day-3-data-mining/02 - More stats with Python.ipynb

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     "start_time": "2019-07-03T11:38:43.173953Z"
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    "from IPython.core.display import HTML\n",
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   "source": [
    "# Synopsis\n",
    "\n",
    "In this unit we will discuss an important part of data analysis, fitting distributions to data. In the process we will cover:\n",
    "\n",
    "* How to fit a distribution to data using `scipy`\n",
    "* Different distributions that may fit data\n",
    "* How to evaluate the fit of a distribution to data at a basic level"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:38:49.610042Z",
     "start_time": "2019-07-03T11:38:48.963926Z"
    }
   },
   "outputs": [],
   "source": [
    "import json\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import scipy.stats as stat\n",
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:38:50.357029Z",
     "start_time": "2019-07-03T11:38:50.349842Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:38:51.765775Z",
     "start_time": "2019-07-03T11:38:51.757275Z"
    }
   },
   "outputs": [],
   "source": [
    "def half_frame(sub, xaxis_label, yaxis_label, font_size = 15, padding = -0.02):\n",
    "    \"\"\"Formats frame, axes, and ticks for matplotlib made graphic with half frame.\"\"\"\n",
    "\n",
    "    # Format graph frame and tick marks\n",
    "    sub.yaxis.set_ticks_position('left')\n",
    "    sub.xaxis.set_ticks_position('bottom')\n",
    "    sub.tick_params(axis = 'both', which = 'major', length = 7, width = 2, direction = 'out', pad = 10,\n",
    "                    labelsize = font_size)\n",
    "    sub.tick_params(axis = 'both', which = 'minor', length = 5, width = 2, direction = 'out', labelsize = 10)\n",
    "    for axis in ['bottom','left']:\n",
    "        sub.spines[axis].set_linewidth(2)\n",
    "        sub.spines[axis].set_position((\"axes\", padding))\n",
    "    for axis in ['top','right']:\n",
    "        sub.spines[axis].set_visible(False)\n",
    "\n",
    "    # Format axes\n",
    "    sub.set_xlabel(xaxis_label, fontsize = 1.6 * font_size)\n",
    "    sub.set_ylabel(yaxis_label, fontsize = 1.6 * font_size)\n",
    "    \n",
    "    return"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting data to statistical models\n",
    "\n",
    "When doing science, one wants to develop a parsimonious description of data or of a system. For example, it is much more parsimonious to describe some data as being drawn from a Gaussian distribution with $\\mu = 0$ and $\\sigma = 1$ than storing all the data. \n",
    "\n",
    "Once we know what disctribution may reproduce the properties of the data, we can test that hypothesis. However, first we must determine the parameters values for the distribution.  \n",
    "\n",
    "\n",
    "## GPAs of applicants to Chemical Engineering Graduate Program\n",
    "\n",
    "In order to explore this type of statistical analysis with Python, we will study the undergraduate GPA of the applicants to the Chemical Engineering Graduate Program in 2014.\n",
    "\n",
    "### Import the data\n",
    "\n",
    "If you look at the contents of the file, this is what you see:\n",
    "\n",
    "`GPA UG,GPA UG Max`\n",
    "\n",
    "`9.1,10`\n",
    "\n",
    "`\"3.61, 3.65 (updated)\",4`\n",
    "\n",
    "`3.27,4`\n",
    "\n",
    "`3.966,4`\n",
    "\n",
