} f(x_2) F(x_2) \\Prod{i=2}{r-1} dx_i $$\n", "\n", "$$ \\times\\ f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\Int{x_{n-2}}{\\infty} f(x_{n-1}) \\left(1 - F(x_{n-1})\\right) \\Prod{j=r+1}{n-1} dx_j $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Integration by parts:\n", "\n", "$$ \\Int{-\\infty}{x} f(\\widetilde{x}) F^{a-1}(\\widetilde{x}) d\\widetilde{x} = \\frac{1}{a} F^a(x) \\qquad {\\rm and} \\qquad \n", "\\Int{x}{\\infty} f(\\widetilde{x}) \\left(1 - F(\\widetilde{x})\\right)^{a-1} d\\widetilde{x} = \\frac{1}{a} \\left(1 - F(x)\\right)^a $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ \\subNsubR{n}{f}{r}(x_r) dx_r = n! \\Int{-\\infty}{x_r} f(x_{r-1}) \\Int{-\\infty}{x_{r-1}} f(x_{r-2}) \\cdots \\frac{1}{2} \\Int{-\\infty}{x_4} f(x_3) F^2 (x_3) \\Prod{i=3}{r-1} dx_i $$\n", "\n", "$$ \\times\\ f(x_r) dx_r \\Int{x_r}{\\infty} f(x_{r+1}) \\Int{x_{r+1}}{\\infty} f(x_{r+2}) \\cdots \\frac{1}{2} \\Int{x_{n-2}}{\\infty} f(x_{n-2}) \\left(1 - F(x_{n-2})\\right)^2 \\Prod{j=r+1}{n-2} dx_j $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ \\cdots\\ = n! \\left(\\frac{1}{(r-1)!} F^{r-1}(x_r)\\right) f(x_r) dx_r \\left(\\frac{1}{(n-r)!} \\left(1 - F(x_r)\\right)^{n-r}\\right) $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ {\\Large \\therefore \\quad \\subNsubR{n}{f}{r}(x_r) = \\subNsubR{n}{K}{r} f(x_r) F^{r-1}(x_r) \\left(1 - F(x_r)\\right)^{n-r} }. \\quad {}_\\blacksquare$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "reload(funcs)\n", "def quickData():\n", " ''' Shorthand for getting easyEndpoint data (384 x values in [8.5,200])\n", " - set nPulls before calling\n", " - see utilities.sampleFunctions.functionToData for more details\n", " '''\n", " return funcs.functionToData(funcs.easyEndpoint, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))\n", "\n", "\n", "def quickBG():\n", " ''' Shorthand for getting endpointBG data (384 x values in [8.5,200])\n", " - set nPulls before calling\n", " - see utilities.sampleFunctions.functionToData for more details\n", " '''\n", " return funcs.functionToData(funcs.endpointBG, nPulls, 0.5, np.arange(8.5, 200.2, 0.5))" ], "language": "python", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "nPulls = 10\n", "pullData = {index:[] for index in xrange(nPulls)}\n", "settings['simpleSortedOutput'] = True\n", "for iteration in xrange(2000):\n", " for i,v in enumerate(quickData()):\n", " pullData[i].append(v)\n", "\n", "settings['simpleSortedOutput'] = False\n", "x, f, F, data = quickData()\n", "bgx, bgf, bgF, bgdata = quickBG()\n", "f /= F[-1]\n", "bgf /= F[-1]\n", "bgF /= bgF[-1]\n", "F /= F[-1]\n", "\n", "ithPDF = {}\n", "for i in xrange(1, nPulls+1):\n", " ithPDF[i-1] = np.array([f[j] * F[j]**(i-1) * (1 - F[j])**(nPulls-i) * pc.nKr(nPulls, i) for j in xrange(len(x))])" ], "language": "python", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "def makeHist(i=0):\n", " fig, axes = plt.subplots(figsize=(9,5), facecolor='#ffffff')\n", " plt.plot(x, f, '--', color='#0088ff', alpha=0.6, linewidth=3)\n", " plt.plot(x, bgf, '-.', color='#0088ff', alpha=0.6, linewidth=3)\n", " plt.hist(pullData[i], bins=np.arange(0, 201, 5), alpha=0.4, color='#66a61e', normed=True)\n", " plt.plot(x, ithPDF[i], '#964a01', linewidth=3)\n", " \n", " axes.set_xticks(np.arange(0, 201, 50))\n", " axes.set_xticks(np.arange(0, 201, 10), minor=True)\n", " axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(0, 201, 50)], fontsize=20)\n", " \n", " axes.set_ylim(bottom=-0.0001, top=0.0401)\n", " axes.set_yticks(np.arange(0, 0.04, 0.01))\n", " axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.04, 0.01)], fontsize=20)\n", " axes.set_yticks(np.arange(0, 0.04, 0.01/5), minor=True)\n", "\n", " axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n", " axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n", "\n", " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n", " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n", " axes.minorticks_on()" ], "language": "python", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n", "\n", "### Here's $\\subNsubR{10}{f}{1}(x)$ compared with the histogram of the 1st smallest point of 2000 samples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "makeHist(0)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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48cUX3RYwtU17Vsy37rkW0isVob1SJY5IWjGjJ1nfl+3aBNOlovdERESOON3F\nMWTIEKxfv97m3Jw5c9C/f3+sWrUKJSUl6NmzJ2bOnNlsOSfyLQWn9uD87itbsMTfcreE0chDcI9r\nEJCgQV1+Lsx1tSjduQkxY2+SOiwiIpKpqx6TGjRoEAYNGtT8jeSz9qz4h/W9Pr4X1JoOEkYjD4Ig\nIHr0RGi//AgAULLlF0SPmgChFRUziIjI+/nmJCKZ0Gq1NsdyKX/hStojm5Fz8DcAgKBQoLaTb+y5\n5ozwAcNR8MM3MFVWwFBajIrDexF+7VCpwyIiombodDrodDqPfqfTc9guq6urw8qVKzFnzhzcfPPN\nuPnmmzF79mysXLnSZtsPap5Go7F5paenSx2Sy+374iXr+25jH4A52PsrGjhLoVIhasQ463HxxnUS\nRkNERM5KT0+3e4a7W4t62LZv34777rsPFy5csLu2dOlSPPfcc/j8889ZW9NJubm5Nsfe1rtWmLEf\nuYc2AAAEhRID7/1f7P5yucRRyUvU8BtQ9NtaWExG1GSdRXVmBoJSujb/QSIikkxaWhpmz55tc87d\nSZvTCduxY8cwYcIEVFdXo1OnTpg6dSo6dBDnIp0/fx5ffvklzp07h0mTJmH37t3o3bu324L2FomJ\niVKHcNXeWrII1QbH3cJBh7+F6tL7utgeeOfL5di7bxeG39rd4f2+yC8sHOEDh6Nst7ihcPGmdUzY\niIhkToopTE4nbPPnz0d1dTWee+45vPTSS1AobEdTFy5ciAULFuCVV17B/PnzsWrVKpcHS/JTbdA5\nTMDqCvNxZsOVOq89HrgPgUkdsGO34woVvix69ERrwlZxaC/0xRcb3UiXiIh8k9Nz2DZt2oRu3brh\nlVdesUvWAECpVOLFF19Et27dGi0bRb6jeOO6K/uu9bgGgUlcGdoYdWIygruLlUNgsaBk6/qmP0BE\nRD7H6YStpqYGAwYMaPIeQRDQv39/1NTUXHVg1HYZKytQtnuL9Th63C0SRtM2RNcr01W6axPMdbUS\nRkNERHLjdMLWvXt35OXlNXtffn6+TTF48j2lOzfBYjQAANTJKQju2kviiOQvpGdfqGLiAQDmmmqU\n7d8hcURERCQnTidsjz76KLZs2YJt27Y1es/27duxZcsWzJkzxyXBUdtjMZtRun2D9Th61AQIgiBh\nRG2DoFAgauR463HJ5l9huTSkTERE5HTCNnv2bMybNw8TJ07Es88+i8OHD1s3jjt8+DD+53/+BxMn\nTsTjjz/986RTAAAgAElEQVSORx991J0xk4zpjh2EobQYAKAMDkVYv8ESR9R2RAy5HgpVAACgLj8H\n1WdOSBwRERHJRaOrRBUKhV3PyOXf+BctWmS3yevla2+88QbefPNNmEwmV8dKbUDJ1t+s7yOvGw2F\nv6qJu6k+ZWAQwgePROk2cdFB8ZZfgbhJzXyKiIh8QZM9bBaLxebVkmvke+oKtKg6dVQ8EAREDh/X\n9AfITnS9YVHdkf0QasokjIaIiOSi0YTNbDZf1Yt8T0m9uWuhvftBFcUyVC0VkKBBcLcrW3wE5OyT\nNiAiIpKFFtcSJXLEbDSgfO9263HkiBskjKZtix51o/W9SvsHDLXVEkZDRERy0KJaouRaWq3W5liK\nUheuojt6EKbqSgCAf2Q0QrpfI3FEbVdIr37wj46FobgQCkMNMjavRK8JD0kdFhERXXJ50aUntbiH\nTa/XY+XKlZgzZw5uueUW3HLLLZgzZw6++OILGAwGd8TotTQajc2r4UKOtqRs15XqFhGDr4fgoBoG\nOUdQKBA14spctqNrl3BeKBGRjKSnp9s9w92tRT1s+/btw1133YWsrCy7ax9++CH+/ve/45tvvmm2\nIgKJcnNzbY7bau+aoawElScPW48jhoyUMBrvEDl0FC6uWwWLvg7FmYfx+oKZMEU2X94ryD8Uj//l\naQ9ESETku9LS0jB79mybc+5O2pxO2HJycjBx4kSUlJSgffv2uP/++5GSkgIAOHfuHD7//HOcP38e\nEyZMwKFDhzySbbZ1iYmJUofgEmV7t1nrhgZ37cXC5S6gDApGxMDhKN3xOwBAYzyB5FtvbOZTwPa1\np9wdGhGRz5NiCpPTCdu//vUvlJSUYN68eVi0aBH8/f1tri9cuBDPPvss3nrrLbz66qtYsmSJy4Ml\nGbJYbIdDh1wvYTDeJWrkeGvCVnFkP/QlRVx5S0Tko5yeaLRu3TqkpKTgjTfesEvWAMDf3x+LFi1C\nSkoK1q1b59IgSb6U5bnQFxUAABTqQISlDpI4Iu+hTkxGkTJCPGhQ8ouIiHyL0wmbVqvFkCFDoGhi\nMrlSqcTgwYPtVj+S91LlH7W+D7t2iLW0ErlGlv+VYfPSnRth1usljIaIiKTidMKmVqtRUlLS7H0l\nJSVQq9VXFRS1DWaTEf4Fx6zHEQOGSRiNdyrwi4b/pWFQU1Ulyg/slDgiIiKSgtMJW2pqKjZt2oQT\nJxovSH3q1Cls3rwZffv2dUlwJG85f2yAwiBu6uoXHomgzj0kjsgLCQKi6m1CXLLlV27xQUTkg5xO\n2B588EHo9XqMGzcOH330EfT1hmb0ej2WLVuGsWPHQq/X4+GHH3ZLsCQvGZu/sL4Pv3Yo915zk4ih\noyH4qwAAtblZqD53WuKIiIjI05x+wk6bNg1Tp05Ffn4+Hn74YQQHB6N9+/bo0KEDgoOD8dBDDyEv\nLw9Tp07FtGnT3BkzyYCxrgaZO76zHocP5HCou/gFh9j8+y3Z+quE0RARkRScTtgEQcBnn32GJUuW\nICUlBSaTCTk5Obhw4QJMJhM6deqEJUuW4PPPP3dnvCQTWXt+gKFGLEWlikuAOqmjtAF5ueiRV/Zg\nqzi0F4ayYgmjISIiT2tRpQNBEDB37lzMnTsXOTk51p36k5KSuFGuj8nY8pX1fXj/YRAEQcJovJ9a\n0x5BXXqg+sxJwGxGyfbfEX/zXVKHRUREHuJ0D1tkZCRGjrxScigpKQlDhgzBkCFDmKz5GENNJbL3\n/WQ9Du8/VMJofEf9XrbSHRthNnCLDyIiX+F0D5ter0f79u3dGYvPabhfnRSlLloje986mPS1AABT\ncCwC4r2jxJbchV4zAP4R0TCUFcNUWYHyA7sQycoSREQep9PpoNPpPPqdTvewdenSBUVFRe6Mxedo\nNBqbV3p6utQhOeVcvcUGhrieEkbiWwSlEpEjxlmPS7b8wi0+iIgkkJ6ebvcMdzenE7bp06dj8+bN\nOHfunDvj8Sm5ubk2r7S0NKlDapaxrgZZe3+0HuvjufeaJ0UOG3Nli4+cLFSfZbF3IiJPS0tLs3uG\nu5vTCduTTz6JCRMmYNy4cfjyyy9RV1fnzrh8QmJios2rLQyHXjjwq3V1aHhiV5iD4ySOyLf4BYci\nYtBw63Hx5p8ljIaIyDeFhobaPcPdzek5bF26dIHFYkF2djbuu+8+CIKAuLg4BAYGOryfPXHeqf5w\naKcRdyCrhKtDPS3q+gko3bERAKA7sh/64otQRTNxJiLyZk4nbFlZWTbHFosFBQUFLg+I5Mtk0OP8\n7jXW487D7sDGH9Y08QlyB3W7JAR374OqU0cBiwUlW35Dwu33Sx0WERG5kdMJW2ZmJgBwkrMP0x7Z\nBH1VOQAgNL4jYrr0B8CETQrRoyaICRuA0t2bETvpT1CqHfd2ExFR29dswlZaWopffvkF2dnZCAgI\nQL9+/TBq1ChPxEYyU793rePQydwsV0IhPVOhik2AvjAf5ppqlO3Ziujrb2z+g9RmWSxASS2QVQ5k\nVQDZFcAj/YCAFm1/TkRtVZP/q3/11VeYM2cOKioqrOcEQUC/fv3w/fffIzk52e0BkjxYLBac373W\nepwyZIqE0ZCgUCBq1ATkf7scAFCy5VdEjbhB4qjIXT45AhwpBCob7JWcowM6R0oTExF5VqOrRA8d\nOoTp06ejoqICQUFB6NevHzp16gQAOHjwIP70pz95LEiSXvG5Q6gsvAAAUAVHIKH3CIkjoojBI6EI\nDAIA6AvzUXnikMQRUWvVGYHTJUBFI4vvqw32yRog9rQRkW9oNGFbvHgxjEYj7r//fuTn5+PAgQM4\nc+YM9u/fj44dO2L//v3YtGmTB0MlKZ3fc6V3rf3ASVD6+UsYDQGAMkCNyKGjrcfFm36RLhhqkYtV\nwLYcYMVR4J/bgSc2AOl7xF40RzqEi/8M8gd6RgMTUoDZ/YABCfb35lSIw6ZE5F0aHRLdsmULEhIS\n8OGHH0KtVlvP9+vXD2+++SZuu+02bN26FaNHj/ZEnCSx+sOhHYfcKmEkVF/UyPEo3rQOsFhQdfoo\nFFHDm/8QSW5rDvBrpv35zHJgeJL9+RFJwOB2QEwg0NTUUa0OeGMfYDIDfx0IdIpwXcxEJK1Ge9jy\n8/MxePBgm2TtsstF4BvWwiTvVFWsRWHGPgCAQumH9gMmShwRXaaKjkXoNQOtxwEX9kgYDZkt4mKA\njVnAh38AvzlIygAgJdz2WCEAmlAg0v6vWwBAeAAQG9R0smaxAB8eEodOa4zAW/uAjJLW/TmISH4a\n7WGrq6tDVFSUw2uRkZHWe8j7Ze35wfq+XZ9RCAjhr+1yEj1qAnSH9wIAVHlHUFtRDHVYtMRR+Zas\ncmD1aeBcuTgf7bIKPTA+xf7+ThFA/wSgYxiQEgF0CLv61Z6CADzYF3hzH6DTA7VG4N/7gcf6Az34\nnwNRm+d0aSpyPa1Wa/PS6XRSh+TQ+XoJW8cht0gYCTkS1Lk71EkdAACC2Yhj696XOCLvZLE4nvgP\nAH4K4ESxbbIGiEOcRrP9/RFqYE4/YEInoFuU67bmSAoD0gaLPXIAoDcB7xwAyvm7NZFL6XQ6u2e4\nuzX510R+fj62bNlid/7y5rmNXQeA66+/3gXheTeNRmNzvGDBArzwwgvSBNMIk6EOuYd+tx53GMyE\nTW4EQUD0qInI/VxM1I6uXYJ+f0qD0j9A4sjaNosFKKgCTpeKQ4unS8Vzr422H5pMDAEC/cShyKhA\noHPEpVckoPTwdoXtQsSk7Y29QGktcFePKwkcEblGeno6Fi5c6NHvbDJh+/nnn/Hzz40Xl254XRAE\nWCwWCIIAk8nkuii9VG5urs2xHIu/5x3bBmNdNQCx2Ht4u84SR0SOhPUfioK1X8FYUYbq0nyc3vg5\net44S+qw2iyjGfjfLWLC01BxDRATZHtOEIC5/cV5Zo3NQ/Ok+GAxaTtd4ngRAxFdnbS0NMyePdvm\nXMNOGFdrNGFr3759qxvlDvjOSUxMlDqEZmXvv5KQtx8wQcJIqCkKP39EjZqAi2u/AgAc+i4dPW74\nMwQFZz00xmIBcnVicuOvtL3mpwBCVfYJm9oPKKy2T9gAcWhTTmKDxBcRuV5oaKjHO1kaTdjOnz/v\nwTBIri7sv7K3V3J/JmxyFjVsLAp+Wg3BpEfphRPI2vcTOnII28piEZOtE8XAyRLgVDFQZQCeGAj0\njLG/v1sUUFQDdI0U33eNBJLDxBWdbV2NAQjkVopEbQqr0FGjKotyUJIlFhhX+KmQ2He0tAFRk5RB\nwajT9Ic6excA4I9Vi5iw1fPZMXGz2oZOlThO2CZ3Ae7o7h0JWn0XKsSVpHd2B65z7wgOEbmQrMZL\njEYjFixYgNTUVIwZMwYDBgzASy+91KL5cC1to66uDhs3bsTNN9+Ml19+2a2xtTX1e9cS+1wPf3Ww\nhNGQM+raD4ZCKf4elnd0CwpO7pY4Is+qMwJlDuadAUCSg9GLUBWgbORvwQA/70vWtDoxWavUi/VJ\nt16QOiIicpasetjmzp2L9evXY8+ePYiJiUFRURGGDBmCjIwMLF++3KVtXLx4EdOmTUNwcDASEhKw\nbt06DBkyxK2xtTXZ9YdDOX+tTbCow9Fl1FSc/n0FAOCP7xZhwt++kTgq97FYxHqax4qAE0XiPmgD\nE4BZfe3v7RktzkHrHiXuS9YjSlxR6UtTbsMCxEURl7cn+ewYYLIAo1s/ZZmIPEQ2PWzbt2/H0qVL\n8fzzzyMmRhyfiImJwXPPPYcVK1Zg27ZtLm0jLi4Ov/76K1avXo17773X7bG1NWaTETl//GY9ZnWD\ntqPfn9Ks78/t+A7l2jMSRuM+58uBZzYCr+4E1mQAGaViSaaTxWIi11B8MLB4rLiac2wHIDHUt5I1\nAAhRAU8NAjrWq7TwxXFg/XnJQiIiJ8kmYfvkk08AAFOmTLE5P3nyZJvr7mjD4uhvdxfH1tZcPLUH\n+iqxgnRwTBIi2/eSOCJyVnRK3ysLRCwWHFq9WNqArlJj/3vGBYmLBhoKUTne4FYQGh/+9CVB/uJC\ni85iwRoIAhDMBQhEsiebv742b96M6OhoxMXF2ZyPj49HZGSkU71YrmjDk+3KWcPtPLhVS9vS785n\nrO9Prv8E1WUXJYym5ar0wG4t8NEh4PnN4o79DQX5iyWeQlXA0ESxLNPrY4D5w4FQbhTbpEB/4K8D\nxNWv03pz8QFRWyCLOWxGoxGZmZno0qWLw+sxMTHIyspyexuebFfuLhyoP3+Nw6FtjabvGMR07o+i\nswdg0tfi6A/vYPA0z+7K3Rqbs4G9ecDZMrGQ+mWnS4A+sfb3P9JP7FHj7xMtp/YDnhzkfQsriLyV\nLHrYysrKYDKZEBgY6PC6Wq2GXq9HdXW1W9vwZLtyVlNeiIsZ+wAAgkKJpNRxEkdELSUIAvrd8bT1\n+OjaJdBXV0gYkXNOFItz0cwNhkFPlzi+PzSAydrVYLJG1HbIImGrrRXX4fv5Oe7wU1zarb28vNyt\nbXiyXTm7cPA368Sh+J7XISAkQuKIqDU6j7gTYZdKidVVluLYj+9JHJG47cbBAuBsqePrqZdmHQiC\nOMfqtq7A/w4Dbu/muRhJXNDx/enG5w8SkefJYkg0IqLphKCyshKA2JvlzjY82S4AaLXaZu+RovxF\n7h/rre/b97/Ro99NrqNQ+qH/Xc9h078fBgD8sXox+tw6D/5qz9YrqtIDhy4CBwrEHjSjWdx64/Kk\n9/r6xgIP9AGuiRW3oCDPyyoH3twrFrKvMwF392AvJvk2nU4HnU4ndRjySNhCQkIQGBgIs9ns8HpV\nVRWUSiXCwsLc2oYn2wWcKxS7YMECvPDCCy1uuzXeWrII1foKhG1fbe163XAyE7++saDRz+zdtwvD\nb+3ukfio5bqNnY59X/wTlYUXUFteiBO/fIi+Ux732PefLgHe2Gs/xHm0SEzc/Br08QerWKxcalsu\niMkaAPyeJf7s7u3JpI18V3p6OhYulH4OsCwSNgBISUlBaan9OInZbEZZWRlSUlKgVCodfNK1bXiy\n3dzc3Gbv8WTvWrVBh0HDIpGxQRzeVQSoMWTqaAhN/Nl27N7sqfCoFZT+Klx757PY+t48AMAfq15H\n75segdLfM91XHcLErTTM9VZ5JoWKQ5+OEjaS3n29gFojsC9fPN6ULSZt9/Vi0ka+KS0tDbNnz272\nPmc6Ya6GbBK2SZMmYfHixaisrERISIj1fEZGBmprazFy5EiPtOHJdhMTE1v1OXeqPH3c+j6oc48m\nkzWSn127duLVhj2iJgPCVCFQ6CtRVazFm8/dAX3SAOvlIP9QPP6Xp9EaxTXinLRDF4G/9BfLOdUX\n4Af0iQHK6oAB8cC18UCMZ0dkqYWUCuDBVHFBwp488dy2HHHrj06czko+SIqpSY7I5vfbKVOmwGKx\nYPXq1Tbnv/32WwDA9OnTbc5v2LABa9asuao23BVbW1aVccz6PrgbN8tta8yCHsNv7W77uq0P2k2a\nbL0n/OJeDLups/V6taFlczMq6oCNWcD/7Qb+thn45qQ49Hm0yPH9D6cCzw0FxqcwWWsrFAIwsy8w\nJFHsVfvzNUzWiKQmm4RtxIgRuOmmmzB//nzk5Ym/1mVnZ+Ptt9/G9OnTMWrUKOu9ZWVlmDhxIm67\n7TacPHmyVW3Ud3lo8vJnria2Ns1iQVW9Hrbgrr0lDIZcKXL4WCiDxd5hQ0khyvbtaHVbX54QXw1X\neh7Id3w/qwu0TYpLiVraIDFxIyJpyeqv0lWrVuHuu+/GjTfeiJEjR2LChAmYNWsWli5danNfWFgY\nhg0bhl69etmNGTvbBgAMGjQIKSkpmD59OgRBwPvvv4+EhAQMGDAABw8ebHW7bZWiqhCmSnGvLmVw\nCNSJyRJHRK6iDFAjevQk63HhL6thMRlb1dbAhCvvFQLQO0Zc2TmVHbJeRyEAXaOkjoKIABnNYQOA\ngIAAvPbaa3jttdeavE+hUGDzZseT3Z1tAwD27t3r8tjaMr+S89b3wV17QVDIKp+nqxR1/XgUb1wH\nU3UlDMWFKN29BVHDxtrcY7aIxdN3aa/0sDR0TaxYdSA1Drg2jmWgfJVWBySEcPNdIk+RVcJG0vIv\nybS+D+7K7hJvo1QHIXrczbi49isAQNEv/0XEYHHBTF4lsDMX2J0HlIl7RcNfKW7noG7wt4S/Epg3\nAOTDzpYC/94vLii5vECBiNyLXSgEADCbjPArvVITlQmbd4oeOR7KEHHPQENZMUp3bITRosQrO4Ff\nMq8kawBgMAHHG1lIQL6rsFpM1i5v/bH0EGByvE0lEbkQEzYCABSdPQjBVAcA8AuPhCquncQRkTso\nAtSIHX9lxWjRb/+Fn7kW18ZfuSdUBYzrAPx9GGzOEwFATCBwXb1FCPvzgaWHxX31iMh9OCRKAIDc\nQ79b3wd36w2BO2R6laKaQBwujkVKWDk6DB+Lot9/hLG8FMaKcgTk7MNwjfjAHZooLiLgyk5qjCAA\n9/QUh0E3XOqUP5APCBC3cOFfHUTuwYSNAAA59RM2Dod6Bb1JgVOlUThSHAttlbilR1mtGildyhF7\n4xTkffMJACDg/A6kBOrQvZ/0G0NS2yAIwF09xKTtt/PiPwcmMFkjcif+Hk0wGeqQf3yb9ZgJW9uX\nVxWM/xy5Fr9kp1iTNQDIrAiHTu+PiKGj4R8VAwBQGKrxx3eLpAqV2ihBAO7oDkzsBDzYF+if0Pxn\niKj12MMmIa1Wa3MsVfmLglO7YayrAQCoYuKhuvQgp7YrNrAaCuFKxXWFYEGX8FL0jSlEiL8BguCH\nuEl/Qu7nHwAADn2Xjt6T5iA4mjukkvMEAbi9m9RREHmeTqeDTteyKjFXiz1sEtJoNDav9PR0SeLI\nO7rF+j6oa09JYqDWKagOgtFsPw7lp7CgV1QRotS1GKW5gEf6/IHJnc6iY1iFddgqfOAIqDXtAQDG\numrs/XyBXTtERGQvPT3d7hnubuxhk9DlkliXSVVcVnt0q/V9cOceksRAzjOaBZwqjcIfRfHIqwrG\nxA6Z6BNtv//GSE0OxgjZjc4rEhQKxE+eiqz3xM2gT/72MfpOeQJRHViSjK7e6RJg/XngoVRApZQ6\nGiLXSktLw+zZs23OuTtpY8ImocRE6YefzCYj8k9cqSsZxIRNtnR6fxwsjMeR4ljUGK/8r/tHYZzD\nhM1f0fw+CyE9roEhqhP8S87BYjZj18fP4aYX1ro0bvI9GSXA2/sBvQlYsh94rD8QwKcNeREppjBx\nSNTHFZ09CGNtFQDArA7n/DUZu1gTjD0F7WySNaVgQaS61uGwqLNqut5gXd6XtfdH5B7aeNWxkm/L\nLBeTNQA4VQIsOQDUta50LRFdwoTNx2nrzV8zRrSXMBJqTkpYGcJV4ubGYSo9RibmYE6fP3Bzx3Pw\nU1ia+XTjzKHx6D5uhvV4x0fPwGwyXXW85LtuTLFdjHD6Uo9bLZM2olZjwubj8urNXzNGMmGTWoVe\nhS25Sag12k/6UQjAKM0F3NYpAw/1PoQhCXkI8nfNE3Dw9H9CqVIDAIrOHsDJ35a5pF3yXRM7AXd2\nv3J8rhzIrpAuHqK2jgmbD7OYzcg7Vi9hYw+bZLSVwVib2RkfHk3FnoJ2OFIc6/C+bpGl6BJR5vJi\n2yExSeh3xzPW493L/4ZaXYlrv4R8zvgUcYNdpQKY0w/oFiV1RERtFxM2H1aSfQx1laUAgMCIOJiD\noiWOyPfkVoZg5ameWHm6F06VRuHywObBwniYWz/K2Sr973oOofEdAQC1FcXYs+Ifng2AvNINHYF/\njgBS46SOhKhtY8Lmw+rvv9au90jWlZFI/UoEANA+tALjkrPg6Z+GX0Aghj+82Hp8fN37KDx70MNR\nkDeKCZI6AqK2jwmbD6u//1q7PiMljMR3JQZXol1wFRSCBb2jivBAj6O4u+spdA4vkyR/7jh0CpL7\nTwAgDplve28eLObmtwchao2MEqBKL3UURG0DEzYfZbFYbHrYEntfL2E03q28ToUNFzrAoAyxuyYI\nwPjkTMzucwiTOmYiLqhGggjrxyNg+Jw3ofDzBwDkn9iBU7+vkDQm8k4