lectures/Lecture_7.ipynb

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    "# Classical/Frequentist Statistical Inference: III\n",
    "\n",
    "*S. R. Taylor (2022)*\n",
    "\n",
    "Material in this lecture and notebook is based upon the \"Maximum Likelihood and Applications in Astronomy\" lectures of A. Connolly's & Ž. Ivezić's \"Astrostatistics & Machine Learning\" class at the University of Washington (ASTR 598, https://github.com/dirac-institute/uw-astr598-w18). Also the \"Inference\" and \"Histograms\" lectures of G. Richards' \"Astrostatistics\" class at Drexel University (PHYS 440/540, https://github.com/gtrichards/PHYS_440_540), J. Bovy's mini-course on \"Statistics & Inference in Astrophysics\" at the University of Toronto (http://astro.utoronto.ca/~bovy/teaching.html). \n",
    "\n",
    "##### Reading:\n",
    "\n",
    "- [Textbook](http://press.princeton.edu/titles/10159.html) Chapter 4.\n",
    "- [David Hogg's \"Fitting A Model To Data\"](https://arxiv.org/abs/1008.4686)\n",
    "\n",
    "***Exercises required for class participation are in <font color='red'>red</font>.***\n",
    "\n",
    "---"
   ]
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    "## Contents\n",
    "* [Hypothesis Testing](#one)\n",
    "* [Comparing Distributions](#two)\n",
    "* [Nonparametric Modeling & Histograms](#three)\n",
    "---"
   ]
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    "## Hypothesis Testing <a class=\"anchor\" id=\"one\"></a>\n",
    "\n",
    "A common problem in statistics is **hypothesis testing**, i.e., testing whether an observation or observations agree with a certain hypothesis. \n",
    "\n",
    "The simplest example is whether a measured value $x_i$ or an entire dataset $\\{x_i\\}$ are consistent with having been drawn from a Gaussian distribution, $\\mathcal{N}(\\mu,\\sigma)$. In this example, $\\mathcal{N}(\\mu,\\sigma)$ is the ***null hypothesis***, and we are trying to reject it in order to claim that we have measured some effect. \n",
    "\n",
    "A great example in astronomy is ***source detection*** in images that suffer from a substantial noise background (e.g., atmospheric fluctuations in optical images).\n",
    "- Since the background fluctuates, we need the source flux in a given image resolution element (e.g., pixel) to be substantially larger than the background variation in order to give a robust detection.\n",
    "- Here the null hypothesis is that the flux in each pixel is caused by background fluctuations, and if we can reject it then we can achieve source detection. \n",
    "- But note that *rejecting the null hypothesis is not the same as favoring the source hypothesis*! Our understanding of the background could be poor or incomplete, rendering our model of the null hypothesis similarly lacking.\n",
    "\n",
    "In the image below (from the [photutils](https://photutils.readthedocs.io/en/stable/background.html) package) we have sources embedded in Gaussian image noise. \n",
    "- Ideally we would like to be able to find the real sources in here and assign a number that says how much they reject the null background hypothesis. \n",
    "- We would establish a threshold in these numbers above which we could accept sources, knowing that we might be falsely rejecting some real ones, but hopefully not accepting too many spurious noise sources."