    "These data have lots of mistakes. For simplicity, we are only going to consider here data that has no issues and for which the maximum GPA is 4.0.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:39:13.544305Z",
     "start_time": "2019-07-03T11:39:13.533570Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "364 [['9.1', '10'], ['\"3.61', ' 3.65 (updated)\"', '4'], ['3.27', '4']]\n",
      "237 [3.27, 3.966, 3.25]\n"
     ]
    }
   ],
   "source": [
    "with open(\"../Data/Day3-Visualization-and-Functions/gpa_data.csv\", \"r\") as data_file:\n",
    "    all_lines = data_file.readlines()\n",
    "\n",
    "gpa_list = []\n",
    "for line in all_lines[1:]:      # Ignore first line with field names\n",
    "    gpa_list.append( line.strip().split(\",\") )\n",
    "    \n",
    "print(len(gpa_list), gpa_list[:3])\n",
    "    \n",
    "gpa = []\n",
    "for x in gpa_list:\n",
    "    try:\n",
    "        if (float(x[1]) == 4.):  # consider only cases for which maximum GPA is 4.0\n",
    "            try:\n",
    "                gpa.append(float(x[0]))\n",
    "            except:\n",
    "                pass\n",
    "    except:\n",
    "        pass\n",
    "\n",
    "print(len(gpa), gpa[:3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:39:15.572773Z",
     "start_time": "2019-07-03T11:39:15.562185Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mode of the sample is 3.80\n",
      "The first quartile of the sample is 3.47\n",
      "The median of the sample is 3.64\n",
      "The third quartile of the sample is 3.80\n",
      "The skewness of the sample is -0.947\n"
     ]
    }
   ],
   "source": [
    "#import scipy.stats as stat\n",
    "#import numpy as np\n",
    "\n",
    "mode = float(stat.mode(gpa)[0])\n",
    "print(\"The mode of the sample is {0:4.2f}\".format(mode))\n",
    "\n",
    "first_quartile = stat.scoreatpercentile(gpa, 25)\n",
    "print(\"The first quartile of the sample is {0:4.2f}\".format(first_quartile))\n",
    "\n",
    "median = stat.scoreatpercentile(gpa, 50)\n",
    "print(\"The median of the sample is {0:4.2f}\".format(median))\n",
    "\n",
    "third_quartile = stat.scoreatpercentile(gpa, 75)\n",
    "print(\"The third quartile of the sample is {0:4.2f}\".format(third_quartile))\n",
    "\n",
    "skew = stat.skew(gpa)\n",
    "print(\"The skewness of the sample is {0:5.3f}\".format(skew))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:40:21.001542Z",
     "start_time": "2019-07-03T11:40:20.601186Z"
    }
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   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 432x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure( figsize = (6, 9) )\n",
    "sub1 = fig.add_subplot(2,1,1)\n",
    "my_font_size = 15\n",
    "\n",
    "half_frame(sub1, \"\", \"Probability density\", font_size = my_font_size)\n",
    "\n",
    "# Calculate and plot histogram\n",
    "#\n",
    "sub1.hist(gpa, 25, normed = 1, rwidth = 0.75, color = \"g\", alpha = 0.5, histtype = \"bar\", \n",
    "          label = \"data\", cumulative = False)\n",
    "\n",
    "sub1.vlines([first_quartile, median, third_quartile], ymin = 0, ymax = 1.8, lw = 3, color = \"red\", \n",
    "            label = \"quartiles\")\n",
    "\n",
    "# Format legend\n",
    "sub1.legend(loc = \"best\", frameon = False, markerscale = 1.8, fontsize = my_font_size)\n",
    "\n",
    "# Plot cumulative probability\n",
    "#\n",
    "sub2 = fig.add_subplot(2,1,2)\n",
    "half_frame(sub2, \"GPA\", \"Cumulative probability\", font_size = my_font_size)\n",
    "sub2.hist(gpa, 25, normed = 1, rwidth = 0.75, color = \"g\", alpha = 0.5, histtype = \"bar\", \n",
    "          label = \"data\", cumulative = True)\n",
    "sub2.vlines([first_quartile, median, third_quartile], ymin = 0, ymax = 1., lw = 3, color = \"red\", \n",
    "            label = \"quartiles\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data appears to be sort of Bell shaped but the median does not coincide with the mode... we could use the sample mean and sample standard deviation to generate a Gaussian distribution and compare it to our data. \n",
    "\n",
    "\n",
    "\n",
    "## Aside: Pre-defined distributions\n",
    "\n",
    "The `stats` library of `Scipy` gives us access to lots of modules for well-known distributions.  These include, **but are not at all limited to**,  the binomial, the Poisson, and the Gaussian.\n",
    "\n",
    "**Binomial distributions** occurs as the result of the repetition of independent trials. Flipping a coin several times.  Throwing one or more dice.\n",
    "\n",
    "A fair coin has 50% chance of landing on heads and a 50% chance of landing on tails. The binomial distribution with p = 0.5 and n = 50 specifies the probability of tossing k heads. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:41:02.674840Z",
     "start_time": "2019-07-03T11:41:02.482287Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 0.05\n",
    "n = 50\n",
    "\n",
    "# We can use the properties of the binomial function to define the plot ranges \n",
    "x = np.arange(stat.binom.ppf(0.0001, n, p), stat.binom.ppf(0.9999, n, p))\n",
    "rv = stat.binom(n, p)\n",
    "\n",
    "fig = plt.figure( figsize = (6, 4.5) )\n",
    "sub1 = fig.add_subplot(1,1,1)\n",
    "my_font_size = 15\n",
    "half_frame(sub1, \"k\", \"Probability mass\", font_size = my_font_size)\n",
    "\n",
    "# Calculate and plot histogram\n",
    "sub1.vlines(x, 0, rv.pmf(x), color = \"g\", linewidth = 20, alpha = 0.5, label = \"Binomial\")\n",
    "\n",
    "# Format legend\n",
    "sub1.legend(loc = \"best\", frameon = False, markerscale = 1.8, fontsize = 1.5 * my_font_size)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:42:07.466339Z",
     "start_time": "2019-07-03T11:42:07.201622Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample mean:  3.609\n",
      "Sample std. dev:  0.265\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure( figsize = (8, 4.5) )\n",
    "sub1 = fig.add_subplot(1,1,1)\n",
    "my_font_size = 15\n",
    "half_frame(sub1, \"GPA\", \"Probability density\", font_size = my_font_size)\n",
    "\n",
    "# Calculate and plot histogram\n",
    "#\n",
    "sub1.hist(gpa, 30, normed = 1, rwidth = 0.75, color = \"g\", alpha = 0.5, histtype = \"bar\", \n",
    "          label = \"data\", cumulative = False)\n",
    "\n",
    "# Gaussian null model: Use the sample's mean and st_dev \n",
    "#\n",
    "mu = np.mean(gpa)\n",
    "sigma = np.std(gpa)\n",
    "print('Sample mean: {0:6.3f}\\nSample std. dev: {1:6.3f}'.format(mu, sigma))\n",
    "\n",
    "x3 = np.linspace(stat.norm.ppf(0.0001, loc = mu, scale = sigma),\n",
    "                 stat.norm.ppf(0.9999, loc = mu, scale = sigma), \n",
    "                 100)\n",
    "rv3 = stat.norm(loc = mu, scale = sigma)\n",
    "sub1.plot(x3, rv3.pdf(x3), color = \"b\", lw = 2, label= \"Gaussian\")\n",
    "\n",
    "# Format legend\n",