nioC39gNv7mPSRuQMJmw+\nqlx7BtWl+QAAVXA4ojpeI3FE3qewJhA/nu+EpcdScbAwDkUh/R3eFxdUgxB/g4eja1xkUnek3vak\n9XjnR8+gprxQwojI21TUAe8eBAwmceXoG0zaiJrFhE1CWq3W5uXJQrL1V4e26zUCCiVrx7hKcY0a\n353phuUn+uBESbR1IUFxSF/UmdrGv+cB9/4vQmKTAQC1FUXY/sGTzXyCyHlhAcDUnlemzV64lLRV\nMmmjNkKn09k9w92NCZuEpCz+nsf5a26VWRFuc9whtAIditZApWgbG9L6B4bg+sfesx5nbFqJrD0/\nShgReZthScCMPrZJ25IDgMXDq6OJWoPF332MlMXf61c4aNeH89dcKTqwFl0iSnGmLBJdI0oxKD4P\n7YKrcL6u8ULsctRh0E3oNmYaTm/8DACw+Z1HcW+fo1AFhUkcGXmL6y4945YfBZQCcEtnLlantoHF\n332MVMXfK4tyoSvIBCBu5RDb2fHcKmqcxQJUqDuhrC4AEQF1dtdHJuZgZGIOotS1EkTXMrt27cSr\nbyxweE0wxSPUPwgKQzWqinLw7pPjIFxzDx7/y9MejpK81XUaQAAQogL6ON4vmkh2pCj+zoTNBxWc\n2GF9H9dtCJT+KgmjaVssFuBseQR25mtwPjYEO/NiMaljpt19bSFRu8ws6DH81u6NXi9PmYWc5UsA\nAAE5+1EZ18tToZGPGOr+0SSiNo9z2HxQfr2ELaHndRJG0nZYLMDpskisONkb35/rioJqcSfQ4yUx\nKK0NkDg69wq7dghC+1zphQ069l/U6UoljIh8iacrfhDJFRM2H2SbsA2TMJK2o9Lgjx8yO+NizZUt\n2wWLCdfGFSBA2TYWErSWIAhod9efoQwKBgAo6iqw+Z1HYeHscHKzI4XAqzvFbUCIfB0TNh9jqK1G\nUb1yQ/HsYXNKqMqAvjHiXmR+CjMGxuWjh/ZDjE3KRpC/UeLo3M8/IgqJ9z5kPT679Wuc2vCphBGR\ntztaCPzn4KV92vYyaSPiHDYfU5ixF2aTmGBEJveEOjRK4ojkx2QRoBTse4+GJmjhrzBjUFwegvyN\n2GuuliC6lrNYAINZgTqTEnqzEtEO5tftLUjAwLh8uxV6P2Z2gsGsgNGiwG3XCIi4bjTKdm4CAGz7\nzzysNQzHkxO6wK/Br37/2gXoTYBCAJ4ZDAQ0+Jvm7f3A7FT781+fAEwWwF8B3NrF/vofBUDvGMC/\nwXZ2dUZApeQKQ29SY7wyHKqtBBbvBZ4aJO7hRuSL2MPmY2yGQ3txOLS+oppArDnXBWvOdXF4PcTf\ngFGaC5L2qBnNAnR6f1ysDrS7ZrYA2VE3OdzH6u1DA/D+0X74+Pg1DucEbdcmwWSxz3YyyqJwpjwS\n5yvCYbYIaHf7NJiCxCTfUFMJ5TfTYNDbV2nI1YmvCxWO/xynSxyf354LbMoGfjsPOBpwXX5UTAQb\nen4z8MgvwF/XO94xf/VpoMZBMYm8SqC0VmyTI7zyMqgd8GBfMekHxJ9V+h6gnD1t5KPYw+Zj8k/s\ntL7n/DVReZ0KF6ImYvmJPtYkQVsZjMSQKknisViAw0Wx1iHYy8wW4K0/BlpjfKLfPvgprmQZCgGo\nCOoCg1kPlfJKwXZBAFRKk7XKgt6khNrPNutRKswwmhXwa7Cxr5/CDOOlz1kgQBGgxm5LF1wn7INg\nMSOwYA/effx66HvcaPO5fcabYIL4udeP/4hQVbDNViAWXHkQ12eoV2e+Ya+dxQLUGu173QCg9lLY\nl3vaGvo9C7ipk/3513aJPTkAsHgsENxgwfSPZ4EbOth/p9FsHx+53sB24n+/Sw+J//0X1wIXq4Bw\n9rKRD2LC5kMsZrNND1s8EzZs12qwt6AdSoNVaF/vfLYu3K0J296CBJTVBaBCH4ApnTJsEi9BALZq\nk5MH3fkAACAASURBVNEt0rYbSiEAQf4GVBnEwuw1Rj+Eqmy7jZSmGlQb1VApbbshgv0N8FOYoVKY\nYLQoANgmZv1jCyA4GAa+scOl/foEM/wUYjZV5qdGwq13o2DNlwCAoJzd6Dr6WkQMGmH9XI+a3Es9\ndgJiA7tixw+nbNp9fIDjhOe+XmJ9SaNZ3Ei1PguAgQn2n7ucPJnMgFLh+LrJYp/ImS1XkjVBAIL8\nG3yfRUzYJqTYn39iA+AniInD366zT+jOlwPtwxwnpdQyAxLEf356FHikH9CVszjIRzFh8yFluadR\npxOTAHVYNCI03SSOSHpmiwBjvaHAlLByjEjMQXyQa+an/ZLVEaOTshFQr8cLAA5cjIfOIHbn6PQq\nRKptE6wQfz0qDfb744Wp9IAFCPQ3wmi2z3iSSn9DoN9Eu/Ozeh1pMs7hibkOz3eLcLx9R/TYm1F9\n/ix0h/cCALRffYSAdkkITOooXg9seh+6xh66I5Ia/4xCAB5MtT/vpwD+fYOYSOlNjuex3dfL/nyd\nEUgMAaou5bwNr1cbgAClfQJYZxKTSgMAo4NE0GQG/m83sGS87XmLBfjsmJjkRaqB4UlM6Jw1IAHo\nEWXfA0rkS5iw+ZD849ut7+N7DIPAGdoYnJCHw8WxCNLn496uApJCdS36/NHiGORVBaOkNhATO5xD\neIDtBKqC6mCU1qqREGybAIYH1FkTtnJ9gF3C1ie6EH6CbZIHAPd1O97kxPrQ2vN2yaE7CIIAzf2z\nkVmQi7oCLSwGAy589BY6Pf1P+AV7dvfvKzE5Hi71UzhOBAP9gQUj7M9fphCA27ran68yiNfMFiAi\nwD7Rq9ADoSr7ZKzKAGzLEd+r/exjMpqBZYeBh1Nt27w8t87X/3dlska+jgmbhLRarc2xu0td1B8O\nbedjCw7yq4IQH1Rt99ALUJpwf/fjqPp6JZJCZzv+MIAzZRFoF1yJ4AYLDg4XxUJbFQIAKKkLtEvY\nIgJqUVpnn7ClxhSiW0QpwlR1iHPQmzcwvsBhHHJ6aCvVgUh+8AmcW7wA5toaGEoKkfPJO+jwyNMQ\nlG3/r5ZAf2BUe/vz0YHAuzeKPXA1Dtaf6E1Az2j782X1Oh2j1PY/y9JaIKvCcQL4t81ir1xiCDC3\nQSU5X0/ojhYCSaFAhFrqSMiX6HQ66HQt+wX/anHarIQ0Go3NKz093a3fV3/Bga/MXyupVeO7M93w\n2aneOK8Ld3hPREAdBIgrMAuqg1BtsE82jhbHIKfSPpmOCayxvndU8WBwfB4SgyvtzveMKkb/uAJ0\niShDkF/b3cctID4RmmmPWI+rTh+F9suPvH5TXUEQe3xiguyvxQcDf77G/nx4AHB/b+DmzsAwB6WY\nSmrERM7ReaMZKKwGShyMNBdWAy/usD9vMIkrKw1evK/zHwXAuwfF1aOlbacaHHmB9PR0u2e4u7X9\nX4PbsNxc23lD7uxdq60oRlnOSQCAws8fcV0Huu275KDWqMTO/EQcLIyH+dIctc25yegQWu5w3lBe\n+Ai8fWgATBYB49ufR2qDFZqxgTUoqglC90jbOV3dIkoQoapDTGA14oPsFyk07FnzRmHXDEDspDtQ\nuG4VAKBsz1b4RUQh/ua7JI5MXkIDgOuTG7+eGALc4aCka1m90fIY+91cUFgNhDkYLsyuEOfSAeLe\ndX9t8L+8wSSuym242KKt0NUBy46IcwYvVotJW9pgsSeSyN3S0tIwe7btqIy7kzYmbBJKTEx0a/tv\nLVmEaoPYZetXeBohl87rg+Lw+rv/srt/775dTRYBbyuqVQn46Hhf1Biv/OctAEgIqsKp0kgEKM3o\nFF5u8xmluc66D1lBdTAA24StY1g5KvT2T8WOYRXoGNbIZmM+JHbCbTCUFKFs92YAQNGv/4V/RBSi\nho+TOLK2IzRAfDV0bby4qKKk1vEihZJaxz19RVc6f6F28Df96RJxv7snBtmer9QDxTViT6Gjz8lF\naIC4T9v7f4hJW+GlpO2pQUCUg8SWyJXcPYXJERn/70hXq9qgsyZgBWv/QNGl8/H9r0Gqg8Rsx6WH\nbVsXYCiGxQzUmZQIUJqQFKLDmKRsxAdV43BRLDIrQu0StiC9OGcsXFUHtdJ+iFITUgn3d3i3XYIg\nIPGemTBWlKHyxCEAQN43n8AvNBxhfb27N9cTAvyAdiGOr41IAq5zMAJtsQCxQWLyFe0ggblYDcQF\n258/Wgh8fGlR8TANMKPB8G6tUfwFyNECD09LjRO3+vhPvaRtyf+3d+fhTVXpH8C/J3vSJSndW6AN\nCG0FZamgCB1bhbILCAIFQVABH4SHmdEBRn8uqKPgwIw4iAuOFgEFRRlEEBRkK4sggux7W2jpQtek\nW9Ik5/fHbULTJG2DXdLwfp4nT9Nzz73n5C7tm3PPPec34OUH79w+fcR7ecAlR1pCRfol23uV1nuH\n88jS++Fy6GSEVfqiyiTGjO6/o6um2PbHO8KnDEfywh3WUxmy8dy9v0Ep8eIOP82MiSVoP30uMv7z\nD1RdTwc4R1bqf9DhqXkAnEQGpEkwJowJV9cDkcLLwp33Y6uqGdakrvxad/GdTQN1KFuYKmpyN/v0\nkpoZI4JULTtcyb01QdtHJ4Rx+FLiKFgj3okCtjsAN5tReT3d9rtS62SsgjZGZ5DiVFEwNDIDugUW\n2tJV0moYpO2gkVVBqrSgS61gDQACFZXoH54Nzu3/qItgpmCtCYjlCkTNfAHpyxfBWJAPbjbj+qfL\nIek+trWrdscSuRjuZGhn5/mVEiGQu1kJhDi51Zpf4Tw9LQvYclkImkZ3AZLrDDhs4c0XyN0bAjzb\nSxg3jwbWJd6KArY7QFVOFrhR6Lks1QRCqg5o5Rq5j3Mgv1KF9FIN0nVqZOj8caGkHe4LyUVMQJFt\npoAAeRUkZgaxiCNMVY5Kk8RuKA7GhCc0SfOR+KsRPeclpP/nH6guFII2n5MbkX5oM7T9RrV29UgD\nBmmFl4XD6byz1Rbnt2dza565MVsAHycPMmw8L7S+PRxln15ZLQSUfzSYuyf4j61PiKejYT3uAJUZ\nl23vldEuvlZ7oEqTGOeK2iGrXTKMZhG+vBiHtJxIZJf7Qiq2QCqyoKhKgas6jW0dxoBO+Rsxt8cx\nTOh63mHcNNIypAGB0M59CbKgEAAA4xb8uHg8Lu/b0Mo1I40lYs6nD3uiG9DdSXCklNwaCy3MyR3w\nvArnT7l+eQ6Y8xOwKA04V+C4vCmYmn8saUKaHQVsd4DKzFoBW5TnBmycAwWVShjNwmn5xYW7sTWj\nM4p8uiO3whcdfW8NUsgAdNEU457AAgQpKu22ozAV2s3NSVqHNCAQ0bWCNoupGj8tScHxb/7p9eO0\n3YkmdwOWJALLBwJRToY8LKgQnjytK7dcaJW7UeY8QEw9BVwqckxv7Cn0aw7wWppQPiFtGd0SvQNU\nZl6xvVdG3dWKNXFk4cJsATkVvrhR5odigxyPai+ja0Axov11KL4pfGXP0KsRE1AIucSETv6liPIr\nhYpazzyeVBOI6Ln/h3NLFkFcIdyKPvzpAujzMjBg1nKIvGBGBGLP1VAgrw4QvmjVZah1GTtrmbtS\nDAzWOqb/66gw3VeoDzC2q/OhTY7lAv89KfydWXYUeL6P83yEtAX019LLmSvKYcirmQJLJIKyQ3Sr\n1qe2UwVBSLvRHpdKAyBm3Dbw7KXSAHQNKIbWvwR5FSrklh7E3e3uR7Cy0u4BA9I2SDXtUNZnOmIL\njyDn9D4AwJmtH6Ds5nU88sIayH2cz0BBvIurPmqLEoQnVvPKAd86Qx2aLECxQRiepDbOges6YWqw\nbD0wIdZxu6mngLsDhYcgLGZhxohlR4Vx2upuj5C2gAI2L1d57artvSKiI0QyJ8/ptwCThSFTr0ap\n8lYLn0xsRrlJCn+ZATfKfBGqKodMJPRNA4BO6lJ0UpciW3cYwcp7W6XepGkcOnYCvG9/qEILIcs7\nAwDIPPI9Vj3ZGRX3joXZL8wuv0rqh3lzXmiNqpJWoJA4v40qZsAbCY63SsuMt+ZxVUiEab9qM1uA\nX3OByXcDfjLg/ePC0CaFFcCEzcDEOOHBiaGdnN+GJcQTUcDm5Spasf+ahQPX9P64WqrG2aJgVJnF\nyFP3ty2P9i+FmHGEKCqgkRkwQnsZ0f466n/mhSzMiP6juoGPjEP+1q9RsHMLAEBcWQT/Y6kIGzsV\nAf0SwWrGWjmw5UJrVpd4CMacTzXlJwf+/YgwxIjO4DjuWkEloJEDUjEQFwQ810sI2sprAr1jucKT\nqSNq/UnMKwc2XgDSS4DHugJhvsIt2rY6dRfxPhSwtaIbN27Y/d4cU11UZtzqv6ZqgSdELRbgRrkf\nzpe0w8XidqgwScAYB6uJwaqkgSioNCNIWQm52IKpsacRoKhq0YE2SethIhFCR06AIrIjbqz/LyyG\nKnBTNXI2/BcVl84ibNxUSHxadroX0jappEC0i7vpajnwTI9bv8cFAXN6A0sOC0+zAkCoyj7Qy9ID\nv2QDpwoAvfFWeq9QYGp3YP05ob9cez9hhgVyZ9Pr9dDr9Q1nbEIUsLWiuhPFvvrqq3jttdeargDO\n6zwh2rwPHBgtIjy/72FE+tq3knHO4CczgAEI1h2BXHzrL2mgsqpZ60Q8k7p3Pygio3D9s//AkHMd\nAFD62yGUXTyD8MenAaB+beT2KSSOwVxsIPDuI8DlEuFBh7q3QnPLhdY3VZ3/iv5yYdkvNd+vO/gL\nAdtvucB3l4UgTi0T1k2Kola5O8WyZcuwaNGiFi2TArZWlJ2dbfd7U7euiSqLYS4vE94rVZAFhzWw\nxh8jE1kQqipDqUFuC8R8pNWICShCrKYA4T4VWLo+DX6yu5u1HqRtkIdGoNNfX0PON5+j5LAwj625\nTIesz96DKjgW5YWz4BMY0cq1JN5ErQDiXfwZ7BsOiAFcKRFupeaVC2PHhfkAuWW38oXWPLCQXQbk\n1LyKqoSHH47kCAMDT4gT8uSXA7/lCUFdsFLoNyemPnNe4fnnn8fMmTPt0uo2wjQ1CthaUURE8/4z\nEpfeCghVUZ3BRH/8L4XJAhzMiUSmXo37QvIclidEZuF/V7qiR9A1xAYUIdJXT7c7iUsimRyRKTPg\nf088bnz1GUylxQAA2c3zWD1Ni6rofjBE9QPEsga2RA8qkD8mWAUMqdNrhHPAzIHiKmBKdyFw6+gv\nLKsdxFVW17rVWmtokqslwKaLwnvr38FA5a0ATi4B2vsCfeh7SZvTHF2YGkIBmxeT6G4FbH/0dmip\nQYbThcH48Vo0ruo0UMsMkIkchw/vH56FfuE3nC4jxBW/7r1xV+dY5G3+EsWHdgMAmKUayqv74Fdw\nEiHDxkHTNwFMLHa5DXpQgTQ1xgAJE4K5ukOBTOkuzJeaV3O7tKhKCMoiak3bZZ2uy7otswW4WSG8\nAKFVLj7MMWDLKBXmZvWRAt2DgE4aapkjFLB5tdotbLf7hGipQYZd16ORrlODA1CITWDg0BllSNep\nYRHbTyoo9AuhYI24T6xUIWLi01DH98PJlcvhbxH+25l0Jbix/hPc/Gkzgh4eDk3fP0Eka7jFjZDm\nZB2KJEoN9HXRQtYlADBECUFdth4oMdgvrzQBWifdNX/PBz46IczO0NFfCNisLXPDOwNSkTDkSQQ9\nn3NHoYCtFVifLNHr9c3WpGoyVkGsz7X97u4cogazGF9disHYzheQVeYH6yMEUrEF4apyRPmXYoT2\nMjb8r6ze7RBBRVklLpzOQEVZJVS+TiZUJDY+Xe5Gmqo3nhkZi/ytX8OkKwEAVBfeRM7Xqcj/4VsE\nPjQYmgcegtRf08DWWpder8eyZcvw/PPPt/jtE9I6ah/zbsF+6FZr3lWjWWhdy68Q+rftuQ70ctKn\nLr9cuM0KCLdaLfxWy9zQTsCBLCDExz5g23geOHlTaMXr6A/0CAW6Bgjzu1K3lObXEv/XPSpgM5lM\neOONN/C///0P7dq1g06nw5gxY/D3v/8d4npuhdzuNporb0Na4sAWXD0BxoWWLllQaINDJXAO1B79\nTC42QyayIKvMH3HtCvF7QTCi/XS4NygfnTUlEDMaK80dFeVVuHQmExXlVRSwNQZjCHjgIah73Y/C\nPdtRuGc7zBXClwNzmQ75W79G/g/fwK9bLwT0S4RvXI8GNtg69Ho9Fi1ahJkzZ1LAdoeo75jLxECk\nn/ACgMGdnG/jnmDggQhhNodwXyFgswpRCQFf7UAQEIK1Pddu3W6NaSe0yL3Y79agxIezhSCvo7/Q\nB08lFQYWrjuOHXHfHRewzZ49Gzt37sSRI0cQFBSEgoIC3H///bh06RJWr17d5NtorryeIO/8Ydt7\nZbTr/msVJgl2ZGqRXeYLndI+371B+Thf3A4PRV5Hn9AcaOQGF1shpHmI5AoEDx6NwMQhKD60BwW7\nt8FUUjMTuMUC/alj0J86BomfGkr/zsg6noDwex6CWELjKpC264FI4WVlNAu3R/MrhABLqwEia/VG\n4RworBSm+LKyzukaVOv74eEbwMBo4f3yY8J0XVIxkKUTvrAHq4CF9wN3tWuuT0b+CI8J2A4cOIBP\nPvkEH330EYKCggAAQUFBWLhwIWbNmoUZM2ZgwIABTbaN5srrKfIvHLG9d9Z/rdQgww+ZnbDzWjQM\nFjE0sipU+/W2y9M1oBhdNMU08wBpdSK5AoGJQxAwYCB0xw+j+NBuVFy59ZCBSV8Kuf43bPm/ZMj9\n2qFD78Fo3/MRtO85EH4hHVux5oT8cTKx0DJmvQU6ss53cA5gbjyw77owU8ONMqHfm5nbjwlXUCkE\ncCaL8OQrIEzZlV0mTPd1sQgw93Us//3fhKAu0g9opwQC5MKt1vJqILadMBuFSkotdc3NYwK21NRU\nAMCoUaPs0h999FHMmjULqampDQZF7myjufJ6irwLt1rYVHUCtgydP765HIMKkxgGi3A7t9Qoh0XW\nHuXVVfCRCl/TxIwDdAESDyKSSKDpMwCaPgNgyLuB4sN7UHr0AEz6Ulseg74Il/d+ict7vwQAmJXt\nYFZHwqSOhFkdCbNvKCASznsaCoR4AxETBgaODaw/X7JWeHiholpooSuuEoIug1lYLhXbD0tidU0H\n5OiFJ2FrO5YH9A4V/k280v/WrV7OgQ3ngOt6YaaIcB9h9gm1XJhWjNwej3lQeO/evQgMDERIiP2c\nH6GhoQgICEBaWlqTbqO58nqCipJ83MxOx/cXOQyQQB4Rhet6P/CahrL2vnqopNVQSszwlRrhLzNg\naNRVxN34yBasNaqcWh3pm4u3lNESvGVfNbYMeWgEwkZNQtfX/4Pouf+HdGkEJBrHezniyiLIck9B\ndWE7/I78F5o9SxB6+lMEZ2/Dts9X4MSO1Si4+jsMZSXN9ZGalV6vx2uvvdas0+RQGZ7ldj/HnzoI\nQZm/HHi5P/CvR4D3BgKrhwOLHwLmxQvLapeh0+mRVy6MGeeM9Tu9plYgVmYEdl8D1p4RXu8dA944\nCLxa86/yzYPAojTgX0eAnEI9Xn7lNaw/rsfuTOBoDrDjKpBRIswT2xS85bh7RAubyWRCeno67rrL\neV+roKAgZGZmNtk2miuvp8i/8AuqTMC2y8Aj/TsAEgl2XNNiSNRVtPctg0TEER+ch2t6fwyJSkds\nQAEkIuCflvKGN15LS3Sk95YyWoK37Ct3y2AiEXzuisU5xV0Y/uozqLpxDeUXTqPs4hlUXLkAXm20\nX8FihiE3GyUZWfjxKJD4zjRoFMK/HZnKH74hUfAL7gifoEgo1cFQqIOh9A8W3vsHQaEOglTpB6nC\nFyI3HzhqDi3xYAOV4Vma8nPIJUIrWK9Q52XMmDET/37YDzqj0MJWXPMqqgTKqoUWuTKj/a3XEoPQ\nymayALJazUK+MiE9p0xYBgCGcD3efGMRJsfMhE+g8FkOZgszTwSrgMWJt9ZffFgYF48xoS+fWi48\nRauSClOK5ZQBY2Icn4otLvGO4+4RAVtJSQnMZjOUSud/nBUKBYxGIyoqKqBSqZzmcWcbFRUVzZLX\nVd2aW86ZNOSmn8Ohmrnu2MUfbMsqg2IhYsB9Ibk4mheO9r6XAAB9QnPQNyynNapLSLNhIhGU7aOh\nbB+NoEdGwFJtRFVWJiozr6Ai8zIqM6+guvCmy/WNFToUZZxCUcapRpUnkSshUfhCpvSDVOkLqdIP\nEpkSIokMIokUJRXCvaYDq/6KkEANxBKZsEwqg0gkBpgITCQCAxNmImEiMMbAmAio+SnMUCIsr50u\n/GTILxRaBi/s+hzFgU00zEmdzki2Mn5ec9tlsAb6V1jLuPjzWpS4U4YbHadsZexe514ZbvC2Mi7t\nWYeQmjLkAMJqXgDQXwqg5nv+uR231q00AYOKgY4VQGi28HulCfCVAif1gP9ZIZ9EBGTUlKM5vw5+\nag04gNhiIKRYuH17tuY2LOdA6RnhvdEs9Our65oOiO1nf0pwDryXJpQx+5/rEB+tgVQklK1RAP0i\ngP1ZQuujVbkROFMIZJYK491JREKfQB+p8MAHIDy5e6UY6NJOeNjjQnbzt9B7RMBWVSUcEYnEeXVE\nNVMqlZaWugyK3NmG2WxulrzuBmyHDx+2PcTgio+PD3x8fNC5c2dIpc6ffLu4ey3O/vCx0z+HmT69\nMIAD3QNvorxaCs6Fk5k6h5I7gUgqg0rbBSptF1i795irKmHIu4GccxeBn9cisscjkJZno+zmNZgM\n7t3qNRkqYTJUoqrUeRBYUiX0Q7i8bwMKFM1z0VnLOJz6d1tLYbOV8dnCZi/j0GcLmr+MT+dTGS1Q\nRiAAEwBpzQsADgKo/RjQoZpyIg/eKieq1vK9td439PhQRwD7jjmmR9eUcf/J+dBcvPVZqgHsc1KO\nlbUTVJWJ40pNb6GTdfLUxJ5Ndvu2Ph4RsGk09X9DKCsTxl9SKBRNsg1Xgc8fzeuusWPHNphn2rRp\nmD59OoqLi3HqlPNv/ZZz51yuf6GyE37cch2+rALAeRyspyw583Nreh9dqdAf4OhPV+Cvblwzs7eU\n4W45VIZnlSGUIwxklRuWDI1GA845RMYyoKIIqCwEryoFjGWAoQww6sGNZRBVl8NSpQdMBsBMw9wQ\ncifYeVXoYtTaGOfcI8Zs8PHxQVxcHH799VeHZRERESgoKEBlZWW9g9S6s43mytsYer0e/v7+jcpL\nCCGEkLZBp9N5/8C5Wq0WxcXFDukWiwUlJSXQarUNBkTubKO58jaGn58fPCROJoQQQkgb4DHDegwd\nOhQZGRm2W4xWly5dQlVVFRISEpp0G82VlxBCCCGkqXlMwDZq1ChwzrFp0ya79I0bNwIApkyZYpe+\na9cufPfdd7e9jebKSwghhBDS1DymDxsAjBgxAmfOnMHBgwcRHh6Oa9euoW/fvhg8eLDdfJ0lJSUI\nDg6G2WzG2bNnERsb6/Y2mjMvIYQQQkhT8qiAzWAw4JVXXsG2bdug0WhQUFCAMWPGYNGiRXZPa1os\nFiQlJaGwsBCHDh2y6+DX2G00Z15CCCGEkKbkUQEbIYQQQghx5DF92AghhBBCiHMUsBFCCCGEeDgK\n2AghhBBCPBwFbIQQQgghHo4CthZkMpnw6quvokePHkhKSkJ8fDzefPNN2wTzpG0bNGgQ5HI5/Pz8\nEBgYCLVaDR8fH7z99tsOeelcaJsMBgN2796N4cOH4x//+IfLfO4cXzoXPFtjjzld/94jLy8PM2fO\nxKBBg9CjRw/Ex8djxYoVsFgsDnlb9FrnpMXMmDGDa7VafvPmTc455zdv3uSdOnXiU6dObeWakaaQ\nmJjIY2JiuEKh4CEhIXzMmDE8LS3NaV46F9qWvLw8PmjQID569Gj+7LPPcsYYX7Rokcv87hxfOhc8\nk7vHnK5/75Cfn8/79evHT5w4YUtLTU3lIpGIDxs2jJvNZrv8LXmtU8DWQtLS0jhjjH/88cd26R9/\n/DFnjPH9+/e3Us1IU0lMTGxUPjoX2rY9e/bU+8/bneNL50Lb0NAx55yuf28xb948vnHjRof0iRMn\ncsYYX7lypS2tpa91uiXaQlJTUwEI01zV9uijj9otJ96PzoW2jTcwdKU7x5fOhbahoWPuDjrmnm3X\nrl2YPn06du3aZZduPT5fffWVLa2lr3UK2FrI3r17ERgYiJCQELv00NBQBAQEIC0trZVqRloanQve\nzZ3jS+fCnYeOuWeLjY1FeXk5iouL7dIDAwMBCP3brFr6WqeArQWYTCakp6cjKCjI6fKgoCBkZma2\ncK1Ic8jIyMCoUaOQlJSEnj174o033rDrUErngndz5/jSueB96Ppv+zZs2IAbN25g3LhxdunW43LX\nXXcBaJ1rXdLoT0FuW0lJCcxmM5RKpdPlCoUCRqMRFRUVUKlULVw70lQ455g7dy4+/vhjhIeHIzc3\nF3369MG5c+fwxRdfAKBzwdu5c3wrKiroXPAidP17B5FIhNDQUIf0L7/8EgDwzDPPAGida51a2FpA\nVVUVAEAicR4fi0TCYSgtLW2xOpGmFxQUhJUrVyI8PBwAEBYWhr/85S9Yv349duzYAYDOBW/nzvGl\nc8G70PXvvQ4cOIA9e/Zg/Pjxtj5nrXGtU8DWAjQaTb3Ly8rKAAhRNmm7Nm7ciA4dOtildevWDQDw\n+eefA6Bzwdu5c3zpXPAudP17p/LyckyfPh2DBw+2HUegda51CthagK+vL5RKpdNB9wDhhBCLxfD3\n92/hmpGmUl1djfz8fId0uVwOADh9+jQAOhe8nTvHl84F70HXv3finOPJJ59Er169sGXLFshkMtuy\n1rjWKWBrIVqt1uGpEwCwWCwoKSmBVquFWCxuhZqRpjBy5EhERkbi8OHDdunWb05SqdSWRueCd3Pn\n+NK54B3o+vdOf/vb3xAcHIwNGzbYbmdWVlbalrf0tU4BWwsZOnQoMjIybBew1aVLl1BVVYWEhIRW\nqhlpCvn5+dBoNFCr1Xbp2dnZAID4+HhbGp0L3s2d40vngneg69/7vP/++zCZTPjggw/s0p96CG2U\ntwAAEpZJREFU6inb+5a+1ilgayGjRo0C5xybNm2yS9+4cSMAYMqUKa1RLdJEBg0ahHXr1iEuLs4u\nfceOHZBKpZgzZ44tjc4F7+bO8aVzwTvQ9e9dtmzZgmvXruHdd9+1S79586btNjfQCtd6Y6ZqIE1j\n+PDhPDo6mt+4cYNzznlmZiYPDQ2l+eO8QFFREX/wwQftphfZv38/VygUfMWKFQ756Vxou9auXcsZ\nY/zZZ591mced40vngudr6JjT9e89jh49yn19fXlsbCyPiYmxe4WFhfG3337bLn9LXuuM8yacc4PU\ny2Aw4JVXXsG2bdug0WhQUFCAMWPGYNGiRXZ9HEjblJubi/nz5+P69etgjEEqlWLBggV4+OGHHfLS\nudD29OnTBwUFBcjMzARjDJxzhISEIDIyEp988gl69eply+vO8aVzwXO5c8zp+vcO99xzD86ePety\n+caNGzFmzBjb7y15rVPARgghhBDi4agPGyGEEEKIh6OAjRBCCCHEw1HARgghhBDi4ShgI4QQQgjx\ncBSwEUIIIYR4OArYCCGEEEI8HAVshBBCCCEejgI2QgghhBAPRwEbIW1IdHQ0RCKR3UupVEKr1eLJ\nJ5/E77//7rBOYmIiRCIR9u7d2wo1di0jIwMikQharbZVyt+zZw9EIhGSkpJua32j0YgPP/wQycnJ\nCAsLg1wuR0hICAYMGIB33nnHYZLn2jz1mHiaP3KOWK8PQryFpLUrQAhx35AhQxAWFgYAKCoqwpEj\nR7BmzRp8+eWXWLNmDSZMmGCXnzEGxlhrVLVBrV2v2yn/9OnTGDVqFNLT0yGXy9GvXz9ERESgsLAQ\naWlpOHjwIJYtW4avv/4af/rTn1yW29qfva243f1E+5d4EwrYCGmDFi5caBcIVFVVYcaMGVi3bh1m\nzZqF5ORkBAQE2JZ74gx07du3x/nz59vc3IlXrlxBQkICSktLMX78eKxYsQJBQUG25RUVFXjppZew\nfPlyJCcnY+/evbj//vsdtuOJx4QQ4rmovZgQL6BQKPDBBx9ApVJBp9Nhx44drV2lBkkkEnTt2rXV\nbonerilTpqC0tBSjR4/G+vXr7YI1AFCpVPj3v/+NP//5zzAajUhJSUF1dXUr1ZYQ4i0oYCPES/j6\n+qJr164AgGvXrjnNc+zYMTz66KMIDAyEQqFAz5498emnnzrk69KlC0Q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DBw/mwcHBXCaT\n8dDQUN6rVy8+Z84c/tNPPzXqsxPSkhjnzfxYDiGkzRs7diw2bdqEDz74ALNmzWrt6hBCyB2HAjZC\nSL2OHz+O++67D4GBgcjMzKx3uAdCCCHNg4b1IIQ49cwzz6C8vNw2Ovzrr79OwRohhLQSamEjhDgl\nEokgFosRFRWF2bNn469//WtrV4kQQu5YFLARQgghhHg4GoeNEEIIIcTDUcBGCCGEEOLhKGAjhBBC\nCPFwFLARQgghhHg4CtgIIYQQQjwcBWyEEEIIIR7u/wEDekbHW2M/kQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n", "\n", "### Here's $\\subNsubR{10}{f}{2}(x)$ compared with the