   ]
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    "![https://photutils.readthedocs.io/en/stable//background-1.svg](https://photutils.readthedocs.io/en/stable//background-1.svg)"
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Imagine we have data $\\{x_i\\}$. This could be signal strength in time-domain data, or pixel brightness in image data. Under an assumption about the null background distribution, $h_0(x)$, we can compute the probability that a data point would have a value as large or greater than that observed. This is called the ***$p$-value*** of the data:\n",
    "\n",
    "$$ p_i = \\int_{x_i}^\\infty h_0(x)dx \\equiv 1 - \\int_{-\\infty}^{x_i} h_0(x)dx = 1-H_0(x_i),$$\n",
    "\n",
    "where $H_0(x)$ is the CDF (cumulative density function) of the null distribution.\n",
    "\n",
    "In the image below, we show the distribution of a statistic $S$ under a null hypothesis $\\mathcal{H}_\\mathrm{null}$. The $p$-value of the observed statistic $S_\\mathrm{obs}$ is shown graphically.\n",
    "\n",
    "<!--<img src=\"figures/freq_pvalue.png\" alt=\"\" style=\"width: 500px;\"/>-->\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "Typically, a threshold $p$-value is adopted, called the **significance, $\\alpha$**. In a classification scheme, data would then reject the null hypothesis if $p_i\\leq\\alpha$. If $\\alpha=0.05$, such data would reject the null hypothesis at the $0.05$ significance level. \n",
    "\n",
    "**NOTE**\n",
    "- If we can't reject the null hypothesis then it doesn't mean the data belongs to the background. It could be that our sample is simply not large enough to detect an effect. \n",
    "- Rejecting the null hypothesis does not necessarily mean that we've proven a signal hypothesis. Our model of the null hypothesis could be bad, or there could be many other things we have not considered.\n",
    "- There is ***alot*** of mis-use and abuse of p-values in the scientific literature. Take a quick scan of [this](https://fivethirtyeight.com/features/statisticians-found-one-thing-they-can-agree-on-its-time-to-stop-misusing-p-values/) and [this](https://www.wikiwand.com/en/Misuse_of_p-values) during class, and read thoroughly in your own time. \n",
    "\n",
    "**EXAMPLE**\n",
    "\n",
    "Let's flip a coin 10 times. \n",
    "- Defining HEADS as a success event, use `scipy.stats` to define a binomial distribution over $10$ coin flips, where the intrinsic success probability is $0.5$. \n",
    "- Plot the probability mass function (the analog of the probability density function for discrete distributions).\n",
    "- <font color='red'>If we get $8$ HEADS, what is the $p$-value with which we reject the hypothesis that the coin is fair?</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Execute this cell\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='retina'\n",
    "\n",
    "import scipy.stats as stats\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import uniform\n",
    "from scipy import optimize\n",
    "from astroML import stats as astroMLstats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code to plot the binomial distribution in here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code to compute the p-value of 8 tails in here.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We look at our coin more shrewdly. In 20 flips, we get a result with $p$-value of $1$ in $10^3$ (i.e., $p = 0.001$). <font color='red'>How many HEADS did we get?</font> *Hint: check the properties of the `scipy.stats.binom` object for useful functions for this.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When making these kinds of classification decisions, we make two types of errors. These are quite literally described as **Type I** and **Type II** errors by *Neyman & Pearson*.\n",
    "\n",
    "**TYPE I ERRORS**\n",
    "- The null hypothesis is true, but incorrectly rejected.\n",
    "- These are ***false positives*** (or false alarms).\n",
    "- False positive probability is dictated by the significance level $\\alpha$. \n",
    "\n",
    "**TYPE II ERRORS**\n",
    "- The null hypothesis is false, but not rejected.\n",
    "- These are ***false negatives*** (or false dismissals).\n",