    "sub1.legend(loc = \"best\", frameon = False, markerscale = 1.8, fontsize = my_font_size)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That does not look too good.  However, maybe we are being negatively biased by the fluctuations in the data... We could plot the cumulative distribution, which will smooth out the fluctuations.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:44:54.129401Z",
     "start_time": "2019-07-03T11:44:53.877383Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample mean:  3.609\n",
      "Sample std. dev:  0.265\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure( figsize = (8, 4.5) )\n",
    "sub1 = fig.add_subplot(1,1,1)\n",
    "my_font_size = 15\n",
    "half_frame(sub1, \"GPA\", \"Cumulative probability\", font_size = my_font_size)\n",
    "\n",
    "# Calculate and plot histogram, notice how we change the flag value for 'cumulative'\n",
    "#\n",
    "sub1.hist(gpa, 30, normed = 1, rwidth = 0.75, color = \"g\", alpha = 0.5, histtype = \"bar\", \n",
    "          label = \"data\", cumulative = True) \n",
    "\n",
    "## Gaussian null model: Use the sample's mean and st_dev \n",
    "#\n",
    "mu = np.mean(gpa)\n",
    "sigma = np.std(gpa)\n",
    "print('Sample mean: {0:6.3f}\\nSample std. dev: {1:6.3f}'.format(mu, sigma))\n",
    "\n",
    "x3 = np.linspace(stat.norm.ppf(0.0001, loc = mu, scale = sigma), \n",
    "                 stat.norm.ppf(0.9999, loc = mu, scale = sigma), \n",
    "                 100)\n",
    "sub1.plot(x3, stat.norm.cdf(x3, loc = mu, scale = sigma), color = \"b\", lw = 2, label= \"Gaussian\") # Notice we are plotting the cdf now\n",
    "\n",
    "sub1.set_xlim([2.5, 4.5])\n",
    "# Format legend\n",
    "sub1.legend(loc = \"best\", frameon = False, markerscale = 1.8, fontsize = my_font_size)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This does not look too bad, especially around the 3.5 to 3.8 range of GPA values.  But is it good enough? Is this the right description of the data? \n",
    "\n",
    "One thing we are not considering in our analysis is the fact that our data does not include values larger than 4. The distribution is truncated!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:45:23.018357Z",
     "start_time": "2019-07-03T11:45:23.012522Z"
    }
   },
   "outputs": [],
   "source": [
    "# Generated sample cumulative probability\n",
    "gpa.sort()\n",
    "cumulative = []\n",
    "for i, value in enumerate(gpa):\n",
    "    cumulative.append((i+1) / len(gpa))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:45:27.294589Z",
     "start_time": "2019-07-03T11:45:27.259269Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitted mu:  3.722\n",
      "Fitted sigma:  0.322\n",
      "-100.0 0.8796669239013241\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lgaalves/miniconda3/lib/python3.6/site-packages/scipy/optimize/minpack.py:787: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  category=OptimizeWarning)\n"
     ]
    }
   ],
   "source": [
    "# stat.truncnorm requires as input the bounds a, b, and loc and scale\n",
    "popt, pcov = curve_fit(stat.truncnorm.cdf, gpa, cumulative, p0 = [-100, 0.8, 3.7, 0.3])\n",
    "\n",
    "a_model = popt[0]\n",
    "b_model = popt[1]\n",
    "mu_model = popt[2]\n",
    "sig_model = popt[3]\n",
    "print('Fitted mu: {0:6.3f}\\nFitted sigma: {1:6.3f}'.format(mu_model, sig_model))\n",
    "print(a_model, b_model)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well! That is unwelcome!  Why is that?\n",