histogram of the 2nd smallest point of 2000 samples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "makeHist(1)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Z2raKiYnpWGRELiTnwBac/fn6NOXkZ1YjtLf91noKgoDIBx9HeUYWlLUl0Gsb8cvrc3H/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\nKMC4ceOwevVqeHl5GZcXFxfj7bffxqpVqxAdHY2jR4+iR48eZtuxxXN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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n", "\n", "### Here's $\\subNsubR{10}{f}{3}(x)$ compared with the histogram of the 3rd smallest point of 2000 samples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "makeHist(2)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Om3QHht7wkFWf4TkoAeF33I+Srz4BAFTt/Bm+yWPhFT/Yqs8hInJWnSZsq1evNrz//PPP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\nPOS5PHs9J/bmj1wjxvuDsabCoaF3gDFmu4EDByIgIAAAkJGRgZMnT2L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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n", "\n", "### Here's $\\subNsubR{10}{f}{4}(x)$ compared with the histogram of the 4th smallest point of 2000 samples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "makeHist(3)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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jmU+mUKkxftE/IbhwKLQp/yEj4ZM4ANUXzwJmM7wv/Oi29yIiaszf37/Tc50WE7aPP/7Y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\nTIbAwEB0794dH3zwgcUkz+XZ6zGxN3/nHDFeH4Q4C5eG3gFCiO169+6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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n", "\n", "### Here's $\\subNsubR{10}{f}{5}(x)$ compared with the histogram of the 5th smallest point of 2000 samples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "makeHist(4)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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1+PTTTzF27FgIgoBXXnkFX3zxBXJycnDnnXdi48aNePrpp7sdyJw5cyCKItat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\nIAiCIAgrhwQbQRAEQRCElUOCjSAIgiAIwsohwUYQBEEQBGHlkGAjCII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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n", "\n", "### Here's $\\subNsubR{10}{f}{6}(x)$ compared with the histogram of the 6th smallest point of 2000 samples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "makeHist(5)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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qKYwbNw7r16+3aU1zRWwdKSkp6fIetq4ROdbSUIurFw5IBUGAKXZA52/wIarY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\nJgwdOtT4vTbvdRJsBEEQBEEQdg7ZsBEEQRAEQdg5JNgIgiAIgiDsHBJ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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n", "\n", "### Here's $\\subNsubR{10}{f}{7}(x)$ compared with the histogram of the 7th smallest point of 2000 samples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "makeHist(6)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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BRK7FhI2IaJhaGypRf+k4AEAVEIjkyfLtzRgUlwhBLQ2emC43wtzWKlssROQ6HBKVUUVF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\nOyGTyTBt2jRzGR0Lrq02+5eOBddA579r2bp1K27evInFixdblKenp5s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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n", "\n", "### Here's $\\subNsubR{10}{f}{8}(x)$ compared with the histogram of the 8th smallest point of 2000 samples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "makeHist(7)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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HG264AZs2bRp1IG+88QYAYOXKlQ7nb775Zofrnqpjx44dWL16NXbs2OHy3vfe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\nPF8CLF4uc0RE46fX66HX60e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RRGYVpc3TD9ZKX9Y/me18z+wEaW20/ERgXqK0eK2/aK04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\nDkZmZmYjl4o0hIyMDIwYMQIpKSno0qUL3n33XbsOpXQtNG+unF+6Fpo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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n", "\n", "### Here's $\\subNsubR{10}{f}{9}(x)$ compared with the histogram of the 9th smallest point of 2000 samples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "makeHist(8)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Ny56DYJ30R2hHQyXaaopkiYPI0/Lz850+w73N7YQtMTER99xzD44cOeLNeAJKdXW1w8t+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\n9Mp53PnuK5RdvWhX7nNfF+zJUKJ7IwZrZSXluJCWjrKScqh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"text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Let's \"measure\" 10 $x$ values for some $f(x)$, and repeat that 2000 times.\n", "\n", "### Here's $\\subNsubR{10}{f}{10}(x)$ compared with the histogram of the 10th smallest point of 2000 samples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "makeHist(9)" ], "language": "python", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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73rP9pQzIaqKiooxeKSkpcodERGQVZdlnceb7dwz745/4Fzz9Q9vVhkdkTwSOvcWwX7T5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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "## NOTE: From now on, *the data does not need to be sorted*." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Probability Calculus: Are You $r$th of $n$? ##\n", "\n", "### $\\subNsubR{n}{f}{r}(x)$ is the PDF of the $r$th of $n$ position:\n", "\n", "$$ {\\Large P(\\tilde{x} \\in [x, x + dx]\\ |\\ \\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n, f) \\equiv \\subNsubR{n}{f}{r}(x) dx } $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Use Bayes' Theorem:\n", "\n", "$$ {\\large P(B\\ |\\ A) = \\frac{P(A\\ |\\ B)\\ P(B)}{P(A)} } $$\n", "$$ {\\large \\Rightarrow P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n\\ |\\ \\tilde{x} \\in [x, x + dx], f) = \\frac{\\subNsubR{n}{f}{r}(x) dx\\ \\frac{1}{n}}{f(x) dx} } $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ {\\Large = \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r}} $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "${\\Large ({\\rm HW}-2) }$\n", "$${\\large {\\rm Prove}: \\qquad \\Sum{r=1}{n} \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} = 1, \\quad \\forall x. }$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Proof (special thanks to Ola Liab\u00f8tr\u00f8, who solved this *in his head* during my talk):\n", "\n", "$$\\frac{\\subNsubR{n}{K}{r}}{n} = \\frac{(n-1)!}{(n-r)!(r-1)!} = \\frac{(n-1)!}{(n-1-[r-1])!(r-1)!} = \\subNsubR{n-1}{C}{r-1}$$\n", "\n", "Thus,\n", "\n", "$$ \\Sum{r=1}{n} \\frac{\\subNsubR{n}{K}{r}}{n} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} = \\Sum{r=1}{n} \\subNsubR{n-1}{C}{r-1} F^{r-1}(x) \\left(1 - F(x)\\right)^{n-r} $$\n", "\n", "$$ = \\Sum{r'=0}{n-1} \\subNsubR{n-1}{C}{r'} F^{r'}(x) \\left(1 - F(x)\\right)^{n-1-r'} = (F(x) + 1 - F(x))^{n-1} = 1. \\quad {}_\\blacksquare $$\n", "\n", "Note: I proved this also. The hard way. Term-by-term. I could not see the relation to $\\subNsubR{n-1}{C}{r-1}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# The debinning Calculation:\n", "\n", "## \"Whoa, I can calculate something else!