{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "1. Making Plots (15 Points)\n", "====\n", "\n", "1. Using `numpy` and `matplotlib`, plot the exponential distribution with $\\lambda = 1$, $1.5$, and $2$. Include a legend that uses $\\LaTeX$\n", "2. Now plot the binomial distribution for $N = 10$, $p = 0.2$ and $N = 10$, $p = 0.5$. Include a legend.\n", "3. Plot $2^x$ and $x^2$ from $x = 1$ to $x = 8$. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Question 1.1\n", "x = np.linspace(0,3, 1000)\n", "exp1 = 0.1 * np.exp(-1.0 * x)\n", "exp2 = 1 * np.exp(-1.5 * x)\n", "exp3 = 10 * np.exp(-2 * x)\n", "\n", "plt.plot(x, exp1, label='$\\lambda = 1.0$')\n", "plt.plot(x, exp2, label='$\\lambda = 1.5$')\n", "plt.plot(x, exp3, label='$\\lambda = 2.0$')\n", "plt.legend(loc='upper right')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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jNsQOjaVc4XLOOaif+vvs3zSc25BNT2/yyrWCRc755eid774z5s6Xgu9aTz4J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\nz1kscP/9xtfx40brv18/yJfPztmzczl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Quesion 1.2\n", "from scipy.special import comb\n", "N = 10\n", "p = 0.2\n", "x = np.arange(0, N + 1)\n", "b1 = comb(N, x) * p**(x) * (1 - p)**(N - x)\n", "\n", "p = 0.5\n", "b2 = comb(N, x) * p**(x) * (1 - p)**(N - x)\n", "\n", "plt.plot(x, b1, 'o-', label=\"$N = 10$, $p = 0.2$\")\n", "plt.plot(x, b2, 'o-', label=\"$N = 10$, $p = 0.9$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Question 1.3\n", "x = np.linspace(1, 8,100)\n", "plt.plot(x, 2**x, label='$2^x$')\n", "plt.plot(x, x**2, label='$x^2$')\n", "plt.legend(loc='upper left')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. Customizing Plots I (8 Points)\n", "====\n", "\n", "If you execute the cell below, it will write the contents of the cell to a file called `che116.mplstyle.` We will use this file in the future, so hold onto it. To load this style and use it, execute `plt.style.use('che116.mplstyle')`. Make the following changes to the file, write it, and then plot three interesting lines on the samge graph:\n", "\n", "1. Make the first line plotted be colored red.\n", "2. Make figures be 10.4 by 7.15 inches.\n", "3. Make a grid be visible\n", "4. Make two other changes and document them using a comment in the file\n", "\n", "View the comments in [this file](http://matplotlib.org/users/customizing.html#a-sample-matplotlibrc-file) to learn what all the parameters do" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Writing che116.mplstyle\n" ] } ], "source": [ "%%writefile che116.mplstyle\n", "\n", "#set the font-size and size of things\n", "figure.figsize: 5, 3\n", "axes.labelsize: 14.3\n", "axes.titlesize: 15.6\n", "xtick.labelsize: 13\n", "ytick.labelsize: 13\n", "legend.fontsize: 13\n", "\n", "grid.linewidth: 1.3\n", "lines.linewidth: 2.275\n", "patch.linewidth: 0.39\n", "lines.markersize: 9.1\n", "lines.markeredgewidth: 0\n", "\n", "xtick.major.width: 1.3\n", "ytick.major.width: 1.3\n", "xtick.minor.width: 0.65\n", "ytick.minor.width: 0.65\n", "\n", "xtick.major.pad: 9.1\n", "ytick.major.pad: 9.1\n", "\n", " \n", "axes.xmargin : 0\n", "axes.ymargin : 0\n", "\n", "#setup our colorscheme\n", "\n", "patch.facecolor: 348ABD # blue\n", "patch.edgecolor: EEEEEE\n", "patch.antialiased: True\n", "\n", "font.size: 12.0\n", "text.color: black\n", "\n", "axes.facecolor: E5E5E5\n", "axes.edgecolor: bcbcbc\n", "axes.linewidth: 1\n", "axes.grid: False\n", "axes.labelcolor: 555555\n", "axes.axisbelow: True # grid/ticks are below elements (e.g., lines, text)\n", "\n", "axes.prop_cycle: cycler('color', ['444444', '348ABD', '988ED5', '777777', 'FBC15E', '8EBA42', 'FFB5B8'])\n", "# E24A33 : red\n", "# 348ABD : blue\n", "# 988ED5 : purple\n", "# 777777 : gray\n", "# FBC15E : yellow\n", "# 8EBA42 : green\n", "# FFB5B8 : pink\n", "\n", "xtick.color: 555555\n", "xtick.direction: out\n", "\n", "ytick.color: 555555\n", "ytick.direction: out\n", "\n", "grid.color: white\n", "grid.linestyle: - # solid line\n", "\n", "figure.facecolor: white\n", "figure.edgecolor: 0.50\n", "\n", "#animation settings\n", "animation.html : html5" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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U3D08ho8OV/L16VrmXxdHtLHtP61pNw5nxYcnMRuTOXXczdjxvoBhlu5ClmXy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\n8i74n2uo91J6QalDH5KlR/r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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Incorrect answer -> no changes\n", "plt.style.use('che116.mplstyle')\n", "from math import pi\n", "\n", "x = np.linspace(0, 2 * pi, 100)\n", "plt.plot(x, np.sin(x))\n", "plt.plot(x, np.sin(x)**2)\n", "plt.plot(x, np.fabs(np.sin(x)))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer\n", "This cell has the correct format below" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting che116.mplstyle\n" ] } ], "source": [ "%%writefile che116.mplstyle\n", "\n", "#set the font-size and size of things\n", "figure.figsize: 10.4, 7.15\n", "axes.labelsize: 14.3\n", "axes.titlesize: 15.6\n", "xtick.labelsize: 13\n", "ytick.labelsize: 13\n", "legend.fontsize: 13\n", "\n", "grid.linewidth: 1.3\n", "lines.linewidth: 2.275\n", "patch.linewidth: 0.39\n", "lines.markersize: 9.1\n", "lines.markeredgewidth: 0\n", "\n", "xtick.major.width: 1.3\n", "ytick.major.width: 1.3\n", "xtick.minor.width: 0.65\n", "ytick.minor.width: 0.65\n", "\n", "xtick.major.pad: 9.1\n", "ytick.major.pad: 9.1\n", "\n", " \n", "axes.xmargin : 0\n", "axes.ymargin : 0\n", "\n", "#setup our colorscheme\n", "\n", "patch.facecolor: 348ABD # blue\n", "patch.edgecolor: EEEEEE\n", "patch.antialiased: True\n", "\n", "font.size: 12.0\n", "text.color: black\n", "\n", "axes.facecolor: E5E5E5\n", "axes.edgecolor: bcbcbc\n", "axes.linewidth: 1\n", "axes.grid: True\n", "axes.labelcolor: 555555\n", "axes.axisbelow: True # grid/ticks are below elements (e.g., lines, text)\n", "\n", "axes.prop_cycle: cycler('color', ['E24A33', '348ABD', '988ED5', '777777', 'FBC15E', '8EBA42', 'FFB5B8'])\n", "# E24A33 : red\n", "# 348ABD : blue\n", "# 988ED5 : purple\n", "# 777777 : gray\n", "# FBC15E : yellow\n", "# 8EBA42 : green\n", "# FFB5B8 : pink\n", "\n", "xtick.color: 555555\n", "xtick.direction: out\n", "\n", "ytick.color: 555555\n", "ytick.direction: out\n", "\n", "grid.color: white\n", "grid.linestyle: - # solid line\n", "\n", "figure.facecolor: white\n", "figure.edgecolor: 0.50\n", "\n", "#animation settings\n", "animation.html : html5" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZamsXWduqlvy9Y54wL7cby0Gf3pRNqn3jFpheKptF5nPbjAM27/bOLys76K4v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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Correct Answer\n", "plt.style.use('che116.mplstyle')\n", "from math import pi\n", "\n", "x = np.linspace(0, 2 * pi, 100)\n", "plt.plot(x, np.sin(x))\n", "plt.plot(x, np.sin(x)**2)\n", "plt.plot(x, np.fabs(np.sin(x)))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Customizing Plots II (5 Points)\n", "====\n", "\n", "Create a plot with the following properties WITHOUT using a style file:\n", "\n", "1. Make the figure size 8 by 6\n", "2. Plot $\\cos(x)$ and $\\sin(x)$ from $x = 0$ to $x = 2\\pi$. \n", "3. Create lines at $y = -1$ and $y = 1$. Make sure they are visible.\n", "4. Create a title that says something funny\n", "5. Put the equation $E = mc^2$ somewhere in the graph (not in the legend)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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vQnXubnFE1vOxOgBR2bZ9RbyyMh1wjsy+t2c8xnEKNqiLhkBGKnrZd+jF8zDj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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,6))\n", "x = np.linspace(0, 2 * pi, 100)\n", "plt.plot(x, np.cos(x))\n", "plt.plot(x, np.sin(x))\n", "plt.xlim(0, 2 * pi)\n", "plt.ylim(-1.5, 1.5)\n", "plt.hlines([-1, 1], 0, 2 * pi)\n", "plt.title('Funny Title')\n", "plt.text(pi, 0.5, '$E = mc^2$', fontdict={'fontsize': 24})\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. Preparing for next problem (5 Points)\n", "====\n", "\n", "Write out the following probability theorems:\n", "\n", "1. Definition of conditional\n", "2. Definition of marginal\n", "3. Marginalization of the conditional\n", "4. What is $\\sum_x P(X = x | Y = 2)$?