    "\n",
    "Let's think about it. The value of `a` and `b` actually has to be scaled by $\\mu$ and $\\sigma$, so the four parameters are **not** independent.  The lack of independence makes the calculation of the covariance problematic.\n",
    "\n",
    "How can we solve this problem? \n",
    "\n",
    "We should start by noting that `a` and `b` are not really parameters. The value of `b` is determined by the maximum GPA (4.0) and the values of $\\mu$ and $\\sigma$. The value of `a` does not really matter as long as it is far enough from `b`.\n",
    "\n",
    "We can define a new function that incorporates this knowledge!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:47:32.164841Z",
     "start_time": "2019-07-03T11:47:32.160960Z"
    }
   },
   "outputs": [],
   "source": [
    "def truncated_normal(x, mu, sigma):\n",
    "    a = -100\n",
    "    b = (4.0 - mu) / sigma\n",
    "    return stat.truncnorm.cdf(x, a, b, mu, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:47:35.186299Z",
     "start_time": "2019-07-03T11:47:35.167013Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitted mu:  3.729\n",
      "Fitted sigma:  0.327\n",
      "-100 0.827927799335284\n",
      "[[1.03401935e-05 9.19364281e-06]\n",
      " [9.19364281e-06 9.48837634e-06]]\n"
     ]
    }
   ],
   "source": [
    "popt, pcov = curve_fit(truncated_normal, gpa, cumulative, p0 = [3.7, 0.3])\n",
    "\n",
    "mu_model = popt[0]\n",
    "sig_model = popt[1]\n",
    "a_model = -100\n",
    "b_model = (4.0 - mu_model) / sig_model\n",
    "\n",
    "print('Fitted mu: {0:6.3f}\\nFitted sigma: {1:6.3f}'.format(mu_model, sig_model))\n",
    "print(a_model, b_model)\n",
    "print(pcov)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Problem solved!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:47:42.838566Z",
     "start_time": "2019-07-03T11:47:42.433294Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample mean:  3.609\n",
      "Sample std. dev:  0.265\n",
      "Fitted mu:  3.729\n",
      "Fitted sigma:  0.327\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x324 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure( figsize = (12, 4.5) )\n",
    "sub1 = fig.add_subplot(1,2,2)\n",
    "sub2 = fig.add_subplot(1,2,1)\n",
    "my_font_size = 15\n",
    "half_frame(sub1, \"GPA\", \"Cumulative probability\", font_size = my_font_size)\n",
    "half_frame(sub2, \"GPA\", \"Probability density\", font_size = my_font_size)\n",
    "\n",
    "# \n",
    "# Cumulative\n",
    "#\n",
    "sub1.plot(gpa, cumulative, \"go\", label= \"Data\")\n",
    "sub1.set_xlim([2.5, 4.2])\n",
    "\n",
    "## Gaussian null model: Use the sample's mean and st_dev \n",
    "mu = np.mean(gpa)\n",
    "sigma = np.std(gpa)\n",
    "print('Sample mean: {0:6.3f}\\nSample std. dev: {1:6.3f}'.format(mu, sigma))\n",
    "\n",
    "x3 = np.linspace(stat.norm.ppf(0.0001, loc = mu, scale = sigma), \n",
    "                 4., \n",
    "                 100)\n",
    "sub1.plot(x3, stat.norm.cdf(x3, mu, sigma), color = \"b\", lw = 2, label= \"Gaussian\") \n",
    "\n",
    "## Fitted model\n",
    "print('Fitted mu: {0:6.3f}\\nFitted sigma: {1:6.3f}'.format(mu_model, sig_model))\n",
    "sub1.plot(x3, stat.truncnorm.cdf(x3, a_model, b_model, loc = mu_model, scale = sig_model), \n",
    "          color = \"orange\", lw = 2, label= \"Truncated Gaussian\") \n",
    "\n",
    "# Format legend\n",
    "sub1.legend(loc = \"best\", frameon = False, markerscale = 1.8, fontsize = my_font_size)\n",