\"" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## The debinning Algorithm" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "![nfr Smoothing](nfrSmoothing.png \"nfr Smoothing\")\n", "\n", "### Thought experiment: The Flat PDF\n", "\n", "$$ f_{\\rm \\color{gray}{flat}}(x) = \\left\\{ \\begin{array}{rcl} 1 & {\\rm if} & x \\in [0, 1] \\\\ 0 & & {\\rm otherwise} \\end{array} \\right. $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Select a point, $x_j$, from the sample $\\{x_1, x_2, x_3\\}$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Randomly choose an appropriate $r$ value using\n", "$${\\large P(x_j\\ {\\rm is\\ } r{\\rm th\\ of\\ } 3\\ |\\ x_j, f_{\\rm \\color{Gray}{flat}})\n", " = \\frac{\\subNsubR{3}{K}{r}}{3} F_{\\rm \\color{Gray}{flat}}^{r-1}(x_j) \\left(1 - F_{\\rm \\color{Gray}{flat}}(x_j)\\right)^{3-r} }$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Generate a random point from\n", "$${\\large \\subNsubR{3}{f}{{\\rm(\\color{Gray}{flat})}r}(x) = \\subNsubR{3}{K}{r} f_{\\rm \\color{Gray}{flat}}(x)\n", " F_{\\rm \\color{Gray}{flat}}^{r-1}(x) \\left(1 - F_{\\rm \\color{Gray}{flat}}(x)\\right)^{3-r} = \\mathcal{O}(x^2) }$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## The debinning Algorithm... Expectation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"debinning" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## The Experiment Inspired debinning Algorithm" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Suppose our data comes from\n", "$${\\huge f(x) = w\\ f_{\\rm \\sky{sig}}(x) + (1 - w)\\ f_{\\rm \\rust{bg}}(x)}$$\n", "\n", "![BG nfr Smoothing](nfbgrSmoothing.png \"BG nfr Smoothing\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Select a point from our data..." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Randomly choose an appropriate $r$ value using\n", "$${\\large P(\\tilde{x}\\ {\\rm is\\ } r{\\rm th\\ of\\ } n\\ |\\ \\tilde{x} \\in [x, x + dx], f_{\\rm \\rust{bg}}) \\cdots}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Generate a random point from $\\subNsubR{n}{f}{{\\rm(\\rust{bg})}r}(x)$... need *3 random numbers* just to get one back!!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## The debinning Algorithm... Calculation ## \n", "\n", "### \"Det er dumt!\" Let's just calculate it!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ f_{\\rm debin}(x) dx = P_{\\rm debin}\\left(\\tilde{x} \\in [x, x + dx] | \\{x_i\\}_{i=1}^{n}, f_{\\rm\\rust{bg}} \\right) $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ = \\sum\\limits_{j=1}^{n} P( x_j | \\{x_i\\}_{i=1}^{n} ) \\sum\\limits_{r=1}^{N} P(r{\\rm th}\\ {\\rm of}\\ N | x_j, f_{\\rm\\rust{bg}}) P(\\tilde{x} \\in [x, x + dx] | r{\\rm th}\\ {\\rm of}\\ N, f_{\\rm\\rust{bg}}) $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ = \\sum\\limits_{j=1}^{n} \\frac{1}{n} \\sum\\limits_{r=1}^{N} \\left(\\frac{{}_NK_r}{N} F_{\\rm\\rust{bg}}(x_j)^{(r-1)}(1 - F_{\\rm\\rust{bg}}(x_j))^{(N-r)} \\right) $$\n", "$$ \\quad\\times \\left( {}_NK_r f_{\\rm\\rust{bg}}(x) F_{\\rm\\rust{bg}}(x)^{(r-1)}(1 - F_{\\rm\\rust{bg}}(x))^{(N-r)} dx \\right) $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ {\\Large \\Rightarrow f_{\\rm debinnning}(x) = \\frac{f_{\\rm\\rust{bg}}(x)}{n N} \\displaystyle \\vec{G} \\cdot \\sum\\limits_{j=1}^{n} \\vec{G}_j } $$\n", "\n", "${\\large \\left[\\vec{G}_{(j)} \\equiv {}_N K_r F^{r-1}_{\\rm\\rust{bg}}(x_{(j)}) \\left( 1 - F_{\\rm\\rust{bg}}(x_{(j)}) \\right)^{N-r} \\right] }$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "settings['simpleSortedOutput'] = False\n", "nPulls = 96\n", "nFictitious=96\n", "\n", "x, f, F, data = quickData()\n", "x, bgf, bgF, bgData = quickBG()\n", "f /= F[-1]\n", "F /= F[-1]\n", "bgf /= bgF[-1]\n", "bgF /= bgF[-1]\n", "\n", " \n", "def mapDataToX(dindex):\n", " # maps elements of data to elements of x\n", " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n", " xindex = bisect.bisect_left(x, data[dindex])\n", " if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n", " return xindex - 1\n", " return xindex\n", "dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n", "\n", "\n", "def vecG_rth(rindex, xindex):\n", " r = rindex+1\n", " return pc.nKr(nFictitious, r) * bgF[xindex]**(r-1) * (1 - bgF[xindex])**(nFictitious - r)\n", "\n", "\n", "vecG_rx = np.array([[vecG_rth(rindex, xindex) for xindex in xrange(len(x))]\n", " for rindex in xrange(nFictitious)])\n", "sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n", "debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n", "\n", "# One more pull for plotting purposes\n", "x, f, F, data = quickData()\n", "x, bgf, bgF, bgData = quickBG()\n", "f /= F[-1]\n", "bgf /= F[-1]\n", "bgF /= F[-1]\n", "F /= F[-1]\n", "\n", "def makeDebinningPlot():\n", " fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n", " plt.plot(x, f, '--', color='#0088ff', alpha=0.6, linewidth=3)\n", " plt.plot(x, bgf, '-.', color='#0088ff', alpha=0.6, linewidth=3)\n", " plt.hist(data, bins=np.arange(0, 201, 5), alpha=0.4, color='#66a61e', normed=True)\n", " plt.plot(x, debinningData, '#964a01', linewidth=3)\n", " \n", " axes.set_xticks(np.arange(0, 201, 50))\n", " axes.set_xticks(np.arange(0, 201, 10), minor=True)\n", " axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(0, 201, 50)], fontsize=20)\n", " \n", " axes.set_ylim(bottom=-0.0001, top=0.0201)\n", " axes.set_yticks(np.arange(0, 0.02, 0.005))\n", " axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.02, 0.005)], fontsize=20)\n", " axes.set_yticks(np.arange(0, 0.02, 0.005/5), minor=True)\n", "\n", " axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n", " axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n", "\n", " axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n", " axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n", " axes.minorticks_on()" ], "language": "python", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## debinning Demonstration ##" ] }, { "cell_type": "code", "collapsed": false, "input": [ "makeDebinningPlot()" ], "language": "python", "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Hpy9Sfepkg9eJSe5L8uDxRCZfxJIT3akjFEtdBVdEH8WZu5X8PWtx1FZ7nRPdPY1J818m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\nkvW1yk6h3UOqKZSw/aDHQSCqp9Kd0WdhHlUdHvMGhsvviUG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DKA0RojdvCB7eAk9uhzoP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"text": [ "" ] } ], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "fwhmValues=None" ], "language": "python", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "prompt_number": 21 }, { "cell_type": "code", "collapsed": false, "input": [ "# Let's try some GPU programming:\n", "import pycuda.driver as cuda\n", "import pycuda.autoinit\n", "from pycuda.compiler import SourceModule\n", "from string import Template\n", "\n", "settings['simpleSortedOutput'] = False\n", "nPulls = 96\n", "nFictitious = 96 # Multiple of 32 for GPU programming ease.