    "- False negatives probability is dictated by a variable called $\\beta$, related to $(1-\\beta)$, called the ***detection probability***."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at Fig 4.5 of Ivezic, v2. We have two Gaussian distributions; one describing the background noise and one describing the source. These distributions overlap, as they often do in real life.\n",
    "\n",
    "<font color='red'>Execute the following cell. We'll discuss it more below.</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load ./scripts/fig_classification_example.py\n",
    "\"\"\"\n",
    "Example of classification\n",
    "-------------------------\n",
    "Figure 4.5.\n",
    "\n",
    "An example of a simple classification problem between two Gaussian\n",
    "distributions. Given a value of x, we need to assign that measurement to one\n",
    "of the two distributions (background vs. source). The cut at xc = 120 leads\n",
    "to very few Type II errors (i.e., false negatives: points from the distribution\n",
    "hS with x < xc being classified as background), but this comes at the cost of\n",
    "a significant number of Type I errors (i.e., false positives: points from the\n",
    "distribution :math:`h_B` with x > xc being classified as sources).\n",
    "\"\"\"\n",
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Generate and draw the curves\n",
    "x = np.linspace(50, 200, 1000)\n",
    "p1 = 0.9 * norm(100, 10).pdf(x)\n",
    "p2 = 0.1 * norm(150, 12).pdf(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 7))\n",
    "ax.fill(x, p1, ec='k', \n",
    "        fc='#AAAAAA', alpha=0.5)\n",
    "ax.fill(x, p2, '-k', \n",
    "        fc='#AAAAAA', alpha=0.5)\n",
    "\n",
    "ax.plot([120, 120], \n",
    "        [0.0, 0.04], '--k')\n",
    "\n",
    "ax.text(100, 0.036, r'$h_B(x)$', ha='center', \n",
    "        va='bottom', fontsize=15)\n",
    "ax.text(150, 0.0035, r'$h_S(x)$', ha='center', \n",
    "        va='bottom', fontsize=15)\n",
    "ax.text(122, 0.039, r'$x_c=120$', ha='left', \n",
    "        va='top', fontsize=15)\n",
    "ax.text(125, 0.01, \n",
    "        r'$(x > x_c\\ {\\rm classified\\ as\\ sources})$', \n",
    "        fontsize=15)\n",
    "\n",
    "ax.set_xlim(50, 200)\n",
    "ax.set_ylim(0, 0.04)\n",
    "\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$p(x)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we have data $\\{x_i\\}$ drawn from an underlying distribution\n",
    "\n",
    "$$ h(x) = (1-a)h_B(x) + ah_S(x)$$\n",
    "\n",
    "where $h_B(x)=\\mathcal{N}(\\mu=100,\\sigma=10)$ is the background distribution (normalized to unity), $h_S(x)=\\mathcal{N}(\\mu=150,\\sigma=12)$ is the source distribution (normalized to unity), and $a$ is the relative normalization factor that accounts for background noise being $(1-a)/a$ more probable than sources.\n",
    "\n",
    "- ***If we set a classificiation threshold at $x_c=120$, calculate the Type I error (false positive) probability, $\\alpha$.***\n",
    "- ***For the same $x_c$, calculate the Type II error (false negative) probability, $\\beta$.***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a sample of size $N$ (containing background noise and sources), the **expected number of spurious sources (Type I / false positives)** is \n",
    "\n",
    "$$ n_\\mathrm{spurious} = N(1-a)\\alpha = N(1-a)\\int_{x_c}^\\infty h_B(x)dx$$ \n",
    "\n",
    "and the **expected number of missed sources (Type II / false negatives)** is\n",
    "\n",
    "$$ n_\\mathrm{missed} = Na\\beta = Na\\int_0^{x_c}h_S(x)dx.$$\n",
    "\n",
    "The **total number of classified sources** (that is number of instances where we reject the null hypothesis) is\n",
    "\n",
    "$$ n_\\mathrm{source} = Na - n_\\mathrm{missed} + n_\\mathrm{spurious} = N[(1-\\beta)a + (1-a)\\alpha].$$\n",
    "\n",
    "The **sample completeness** (or **detection probability**) is defined as\n",
    "\n",
    "$$ \\eta = \\frac{Na - n_\\mathrm{missed}}{Na} = 1-\\int_0^{x_c}h_S(x)dx = 1-\\beta$$\n",
    "\n",
    "Finally, the **sample contamination** is\n",
    "\n",
    "$$ \\epsilon = \\frac{n_\\mathrm{spurious}}{n_\\mathrm{source}}$$\n",
    "\n",
    "where $(1-\\epsilon)$ is sometimes called the **classification efficiency**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing Distributions <a class=\"anchor\" id=\"two\"></a>\n",