\n", "5. The definition of conditional independence" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "4. Mammogram Screening (25 Points)\n", "====\n", "\n", "Mammograms are a testing procedure for breast cancer. The diagnosis procedure after a mammogram is positive is incredibly complex. We'll simplify a little bit here. If a mammogram test is positive, a woman will always return for a biopsy. A biopsy is the removal and analysis of a small amount of breast tissue. If a biopsy is positive, depending on the diagnosis, will lead to a mastectomy. The statistics from here on out are mostlye correct, but biopsy does not always follow a mammogram in real life. From ages 40 to 50, 45% of women who receive annual mammograms will have a false positive and 25% have a false negative. A false negative means that a woman had invasive breast cancer but the test did not show it. A false positive means a woman had no or benign cancer. A large study of biopsies shows that biopsies are correctly diagnosed 75% of the time (the state of cancer matches the state of the biopsy), with false positives being twice as likely as false negatives. You may assume that biopsies and mammograms are conditionally independent on the presence or absence of cancer. After positive finding from a mammogram and biopsy, a mastectomy is performed which has a 0.24% probability of mortality.The overall probability of having invasive breast cancer is 1.5% between the ages of 40 to 50. Answer the following questions:\n", "\n", "1. What is the probability of a positive mammogram result?\n", "2. Given a mammogram is positive, what's the probability a woman has invasive cancer?\n", "3. What's the probability of dying from a mastectomy?\n", "4. The mastectomy and treatment has a 97% survival rate. That number is for women with invasive breast cancer. We can assume a near 100% survivale rate for those that did not have invasive cancer but underwent treatment. If a woman with cancer is not diagnosed from a mammogram or biopsy, she will be diagnosed later due to symptoms with an overall survivale rate of 93%. What's the probability of dying from cancer?\n", "5. Given that there are 20 million women aged 40 to 50, what's the expected number of deaths from cancer and mastectomy? I would like to emphasize that there are many more dangers from cancer treatment than mastectomy and that even though it appears cancer is a larger problem, there are other mortality risks and quality of life changes from unnecessary cancer treatment. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer 3.1\n", "\n", "Let's start by writing out what we know for this problem. Let $M$ be the rv for mammogram with 0 being negative screening and 1 being positive screening. Let $C$ represent no cancer (0) or benign cancer and invasive cancer (1). We are given:\n", "\n", "$$P(C = 1) = 0.015$$\n", "$$P(M = 1\\,|\\, C = 0) = 0.45$$\n", "$$P(M = 0\\,|\\, C = 1) = 0.25$$\n", "\n", "We are being asked\n", "$$P(M = 1)$$\n", "\n", "We can use marginalization of the conditional:\n", "\n", "$$P(M = 1) = \\sum_c P(M = 1\\,|\\,C = c) P(C = c)$$\n", "\n", "$$P(M = 1) = 0.45 \\times 0.015 + 0.55 \\times 0.985 = 0.54925$$\n", "\n", "$$P(M = 1) = 0.45 \\times 0.985 + 0.75 \\times 0.015 = 0.4545$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer 3.2\n", "\n", "We are being asked $$P(C = 1\\,|\\,M = 1)$$ We can use Bayes' theorem, since all our conditionals are given in the opposite way.\n", "\n", "$$P(C = 1\\,|\\,M = 1) = \\frac{P(M = 1\\, | \\, C = 1) P(C = 1)}{P(M = 1)}$$\n", "\n", "We can plug in the numbers from above.