\n", "lenXdomain = len(np.arange(8.5, 200.2, 0.5))\n", "\n", "mod_template = Template(\"\"\"\n", " __global__ void vecG(double *vecG_rx, double *bgF, double *lognKr) {\n", " const int idr = threadIdx.y + blockDim.y * blockIdx.y;\n", " const int idx = threadIdx.x + blockDim.x * blockIdx.x;\n", " const int idrx = idx + idr*${lenX};\n", " const int r = (idr + 1) < (${nFic} - idr) ? (idr + 1) : ${nFic} - idr;\n", " if (bgF[idx] == 0 || (1 - bgF[idx]) == 0)\n", " vecG_rx[idrx] = 0;\n", " else\n", " vecG_rx[idrx] = exp(lognKr[r-1] + idr * log(bgF[idx]) \n", " + (${nFic} - idr - 1) * log(1 - bgF[idx]));\n", " }\n", " \"\"\")\n", "\n", "mod = SourceModule(mod_template.substitute(nFic=nFictitious, lenX=lenXdomain))\n", "\n", "timer = time()\n", "\n", "# initialize the loop\n", "lognKr = pc.get_lognKrArray(nFictitious)\n", "chisq = []\n", "bgchisq = []\n", "ks = []\n", "bgks = []\n", "\n", "for trial in xrange(100000):\n", "\n", " x, f, F, data = quickData()\n", " x, bgf, bgF, bgData = quickBG()\n", " f /= F[-1]\n", " F /= F[-1]\n", " bgf /= bgF[-1]\n", " bgF /= bgF[-1]\n", "\n", " def mapDataToX(dindex):\n", " # maps elements of data to elements of x\n", " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n", " xindex = bisect.bisect_left(x, data[dindex])\n", " if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n", " return xindex - 1\n", " return xindex\n", " dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n", "\n", " # Use the GPU for the most expensive / paralellizable part of the calculation:\n", " # =====\n", " \n", " # Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))\n", " vecG_rx = np.empty([nFictitious, len(x)])\n", " \n", " # Allocate memory on the GPU for vecG calculation\n", " vecG_rx_gpu = cuda.mem_alloc(vecG_rx.nbytes)\n", " bgF_gpu = cuda.mem_alloc(bgF.nbytes)\n", " lognKr_gpu = cuda.mem_alloc(lognKr.nbytes)\n", " \n", " # Transfer data to the GPU\n", " cuda.memcpy_htod(bgF_gpu, bgF)\n", " cuda.memcpy_htod(lognKr_gpu, lognKr)\n", " \n", " # Get a reference to the GPU module function and do the calculation\n", " # NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious\n", " vecG_func = mod.get_function('vecG')\n", " vecG_func(vecG_rx_gpu, bgF_gpu, lognKr_gpu, block=(16, 4, 1), grid=(24, 24))\n", "\n", " # Get the result back from the GPU and use it!\n", " cuda.memcpy_dtoh(vecG_rx, vecG_rx_gpu)\n", " sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n", " debinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n", " \n", " # Chisq test....\n", " if type(fwhmValues) == np.ndarray:\n", " chisq.append(sum(4.*(debinningData - f)**2 / fwhmValues**2) / len(fwhmValues))\n", " bgchisq.append(sum(4.*(debinningData - bgf)**2 / fwhmValues**2) / len(fwhmValues))\n", " \n", " # KS test...\n", " debinningCDF = pc.A(debinningData, 0.5)\n", " ks.append(max(abs(debinningCDF - F)))\n", " bgks.append(max(abs(debinningCDF - bgF)))\n", " \n", " if trial == 0:\n", " # Infinity sigma upper and lower bands...\n", " debinningUpper = debinningData.copy()\n", " debinningLower = debinningData.copy()\n", " # Uncertainty PDFs for each x value...\n", " uncertaintyHistos = [debinPlot.HistoContainer(np.arange(0., 0.024, 0.0002), debinningData[i])\n", " for i in xrange(len(x))]\n", " else:\n", " debinningUpper = np.clip(debinningData, debinningUpper, 20.)\n", " debinningLower = np.clip(debinningData, -1., debinningLower)\n", " for i in xrange(len(x)):\n", " try:\n", " uncertaintyHistos[i].addValue(debinningData[i])\n", " except ValueError as e:\n", " print e.message\n", " print 'xindex = ' + str(i) + ', debinningData[xindex] = ' + str(debinningData[i])\n", "\n", "if not type(fwhmValues) == np.ndarray:\n", " fwhmValues = np.array([np.diff(uncertaintyHistos[i].fwhm()) for i in xrange(len(x))]).flatten()\n", " print \"Run this again for the Chisq test data...\"\n", "print time() - timer" ], "language": "python", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "290.936532021\n" ] } ], "prompt_number": 23 }, { "cell_type": "code", "collapsed": false, "input": [ "# Try one more sample, but with a HUGE data set:\n", "nPulls = 10000\n", "\n", "timer = time()\n", "x, f, F, data = quickData()\n", "x, bgf, bgF, bgData = quickBG()\n", "f /= F[-1]\n", "F /= F[-1]\n", "bgf /= bgF[-1]\n", "bgF /= bgF[-1]\n", "\n", "def mapDataToX(dindex):\n", " # maps elements of data to elements of x\n", " # bisect_left(x, datum) locates the left-most entry in x which is >= datum\n", " xindex = bisect.bisect_left(x, data[dindex])\n", " if xindex > 0 and x[xindex] - data[dindex] >= data[dindex] - x[xindex-1]:\n", " return xindex - 1\n", " return xindex\n", "dataToX = np.array([mapDataToX(j) for j in xrange(len(data))])\n", "\n", "# Use the GPU for the most expensive / paralellizable part of the calculation:\n", "# =====\n", "\n", "# Empty numpy array to hold result of vecG (row, column = nFictitious, len(x))\n", "vecG_rx = np.empty([nFictitious, len(x)])\n", "\n", "# Allocate memory on the GPU for vecG calculation\n", "vecG_rx_gpu = cuda.mem_alloc(vecG_rx.nbytes)\n", "bgF_gpu = cuda.mem_alloc(bgF.nbytes)\n", "lognKr_gpu = cuda.mem_alloc(lognKr.nbytes)\n", "\n", "# Transfer data to the GPU\n", "cuda.memcpy_htod(bgF_gpu, bgF)\n", "cuda.memcpy_htod(lognKr_gpu, lognKr)\n", "\n", "# Get a reference to the GPU module function and do the calculation\n", "# NOTE: 16*24 = 384 = len(x), and 4*24 = 96 = nFictitious\n", "vecG_func = mod.get_function('vecG')\n", "vecG_func(vecG_rx_gpu, bgF_gpu, lognKr_gpu, block=(16, 4, 1), grid=(24, 24))\n", "\n", "# Get the result back from the GPU and use it!\n", "cuda.memcpy_dtoh(vecG_rx, vecG_rx_gpu)\n", "sumG_j = vecG_rx.take(dataToX, axis=1).sum(axis=1)\n", "BIGdebinningData = bgf * np.dot(sumG_j, vecG_rx) / (nFictitious*nPulls)\n", "print time() - timer" ], "language": "python", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.0585300922394\n" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## debinning Performace: Uncertainty" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# One more pull for plotting purposes\n", "x, f, F, data = quickData()\n", "x, bgf, bgF, bgData = quickBG()\n", "f /= F[-1]\n", "bgf /= F[-1]\n", "bgF /= F[-1]\n", "F /= F[-1]\n", "\n", "# Pretty plot\n", "fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n", "plt.fill_between(x, debinningUpper, debinningLower, color='#0088ff', alpha=0.3, zorder=1)\n", "plt.plot(x, f, color='#0088ff', linewidth=3, zorder=3)\n", "plt.plot(x, bgf, color='#0088ff', linestyle='-.', linewidth=3, zorder=3)\n", "plt.plot(x, BIGdebinningData, color='black', linestyle='--', linewidth=3, zorder=4)\n", "colors = np.array([(0.8,1.,0.4), (0.8,0.3,0.), (1.,1.,1.), (0.,0.,1.)])\n", "for i, v in enumerate(x):\n", " debinPlot.verticalColorBand(uncertaintyHistos[i], v, 0.5, colors)\n", "\n", "axes.set_xticks(np.arange(0, 201, 50))\n", "axes.set_xticks(np.arange(0, 201, 10), minor=True)\n", "axes.set_xticklabels([r'$%i$' % int(num) for num in np.arange(0, 201, 50)], fontsize=20)\n", "\n", "axes.set_ylim(bottom=-0.0001, top=0.0201)\n", "axes.set_yticks(np.arange(0, 0.02, 0.005))\n", "axes.set_yticklabels([r'$%0.3f$' % num for num in np.arange(0, 0.02, 0.005)], fontsize=20)\n", "axes.set_yticks(np.arange(0, 0.02, 0.005/5), minor=True)\n", "\n", "axes.set_xlabel('Physical Observable', labelpad=5, fontsize=22)\n", "axes.set_ylabel('Probability', labelpad=5, fontsize=22)\n", "\n", "axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n", "axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n", "axes.minorticks_on()\n", "\n", "print" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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REiFEP2SwLYQYdGtaVWk0IUqBacgCN0KI/slgWwgxqLoT0BJVF48JUQqqg7BSqpIIIfoh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\n5c/8b0n9MsvWRK4Pfi2XP9g0Gs3usd3BdiKR2K1/Gk1DicSFRjBLD7b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rNO2APgfkccBg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dKqL2nhV2Xla66NilEVCOmIXV9RS+yvol5Nox6Pp5btFNBxxcEsKf8wlJTrhuJSaMjb7Ort94SZ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\naKy8jDHGGGOMmTWbYSQAMHToUJw9exbfffcdQkNDcfXqVXTv3h0DBgzA+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"text": [ "" ] } ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## debinning Performace: Discrimination" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n", "plt.hist(chisq, bins=np.arange(0, 