    "\n",
    "Hypothesis testing is strongly linked to the **comparison of distributions**. Common questions are whether two samples are drawn from the same distribution, or whether a sample is drawn from some known distribution (like a Gaussian).\n",
    "\n",
    "Sometimes we may be only interested in the location parameter of some underlying distribution. For example, do two gravitational-wave detectors with different measurement uncertainties and local effects measure consistent masses of a merging system of black holes?\n",
    "\n",
    "There is enormous variety in the nonparameteric and parameteric statistics to compare distributions, and we'll only look at a few. See the textbook and wider literature for further examples.\n",
    "\n",
    "### Kolmogorov-Smirnov (KS) Test\n",
    "\n",
    "By far the most popular nonparametric statistic to compare distribution is the KS test. We compute the empirical cdf $F(x)$ for two samples $\\{x1_i\\} = (1,\\ldots,N_1)$ and $\\{x2_i\\} = (1,\\ldots,N_2)$. *Recall that the empirical cdf can be calculated by sorting the samples and dividing by the sample size.*\n",
    "\n",
    "The KS test is based on a statistic that measures the maximum difference in the cdfs of our two samples\n",
    "\n",
    "$$ D = \\mathrm{max}|F_1(x1) - F_2(x2)|$$\n",
    "\n",
    "where $0\\leq D\\leq 1$. \n",
    "\n",
    "> The core idea is to know how often the value of $D$ computed from our data would arise by chance if both samples were drawn from the same distribution (which is our *null hypothesis* here). \n",
    "\n",
    "Amazingly, ***this does not depend on the underlying distribution we care about!*** Kolmogorov published the following result in 1933 and Smirnov published numerical tables in 1948. The probability of obtaining a value of $D$ larger than that observed in our data is\n",
    "\n",
    "$$ Q_\\mathrm{KS}(\\lambda) = 2\\sum_{k=1}^\\infty (-1)^{k-1}\\exp(-2k^2\\lambda^2)$$\n",
    "\n",
    "where \n",
    "\n",
    "$$\\lambda = \\left(0.12 + \\sqrt{n_e} + \\frac{0.11}{\\sqrt{n_e}} \\right)D $$\n",
    "\n",
    "and the ***effective number of data points***, $n_e$, is\n",
    "\n",
    "$$ n_e = \\left( \\frac{1}{N_1} + \\frac{1}{N_2}\\right)^{-1} = \\frac{N_1 N_2}{N_1 + N_2}$$\n",
    "\n",
    "If the probability that $D$ were drawn by chance is very small (low $p$-value) then we can reject the null hypothesis that the two samples were drawn from the same distribution."
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For large $n_e$ we have $\\lambda\\approx\\sqrt{n_e}D$. In fact, for $n_e>10$ we can bypass $Q_\\mathrm{KS}$ entirely and compute the value of D that would correspond to a given significance level $\\alpha$,\n",
    "\n",
    "$$ D_\\mathrm{KS} = \\frac{C(\\alpha)}{\\sqrt{n_e}}$$\n",
    "\n",
    "where $C(\\alpha) = \\sqrt{-\\frac{1}{2}\\ln(\\alpha/2)}$. Some instructive significance levels are shown below (from [here](https://www.wikiwand.com/en/Kolmogorov%E2%80%93Smirnov_test)).\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The KS test and variants can be accessed in the `scipy.stats` modules `kstest`, `ks_2samp`, and `ksone.` Let's look at a simple example for comparing a Gaussian sample to a Gaussian null hypothesis distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the kstest function is appropriate for this\n",
    "np.random.seed(0)\n",
    "x = np.random.normal(loc=0, scale=1, size=1000)\n",
    "print(stats.kstest(x, 'norm'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now compare a $t$-distribution with $100$ degrees of freedom to a Gaussian distribution. <font color='red'>Complete the following cell. Discuss with your colleagues whether the result makes sense.</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(987654321)\n",
    "print(stats.kstest(stats.t.rvs(___, size=100), 'norm'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>Try again and discuss for a $t$-process with only $3$ degrees of freedom.</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many other nonparametric tests, in particular the **Anderson-Darling test** to check whether a sample is consistent with having been drawn from a Gaussian distribution. We don't have time to do a deep dive here, but see the textbook for further details.\n",