    "\n",
    "#\n",
    "# Density\n",
    "#\n",
    "sub2.hist(gpa, 20, normed = 1, rwidth = 0.75, color = \"g\", alpha = 0.5, histtype = \"bar\", \n",
    "          label = \"Data\", cumulative = False) \n",
    "\n",
    "sub2.plot(x3, stat.norm.pdf(x3, mu_model, sig_model), color = \"b\", lw = 2, label= \"Gaussian\") \n",
    "\n",
    "sub2.plot(x3, stat.truncnorm.pdf(x3, a_model, b_model, loc = mu_model, scale = sig_model), \n",
    "          color = \"orange\", lw = 2, label= \"Gaussian\") \n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These fits look really good. However, they do not tell us whether they provide an adequate representation of the data.  To answer that question we need to determine whether the data is statistically compatible with distributions generated using the truncated Gaussian distribution with the fitted parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:48:15.684505Z",
     "start_time": "2019-07-03T11:48:15.677341Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-test 1 sample for model: \tt = -0.243399 \tp = 0.807908\n",
      "KS 1 sample test for model: \tD = 0.035253 \tp = 0.929952\n"
     ]
    }
   ],
   "source": [
    "# t-test 1 sample\n",
    "popmean = stat.truncnorm.stats(a_model, b_model, mu_model, sig_model, moments = 'm')\n",
    "t_data, p = stat.ttest_1samp(gpa, popmean)\n",
    "print('t-test 1 sample for model: \\tt = {0:6.6f} \\tp = {1:6.6f}'.format(t_data, p))\n",
    "\n",
    "# KS test\n",
    "D_data, p = stat.kstest(gpa, stat.truncnorm.cdf, args = (a_model, b_model, mu_model, sig_model))\n",
    "print('KS 1 sample test for model: \\tD = {0:6.6f} \\tp = {1:6.6f}'.format(D_data, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wonderful. Our null hypthesis passed with flying colors!  But did it?\n",
    "\n",
    "Was what we did even correct?\n",
    "\n",
    "Let us explore this with a simple computational experiment.  We will generate a number of synthetic data sets drawn from the fitted truncated Gaussian and what these statistical test tell us when we do the test against the generated parameter values vs when we perform a fit to estimate the parameter values.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:51:33.794769Z",
     "start_time": "2019-07-03T11:51:33.781858Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input mu:  3.729\n",
      "Input sigma:  0.327\n",
      "\n",
      "Fitted mu:  3.743\n",
      "Fitted sigma:  0.337\n"
     ]
    }
   ],
   "source": [
    "# Generate synthetic data set and make fit\n",
    "print('Input mu: {0:6.3f}\\nInput sigma: {1:6.3f}'.format(mu_model, sig_model))\n",
    "print()\n",
    "\n",
    "xv = stat.truncnorm.rvs(a_model, b_model, loc = mu_model, scale = sig_model, size = len(gpa))\n",
    "xv.sort()\n",
    "cumulative = []\n",
    "for i, value in enumerate(xv):\n",
    "        cumulative.append((i+1) / len(xv))\n",
    "\n",
    "popt, pcov = curve_fit(truncated_normal, xv, cumulative, p0 = [3.7, 0.3])\n",
    "\n",
    "mu_fit = popt[0]\n",
    "sig_fit = popt[1]\n",
    "a_fit = -100\n",
    "b_fit = (4.0 - mu_fit) / sig_fit\n",
    "print('Fitted mu: {0:6.3f}\\nFitted sigma: {1:6.3f}'.format(mu_fit, sig_fit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T11:51:40.737886Z",
     "start_time": "2019-07-03T11:51:40.725466Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-test 1 sample for model: \tt = 0.333946 \tp = 0.738717\n",
      "t-test 1 sample for fit: \tt = 0.280525 \tp = 0.779320\n",
      "\n",
      "KS 1 sample test for model: \tD = 0.043108 \tp = 0.770586\n",
      "KS 1 sample test for fit: \tD = 0.044598 \tp = 0.733436\n"
     ]
    }
   ],
   "source": [
    "# t-test 1 sample\n",
    "\n",
    "popmean = stat.truncnorm.stats(a_model, b_model, mu_model, sig_model, moments = 'm')\n",
    "t, p = stat.ttest_1samp(xv, popmean)\n",
    "print('t-test 1 sample for model: \\tt = {0:6.6f} \\tp = {1:6.6f}'.format(t, p))\n",
    "popmean = stat.truncnorm.stats(a_fit, b_fit, mu_fit, sig_fit, moments = 'm')\n",
    "t, p = stat.ttest_1samp(xv, popmean)\n",
    "print('t-test 1 sample for fit: \\tt = {0:6.6f} \\tp = {1:6.6f}'.format(t, p))\n",
    "\n",
    "print()\n",
    "\n",
    "# KS test\n",
    "D, p = stat.kstest(xv, stat.truncnorm.cdf, args = (a_model, b_model, mu_model, sig_model))\n",
    "print('KS 1 sample test for model: \\tD = {0:6.6f} \\tp = {1:6.6f}'.format(D, p))\n",
    "D, p = stat.kstest(xv, stat.truncnorm.cdf, args = (a_fit, b_fit, mu_fit, sig_fit))\n",
    "print('KS 1 sample test for fit: \\tD = {0:6.6f} \\tp = {1:6.6f}'.format(D, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The t and D statistics systematically take lower values when compared to the fitted parameters.  That means that the `p-value` we are calculating may be an over-estimate...\n",
    "\n",
    "## Monte Carlo methods\n",
    "\n",
    "So called Monte Carlo methods, make use of computers to simulate stochastic processes. We will use such stochastic simulations now to investigate this problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T12:05:53.653914Z",
     "start_time": "2019-07-03T12:05:53.649494Z"
    }
   },
   "outputs": [],
   "source": [
    "def truncated_normal(x, mu, sigma):\n",
    "    a = -100\n",
    "    b = (4.0 - mu) / sigma\n",
    "    return stat.truncnorm.cdf(x, a, b, mu, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T12:09:06.181833Z",
     "start_time": "2019-07-03T12:09:00.938611Z"
    }
   },
   "outputs": [],
   "source": [
    "# Write your code here\n",
    "N_repetitions = 1000\n",
    "D_statistic = []\n",
    "t_statistic = []\n",
    "D_statistic_fit = []\n",
    "t_statistic_fit = []\n",
    "\n",
    "# Fitting the data to the model \n",
    "popt, pcov = curve_fit(truncated_normal, gpa, cumulative, p0 = [3.7, 0.3])\n",
    "mu_model = popt[0]\n",
    "sig_model = popt[1]\n",
    "a_model = -100\n",
    "b_model = (4.0 - mu_model) / sig_model\n",
    "\n",
    "for i in range(0,N_repetitions):\n",
    "    # Generate synthetic data set and make fit\n",
    "    #print('Input mu: {0:6.3f}\\nInput sigma: {1:6.3f}'.format(mu_model, sig_model))\n",
    "    xv = stat.truncnorm.rvs(a_model, b_model, loc = mu_model, scale = sig_model, size = len(gpa))\n",
    "    xv.sort()\n",
    "    cumulative = []\n",
    "    for i, value in enumerate(xv):\n",
    "            cumulative.append((i+1) / len(xv))\n",
    "    popt, pcov = curve_fit(truncated_normal, xv, cumulative, p0 = [3.7, 0.3])\n",
    "    mu_fit = popt[0]\n",
    "    sig_fit = popt[1]\n",
    "    a_fit = -100\n",
    "    b_fit = (4.0 - mu_fit) / sig_fit\n",
    "    #print('Fitted mu: {0:6.3f}\\nFitted sigma: {1:6.3f}'.format(mu_fit, sig_fit))\n",
    "\n",
    "    # Statistical tests. \n",
    "    #t-test 1 sample\n",
    "    popmean = stat.truncnorm.stats(a_model, b_model, mu_model, sig_model, moments = 'm')\n",
    "    t, p = stat.ttest_1samp(xv, popmean)\n",