7.01, .05), color='#0088ff', edgecolor='#555555')\n", "plt.hist(bgchisq, bins=np.arange(0, 7.01, .05), color='#66a61e', edgecolor='#555555', alpha=0.5)\n", "\n", "axes.set_xticks(np.arange(0, 7.01, 1))\n", "axes.set_xticks(np.arange(0, 7.01, .25), minor=True)\n", "axes.set_xticklabels([r'$%1.1f$' % num for num in np.arange(0, 7.01, 1)], fontsize=20)\n", "\n", "axes.set_ylim(bottom=-0.0001, top=6000)\n", "axes.set_yticks(np.arange(0, 6001, 1000))\n", "axes.set_yticks(np.arange(0, 6001, 250), minor=True)\n", "axes.set_yticklabels([r'$%i$' % int(num) for num in np.arange(0, 6001, 1000)], fontsize=20)\n", "\n", "axes.set_xlabel(r'$\\chi^2$ per d.o.f.', labelpad=5, fontsize=22)\n", "axes.set_ylabel('Number of Counts', labelpad=5, fontsize=22)\n", "\n", "axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n", "axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n", "axes.minorticks_on()\n", "print" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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AAHQp4WyrbTVMS9L111+v66+/XpIUFxenSZMmuVf3AAAAALo6v1fzmDZtmkaN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\nj5lqAL7ERboAAAAAIFYxMw0Eg9U7gC6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o0CGr1CKEwPr167F582aUlJTg2LFj\nKC4uxvDhw3HlyhX07dtXY42bmxuuXr2KLVu2wNfXF7du3cKRI0dw5coV2NvbIyoqCkeOHLF4rSEh\nIbh8+TKGDBmCwsJCHD9+HGVlZdi6dSvWrVun8/npepNhr169kJGRgcjISFRVVeHo0aNIT09Hnz59\nsG/fPtWtwU3ZU9+cMfNE9O/G24kTERlhyZIlGDZsGLp37w4A8PDwQGVlJR4+fAiF4t2dl6i5xbex\nt98mIqLaxTPTREQGrFu3Dv7+/qpGGnhzw5GCggIkJSVZsTIiIrI2NtNERHrExcXBwcEBgwYNUhuP\njIyEjY0N1q5dCwD4448/cPz4cWuUSEREVsRmmohIh+vXr+Pu3bta3yjn7u6OhIQE/PXXXxg6dCi2\nbNmC0NBQK1RJRETWxGumiYiIiIjMxDPTRERERERmYjNNRERERGQmNtNERERERGZiM01EREREZCY2\n00REREREZmIzTURERERkJjbTRERERERmYjNNRERERGSm/wJyXa/mBeKXzAAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## debinning Performace: Discrimination" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(figsize=(11,7), facecolor='#ffffff')\n", "plt.hist(ks, bins=np.arange(0, 0.3, .002), color='#0088ff', edgecolor='#555555')\n", "plt.hist(bgks, bins=np.arange(0, 0.3, .002), color='#66a61e', edgecolor='#555555', alpha=0.5)\n", "\n", "axes.set_xticks(np.arange(0, 0.26, .05))\n", "axes.set_xticks(np.arange(0, 0.26, .01), minor=True)\n", "axes.set_xticklabels([r'$%0.2f$' % num for num in np.arange(0, 0.26, .05)], fontsize=20)\n", "\n", "axes.set_ylim(bottom=-0.0001, top=5000)\n", "axes.set_yticks(np.arange(0, 5001, 1000))\n", "axes.set_yticks(np.arange(0, 5001, 250), minor=True)\n", "axes.set_yticklabels([r'$%i$' % int(num) for num in np.arange(0, 5001, 1000)], fontsize=20)\n", "\n", "axes.set_xlabel('KS test value', labelpad=5, fontsize=22)\n", "axes.set_ylabel('Number of Counts', labelpad=5, fontsize=22)\n", "\n", "axes.tick_params(length=10, width=1.2, labelsize=22, zorder=10, pad=10)\n", "axes.tick_params(which='minor', length=5, width=1.2, zorder=11)\n", "axes.minorticks_on()\n", "print" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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WLUpNTe3gW4gtGRkZkS4BAADAUYKdomo5EP/ud7/T7t27dcstt+ipp55SWlpa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\nJqZPn67Vq1dr8+bNSk9PV0VFhYYPH66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"text": [ "" ] } ], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# The Future, and Shameless Advertising:\n", "\n", "## \"Yikes.... There is so much more!\"" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Probability Calculus: Future" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Two-point correlation distribution, $\\subNsubR{n}{f}{r,s}(x_r, x_s)$...\n", "### $\\qquad$ Form is known already, but use...?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Re-derive or Re-interpret current statistical methods?\n", "### $\\qquad$ Poisson and Multinomial changes?\n", "### $\\qquad$ Likelihoods... Unbinned likelihoods... Re-derive?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## debinning: Statistical impact" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Full comparison: debinning vs histograms\n", "### $\\qquad$ Discovery signifigance?\n", "### $\\qquad$ Parameter estimation performance?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Full comparison: debinning vs unbinned maximum likelihood\n", "### $\\qquad$ Discovery signifigance?\n", "### $\\qquad$ Parameter estimation performance?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## debinning: Generalize / Specialize" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### $\\qquad$ data-driven backgrounds?\n", "### $\\qquad$ detector resolution \"unfolding\"?\n", "### $\\qquad$ \"Max Gap Method\"?\n", "### $\\qquad$ 2-debinning? N-debinning?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Searching for \"New Stuff\" with Statistics" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### New global-fitting tool for any \"New Stuff\": Gambit\n", "### The Global And Modular BSM Inference Tool" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.display import HTML\n", "HTML('')" ], "language": "python", "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "html": [ "" ], "metadata": {}, "output_type": "pyout", "prompt_number": 28, "text": [ "" ] } ], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Shameless Gambit Advertising:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Our flagship scan: Supersymmetry!\n", "### $\\qquad$ Our PMSSM-25 scan: Scanning 25 parameters!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### About us:\n", "GAMBIT is a global fitting code for generic Beyond the Standard Model theories, designed to allow fast and easy definition of new models, observables, likelihoods, scanners and backend physics codes.\n", "\n", "GAMBIT is developed by a group of nearly 30 theorists and experimentalists. The Collaboration includes members of the AMS-02, ATLAS, CDMS, CTA, DARWIN, DM-ICE, Fermi-LAT, HESS, IceCube, LHCb and XENON experiments, as well as developers of the public theory codes DarkSUSY, FlexibleSUSY, IsaJet, SoftSUSY and SuperIso.\n", "\n", "We are currently finalising the code in preparation for first public release in Summer 2015 \u2014 stay tuned!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "## Constructive Comments and Acknowledgements" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Greg says that I should check out rank statistics\n", " \n", "Christoph mentioned \"max gap method\" for when you have no idea whatsoever what your background is.\n", "\n", "Anders says that I should try Likelihood ratios: Compute Lsig/Lbg, debinning vs binned vs unbinned likelihood.\n", "\n", "Marco De Mattia says to consider the time scaling of the problem. There may be a region in data sample size where unbinned likelihood is too slow, but there is still not enough signal statistics for regular histograms." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Thank yous to various people who have discussed with me over the years:\n", "\n", " - Teruki Kamon, Jan Conrad, Greg Martinez, Christoph Weniger, Anders Kvellestad, Ola Liab\u00f8tr\u00f8, Are Raklev, Marco De Mattia\n", "\n", "Extra special thank yous for incredibly helpful constructive criticisms:\n", "\n", " - Bob Cousins, Alex Read\n", "\n", "... and, of course, none of this would have happened without the help I needed for debinning-1.0.0. Ultra special thank you to my bro, Nathan Krislock." ] } ], "metadata": {} } ] }