    "\n",
    "Read through and execute the following cell to perform the **KS test**, **Anderson-Darling test**, and the **Shapiro-Wilk test** applied to $10,000$ values drawn from a Gaussian distribution, and separately to a mixture of a Gaussian distribution. `scipy.stats` has many of the relevant functions. The print-out statements give statistic values and $p$-values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load ./scripts/fig_anderson_darling.py\n",
    "\"\"\"\n",
    "Gaussianity Tests\n",
    "-----------------\n",
    "Figure 4.7.\n",
    "\n",
    "The results of the Anderson-Darling test, the Kolmogorov-Smirnov test, and the\n",
    "Shapiro-Wilk test when applied to a sample of 10,000 values drawn from a normal\n",
    "distribution (upper panel) and from a combination of two Gaussian distributions\n",
    "(lower panel).\n",
    "\n",
    "The functions are available in the ``scipy`` package:\n",
    "\n",
    "- The Anderson-Darling test (``scipy.stats.anderson``)\n",
    "- The Kolmogorov-Smirnov test (``scipy.stats.kstest``)\n",
    "- The Shapiro-Wilk test (``scipy.stats.shapiro``)\n",
    "\"\"\"\n",
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "\n",
    "#----------------------------------------------------------------------\n",
    "# This function adjusts matplotlib settings for a uniform feel in the textbook.\n",
    "# Note that with usetex=True, fonts are rendered with LaTeX.  This may\n",
    "# result in an error if LaTeX is not installed on your system.  In that case,\n",
    "# you can set usetex to False.\n",
    "if \"setup_text_plots\" not in globals():\n",
    "    from astroML.plotting import setup_text_plots\n",
    "setup_text_plots(fontsize=8, usetex=False)\n",
    "\n",
    "from astroML.stats import mean_sigma, median_sigmaG\n",
    "\n",
    "# create some distributions\n",
    "np.random.seed(1)\n",
    "normal_vals = stats.norm(loc=0, scale=1).rvs(10000)\n",
    "dual_vals = stats.norm(0, 1).rvs(10000)\n",
    "dual_vals[:4000] = stats.norm(loc=3, scale=2).rvs(4000)\n",
    "\n",
    "x = np.linspace(-4, 10, 1000)\n",
    "normal_pdf = stats.norm(0, 1).pdf(x)\n",
    "dual_pdf = 0.6 * stats.norm(0, 1).pdf(x) + 0.4 * stats.norm(3, 2).pdf(x)\n",
    "\n",
    "vals = [normal_vals, dual_vals]\n",
    "pdf = [normal_pdf, dual_pdf]\n",
    "xlims = [(-4, 4), (-4, 10)]\n",
    "\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Compute the statistics and plot the results\n",
    "fig = plt.figure(figsize=(5, 7))\n",
    "fig.subplots_adjust(left=0.13, right=0.95,\n",
    "                    bottom=0.06, top=0.95,\n",
    "                    hspace=0.1)\n",
    "\n",
    "for i in range(2):\n",
    "    ax = fig.add_subplot(2, 1, 1 + i)  # 2 x 1 subplot\n",
    "\n",
    "    # compute some statistics\n",
    "    A2, sig, crit = stats.anderson(vals[i])\n",
    "    D, pD = stats.kstest(vals[i], \"norm\")\n",
    "    W, pW = stats.shapiro(vals[i])\n",
    "\n",
    "    mu, sigma = mean_sigma(vals[i], ddof=1)\n",
    "    median, sigmaG = median_sigmaG(vals[i])\n",
    "\n",
    "    N = len(vals[i])\n",
    "    Z1 = 1.3 * abs(mu - median) / sigma * np.sqrt(N)\n",
    "    Z2 = 1.1 * abs(sigma / sigmaG - 1) * np.sqrt(N)\n",
    "\n",
    "    print(70 * '_')\n",
    "    print(\"  Kolmogorov-Smirnov test: D = %.2g  p = %.2g\" % (D, pD))\n",
    "    print(\"  Anderson-Darling test: A^2 = %.2g\" % A2)\n",
    "    print(\"    significance  | critical value \")\n",
    "    print(\"    --------------|----------------\")\n",
    "    for j in range(len(sig)):\n",
    "        print(\"    {0:.2f}          | {1:.1f}%\".format(sig[j], crit[j]))\n",
    "    print(\"  Shapiro-Wilk test: W = %.2g p = %.2g\" % (W, pW))\n",
    "    print(\"  Z_1 = %.1f\" % Z1)\n",
    "    print(\"  Z_2 = %.1f\" % Z2)\n",
    "\n",
    "    # plot a histogram\n",
    "    ax.hist(vals[i], bins=50, density=True, \n",
    "            histtype='stepfilled', alpha=0.5)\n",
    "    ax.plot(x, pdf[i], '-k')\n",
    "    ax.set_xlim(xlims[i])\n",
    "\n",
    "    # print information on the plot\n",
    "    info = \"Anderson-Darling: $A^2 = %.2f$\\n\" % A2\n",
    "    info += \"Kolmogorov-Smirnov: $D = %.2g$\\n\" % D\n",
    "    info += \"Shapiro-Wilk: $W = %.2g$\\n\" % W\n",
    "    info += \"$Z_1 = %.1f$\\n$Z_2 = %.1f$\" % (Z1, Z2)\n",
    "    ax.text(0.97, 0.97, info,\n",
    "            ha='right', va='top', transform=ax.transAxes)\n",
    "\n",
    "    if i == 0:\n",
    "        ax.set_ylim(0, 0.55)\n",
    "    else:\n",
    "        ax.set_ylim(0, 0.35)\n",
    "        ax.set_xlabel('$x$')\n",
    "\n",
    "    ax.set_ylabel('$p(x)$')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonparametric Modeling & Histograms <a class=\"anchor\" id=\"three\"></a>\n",
    "\n",
    "Imagine you have some one-dimensional (\"univariate\") data that you would like to try to understand.  Where by \"understand\" we mean \"know the distribution in the measured space\", i.e., you want to know the probability distribution function. Our constant friend is the histogram, and it's usually the first thing any of us do on new data. Simple, right? Not quite...\n",
    "\n",
    "Let's work through some examples to see what problems we encounter and how we might overcome them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Execute this cell to generate a univariate data array, x\n",
    "# this is the same data used in Ivezic, Figure 6.5\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Generate our data: a mix of several Cauchy distributions\n",
    "#  this is the same data used in the Bayesian Blocks figure\n",
    "np.random.seed(0)\n",
    "N = 1000\n",
    "mu_gamma_f = [(5, 1.0, 0.1),\n",
    "              (7, 0.5, 0.5),\n",
    "              (9, 0.1, 0.1),\n",
    "              (12, 0.5, 0.2),\n",
    "              (14, 1.0, 0.1)]\n",
    "true_pdf = lambda x: sum([f * stats.cauchy(mu, gamma).pdf(x)\n",
    "                          for (mu, gamma, f) in mu_gamma_f])\n",
    "x = np.concatenate([stats.cauchy(mu, gamma).rvs(int(f * N))\n",
    "                    for (mu, gamma, f) in mu_gamma_f])\n",
    "np.random.shuffle(x)\n",
    "x = x[x > -10]\n",
    "x = x[x < 30]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next few cells, make a normalized histogram of this data with 10 bins, 20 bins, and 100 bins. It starts off looking unimodal and Gaussian-ish, but clearly when more finely binned the data breaks up into several modes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 10 bins\n",
    "plt.hist(x,___,___); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 20 bins\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 100 bins\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How would you characterize this distribution?  Could we reasonably think of it as a normal (Gaussian) distribution that we could characterize by some mean and standard deviation?  Maybe, but even just by looking at this plot we see that it wouldn't be a particularly good description of the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that small changes in parameters to the histogram function *significantly* change the PDF.  That's bad, because the underlying data clearly have **not** changed. One of the problems with histograms is that some bins end up with little (or no) data.  We can fix this by making **variable-width bin sizes** that have the ***same number of objects in each bin***.  How can we do this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Execute this cell\n",
    "a = np.linspace(1,42,num=42)\n",
    "print(a)\n",
    "print(a[::2])\n",
    "print(a[::3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you are familiar with slicing, then you know that `[::2]` and `[::3]` say to count by 2 and count by 3.  But that isn't what they really do.  They say to take every other index of the array or every 3rd index of the array.  So, if your array is sorted (like `a` is), then you could use this to instead define the number of values in a bin.  That is for any given value of `M`\n",
    "\n",
    "    bins = np.append(np.sort(x)[::M], np.max(x))\n",
    "    \n",
    "would give bins with `M` objects in each bin.  \n",
    "\n",
    "So if `M=3` and $x = [1,3,5,7,9,11,13,21,29,35]$ then $bins = [1 7 13 35]$.\n",
    "\n",
    "*Note:* you need to add the maximum value to set the right edge of the last bin.  \n",
    "\n",
    "Try it for `M=100` and `M=30` (100 and 30 objects in a bin)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "bins100 = np.append(np.sort(x)[::____], np.max(x)) #Complete\n",
    "bins30 = np.append(____,____) #Complete\n",
    "print(len(bins100),len(bins30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Note that the underscores here are suppressing the array output\n",
    "#so that we just see the plots\n",
    "_ = plt.hist(____, bins=____, density=True, histtype=\"step\") #Complete\n",
    "_ = plt.hist(____,____,____,____) #Complete\n",
    "plt.xlim(-5,25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, this can look pretty different depending on what the number of objects you choose as the minimum for each bin and compared to the plots above.  And it looks a lot different from the plots above.\n",
    "\n",
    "So, what is the \"right\" way to set the bin size? There is no \"right\" way, but there are some useful rules of thumb."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**\"Scott's rule\"** suggests that the optimal bin width is \n",
    "\n",
    "$$\\Delta_b = \\frac{3.5\\sigma}{N^{1/3}}.$$\n",
    "\n",
    "That's great, but what if we don't know the standard deviation, $\\sigma$ (e.g., if the distribution isn't really Gaussian)?  \n",
    "\n",
    "We can then instead used the **\"Freedman-Diaconis rule\"**: \n",
    "\n",
    "$$\\Delta_b = \\frac{2(q_{75}-q_{25})}{N^{1/3}} = \\frac{2.7\\sigma_G}{N^{1/3}}.$$  \n",
    "\n",
    "Let's try that. Remember that you can compute $\\sigma_G$ using `astroML`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from astroML import stats as astroMLstats\n",
    "sigmaG2 = astroMLstats.sigmaG(x)\n",
    "print(sigmaG2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='red'>Now set the bin size accordingly</font>, using [np.arange](https://numpy.org/doc/stable/reference/generated/numpy.arange.html) and plot.  Make sure that you don't throw away the last object in data set (append that maximum object to the end)! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "binsize = ____*_____/(N**(____)) #Complete for Freedman-Diaconis Rule\n",
    "print(binsize)\n",
    "binsG = np.append(np.arange(start=x.____, stop=x.____, step=____) , x.____) #Complete\n",
    "print(len(binsG))\n",
    "print(binsG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "_ = plt.hist(____,____,____,____) #Complete   \n",
    "plt.xlim(-5,25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Did you find that tedious? Me too. Try the following shortcut."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from astropy.visualization.hist import hist as fancyhist\n",
    "_ = fancyhist(x, bins=\"scott\", histtype=\"step\",density=True)\n",
    "_ = fancyhist(x, bins=\"freedman\", histtype=\"step\",density=True)\n",
    "plt.xlim(-5,25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that even those don't yield quite the same results!  But we can do better!\n",
    "\n",
    "An obvious thing to do is to simply show all of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# execute this cell\n",
    "plt.hist(x,histtype=\"step\")\n",
    "plt.plot(x, 0*x, '|', color='k', markersize=25) #Note markersize is (annoyingly) in *points*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is called a **rug plot** and now we have a better idea of where most of the data and where the gaps really are (as opposed to where the binning makes them *appear* to be).  However, the markers are all piled up, so we have lost all sense of the relative numbers of objects.  Are there ~10 at x=5 or could there be 100?\n",
    "\n",
    "This is where **[Kernel Density Estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation) (KDE)** comes in:\n",
    "- In short the idea here is to represent each data point not as a delta function, but rather as a distribution (e.g., a Gaussian).  \n",
    "- Those individual distributions (\"kernels\") are summed up to produce the PDF.  \n",
    "- One of the advantages of this is that it combines the best of \n",
    "    1. the histogram (tells us the relative height of the distribution) \n",
    "    2. the rug plot (centers the data points at the actual location of the data instead of within some arbitrary bin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just about any distribution can be used as the kernel, but the most common are a **Gaussian kernel** and an **Epanechnikov kernel**.  One downside of the Gaussian kernel is that the tails are technically infinite in extent.  So each point has some finite probability of being *everywhere*.  The Epanechnikov kernel has truncated wings.  \n",
    "\n",
    "One still has the problem of deciding the width of the kernel (e.g., for the Gaussian the *\"mean\"* is fixed at the value of the point, but how wide should you make the Gaussian?). For now, we'll just play with the widths by hand to see what might work best.  N.B. the widths of the kernel distribution are referred to as **\"bandwidth\"**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# execute this cell to load the KDE module\n",
    "from sklearn.neighbors import KernelDensity\n",
    "xgrid = np.linspace(x.min(),x.max(),1000)  # Use this instead of 'x' for plotting\n",
    "\n",
    "def kde_sklearn(data, bandwidth = 1.0, kernel=\"linear\"):\n",
    "    kde_skl = KernelDensity(bandwidth = bandwidth, \n",
    "                            kernel=kernel)\n",
    "    kde_skl.fit(data[:, np.newaxis])\n",
    "    log_pdf = kde_skl.score_samples(xgrid[:, np.newaxis]) # sklearn returns log(density)\n",
    "\n",
    "    return np.exp(log_pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we try the Gaussian and Epanechnikov kernels, let's first start with a tophat using `kernel = \"tophat\"`, which will produce a plot much like the rug plot.\n",
    "\n",
    "Start with `bandwidth=0.01`.  See what happens when you adjust this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "PDFtophat = kde_sklearn(____,bandwidth=____,kernel=____) #Complete\n",
    "plt.plot(xgrid,____) #Complete"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The defaults give a result that is essentially what you would get if you made a histogram with a really large number of bins.\n",
    "\n",
    "Now let's compare what happens when we adjust the bandwidth (which is just the width of the kernel function).  Try \n",
    "`bandwidth=0.1` and `bandwidth=0.5`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "PDFtophat1 = kde_sklearn(____,____,____) #Complete\n",
    "plt.plot(____,____,label='width=____') #Complete\n",
    "\n",
    "PDFtophat5 = ____(____,____,____) #Complete\n",
    "plt.plot(____,____,____) #Complete\n",
    "    \n",
    "plt.legend(loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's see what we get with the Gaussian `kernel=\"gaussian\"` and Epanechnikov `kernel=\"epanechnikov\"` kernels.  <font color='red'>Play with the bandwidths until you get something that looks reasonable</font> (and roughly matches) for the two kernels.  They need not be the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "PDFgaussian = kde_sklearn(____,bandwidth=____,kernel=\"____\") #Complete \n",
    "PDFepanechnikov = ____(____,____,____) #Complete\n",
    "plt.plot(xgrid,PDFgaussian,label=\"____\") #Complete\n",
    "plt.plot(____,____,____) #Complete\n",
    "plt.legend(____) #Complete"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is pretty different from the histogram that we started out with, isn't it?\n",
    "\n",
    "**HISTOGRAMS TAKE-AWAY MESSAGE:** \n",
    "\n",
    "Making a histogram is the first-cut we make of data, and it's certainly one of the most sensible things to try to get a feel for the data. But we can't just do it without thinking. We need to explore bin sizes and KDE smoothing bandwidths to tease out the structure in the distributions, and overcome any finite sample effects in bins by potentially having variable bin widths.\n",
    "\n",
    "Finally, the normalized bin height of a histogram can simply be understood as\n",
    "\n",
    "$$ f_k = \\frac{n_k}{\\Delta_b N}$$\n",
    "\n",
    "where $k$ indexes the bin, $n_k$ is the occupancy number of the bin, $\\Delta_b$ is the bin width, and $N$ is the total sample size. If we want to assign **uncertainties** to each bin height (not often done, but its good practice) then we can quote\n",
    "\n",
    "$$ \\sigma_k = \\frac{\\sqrt{n_k}}{\\Delta_b N}$$"
   ]
  }
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