    "    #print('t-test 1 sample for model: \\tt = {0:6.6f} \\tp = {1:6.6f}'.format(t, p))\n",
    "    t_statistic.append(t)\n",
    "    \n",
    "    popmean = stat.truncnorm.stats(a_fit, b_fit, mu_fit, sig_fit, moments = 'm')\n",
    "    t, p = stat.ttest_1samp(xv, popmean)\n",
    "    #print('t-test 1 sample for fit: \\tt = {0:6.6f} \\tp = {1:6.6f}'.format(t, p))\n",
    "    t_statistic_fit.append(t)\n",
    "\n",
    "    #print()\n",
    "\n",
    "    # KS test\n",
    "    D, p = stat.kstest(xv, stat.truncnorm.cdf, args = (a_model, b_model, mu_model, sig_model))\n",
    "    #print('KS 1 sample test for model: \\tD = {0:6.6f} \\tp = {1:6.6f}'.format(D, p))\n",
    "    D_statistic.append(D)\n",
    "    \n",
    "    D, p = stat.kstest(xv, stat.truncnorm.cdf, args = (a_fit, b_fit, mu_fit, sig_fit))\n",
    "    #print('KS 1 sample test for fit: \\tD = {0:6.6f} \\tp = {1:6.6f}'.format(D, p))\n",
    "    D_statistic_fit.append(D)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T12:09:06.189150Z",
     "start_time": "2019-07-03T12:09:06.184290Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.12482017814608304 0.02419111669734675\n",
      "0.06781261060642418 0.018984289830221157\n"
     ]
    }
   ],
   "source": [
    "print(max(D_statistic), min(D_statistic))\n",
    "print(max(D_statistic_fit), min(D_statistic_fit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T12:09:11.280635Z",
     "start_time": "2019-07-03T12:09:10.774803Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure( figsize = (6, 9) )\n",
    "my_font_size = 15\n",
    "\n",
    "sub1 = fig.add_subplot(2,1,1)\n",
    "sub2 = fig.add_subplot(2,1,2)\n",
    "\n",
    "half_frame(sub1, \"t statistic\", \"Probability density\", font_size = my_font_size)\n",
    "half_frame(sub2, \"D statistic\", \"Probability density\", font_size = my_font_size)\n",
    "\n",
    "sub1.hist([t_statistic, t_statistic_fit], bins = 21, normed = 1, color = ['r', 'cyan'], histtype = 'bar',\n",
    "         label = ['To model', 'To fit'], cumulative = False)\n",
    "\n",
    "sub2.hist([D_statistic, D_statistic_fit], bins = 10, normed = 1, color = ['r', 'cyan'], histtype = 'bar',\n",
    "         cumulative = False)\n",
    "\n",
    "popt, pcov = curve_fit(truncated_normal, xv, cumulative, p0 = [3.7, 0.3])\n",
    "\n",
    "mu_fit = popt[0]\n",
    "sig_fit = popt[1]\n",
    "a_fit = -100\n",
    "b_fit = (4.0 - mu_fit) / sig_fit\n",
    "\n",
    "#\n",
    "# Plot Student's t distribution for validation\n",
    "#\n",
    "xt = np.linspace(-3, 3, 50)\n",
    "df = len(gpa) - 1\n",
    "sub1.plot(xt, stat.t.pdf(xt, df), lw = 3)\n",
    "sub1.vlines(t_data, 0, 1.4, lw = 3, color = 'darkblue')\n",
    "\n",
    "#\n",
    "# Plot KS distribution for validation\n",
    "#\n",
    "xD = np.linspace(0, 0.15, 50)\n",
    "sub2.plot(xD, stat.ksone.pdf(xD, len(gpa)), lw = 3)\n",
    "sub2.vlines(D_data, 0, 60, lw = 3, color = 'darkblue')\n",
    "\n",
    "\n",
    "# Format legend\n",
    "sub1.legend(loc = \"best\", frameon = False, markerscale = 1.8, fontsize = my_font_size)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These plots make it clear that we still cannot reject the null hypothesis when we do things correctly.  However, they also demonstrate that the thoughtless use of the standard statistical tests could have led us to the wrong conclusion in other situations."
   ]
  }
 ],
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