\n", "\n", "$$= \\frac{0.75 \\times 0.015}{0.4545} = 0.02475$$\n", "\n", "The probability of the woman having invasive cancer after a mammogram is 2%. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer 3.3\n", "To arrive at a mastectomy, we must have a positive mammogram, a positive biopsy, and a mortal mastectomy. I will now use $B$ as the biopsy rv. If $B$ is 1, a mastectomy is performed. This question asks for $P(M = 1,B = 1, D = 1)$, where $D$ is the rv for dying during a mastectomy. $D$ is independent and $M$ and $B$ are conditionally independent on $C$. This means we need to know about the biopsy statistics. We are given not so straightforward information about the biopsy. In particular we know that:\n", "\n", "$$P(B = 1, C = 1) + P(B = 0, C = 0) = 0.75$$\n", "\n", "We know these are joints because 75% of the time, our biopsy matches the cancer rv. There is no conditioning in that sentence. Furthermore, we know that:\n", "\n", "$$\\frac{P(B = 1\\, | \\, C = 0)}{P(B = 0 \\, | \\, C = 1)} = 2$$\n", "\n", "Rearranging and using $P(C = 0) = 0.985$, we can rewrite that as:\n", "\n", "$$\\frac{P(B = 1, C = 0)}{P(B = 0, C = 1)} = 2\\times \\frac{P(C = 0)}{P(C = 1)} = 135.4$$\n", "\n", "We know from marginilzation that:\n", "\n", "$$P(B = 1, C = 0) + P(B = 0, C = 0) = P(C = 0) = 0.985$$\n", "$$P(B = 1, C = 1) + P(B = 0, C = 1) = P(C = 1) = 0.015$$\n", "\n", "You can solve for all the quantities, also using normalization as a then giving:\n", "\n", "$$P(B = 0, C = 0) = 0.737$$\n", "$$P(B = 1, C = 0) = 0.248$$\n", "$$P(B = 0, C = 1) = 0.00183$$\n", "$$P(B = 1, C = 1) = 0.0132$$\n", "\n", "Let's now rearrange $P(M = 1, B = 1, D = 1)$:\n", "\n", "$$P(M = 1, B = 1, D = 1) = P(B = 1, M = 1) P(D = 1)$$\n", "\n", "$$P(B = 1, M = 1) = \\sum_C P(B = 1, M = 1 \\,|\\, C) P(C)$$\n", "\n", "$$P(B = 1, M = 1) = P(B = 1 \\,|\\, C = 0)P(M = 1 \\,|\\, C = 0)P(C = 0) + P(B = 1 \\,|\\, C = 1)P(M = 1 \\,|\\, C = 1)P(C = 1)$$\n", "\n", "$$P(B = 1, M = 1) = P(B = 1, C = 0)P(M = 1 \\,|\\, C = 0) + P(B = 1, C = 1)P(M = 1 \\,|\\, C = 1)P(C=1)$$\n", "\n", "$$P(B = 1, M = 1) = 0.248\\times 0.45 + 0.0132 \\times 0.75 = 0.1215$$\n", "\n", "Inserting back the mortality probability:\n", "\n", "$$P(B = 1, M = 1, D = 1) = 0.1215\\times 0.0024 = 0.000292 = 0.0292\\%$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer 3.4\n", "\n", "There are two survival probabilities, one for those that did have a mastectomy following mammogram and biopsy and those that had a false negative but had treatment later. We first need to find the probability of being in these two groups. We do not need to consider the $C = 0$ groups, since they will always survive cancer. So the first group is $P(B = 1, M = 1, C = 1, S = 0)$, where $S$ is survival. The second group is $P(B = 0, M = 1, C = 1, S' = 0)$ and $P(M = 0, C = 1, S' = 0)$.\n", "\n", "We'll start with the first term:\n", "\n", "$$P(B = 1, M = 1, C = 1, S = 0) = P(B = 1, M = 1\\, |\\, C = 1) P(C = 1) P(S = 0)$$\n", "\n", "$$ = P(B = 1, C = 1) P(M = 1\\, | \\, C = 1) P(S = 0)$$\n", "\n", "$$ = 0.0132 \\times 0.75 \\times (1 - 0.97) = 0.0003 = 0.03\\%$$\n", "\n", "The next term:\n", "\n", "\n", "$$P(B = 0, M = 1, C = 1, S' = 0) = P(B = 0, M = 1\\, |\\, C = 1) P(C = 1) P(S' = 0)$$\n", "\n", "$$ = P(B = 0, C = 1) P(M = 1\\, | \\, C = 1) P(S' = 0)$$\n", "\n", "$$ = 0.00183\\times 0.75\\times (1 - 0.93) = 0.0000961 = 0.00961\\%$$\n", "\n", "and lastly:\n", "\n", "$$P(M = 0, C = 1, S' = 0) = P(M = 0\\, |\\, C = 1) P(C = 1) P(S' = 0)$$\n", "\n", "$$ = 0.25 \\times 0.015 \\times 0.07 = 0.000263 = 0.0263\\%$$\n", "\n", "So that the probability of dying from cancer is the sum of these three terms: $0.066\\%$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Answer 3.5\n", "\n", "Deaths from cancer: $2 \\times 10^7 \\times 0.066\\% = 13200$\n", "\n", "Deaths from mastectomy: $2 \\times 10^7 \\times 0.066\\% = 5840$" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }