{
 "metadata": {
  "gist_id": "6a4c1baf14ff07deda4a",
  "name": "",
  "signature": "sha256:3d3dab068140a690bf18557f98d2bb653b944fb66285160a48a96f797a08a75f"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Bayesian Methods 2"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The material for this notebook is provided via this free online <a href='http://nbviewer.ipython.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Chapter1_Introduction/Chapter1_Introduction.ipynb'>textbook</a> :  \n",
      "\n",
      "I am writing this notebook to document my learning, and hopefully to help others learn machine learning. You can think of it as my personal lecture notes. I would love suggestions / corrections / feedback for these notebooks.\n",
      "\n",
      "<b><a target=\"_parent\" href=\"http://rmdk.ca\">Visit my webpage for more</a></b>. \n",
      "\n",
      "Email me: <a href=\"mailto:email.ryan.kelly@gmail.com?Subject=Hey\" target=\"_top\">email.ryan.kelly@gmail.com</a>\n",
      "\n",
      "I'd love for you to share if you liked this post."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Related Notebooks"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <a target=\"_parent\" href=\"http://nbviewer.ipython.org/github/rmdk/IPython-Notebooks/blob/master/Machine%20Learning/Bayesian%20Methods%20for%20Hackers.ipynb\">Intro to Bayesian Inference</a>\n",
      "\n",
      "* <a target=\"_parent\" href=\"http://nbviewer.ipython.org/github/RMDK/IPython-Notebooks/blob/master/Machine%20Learning/Probability%20Distribution%20Review.ipynb\">Probability Distribution Review</a>\n",
      "\n",
      "* <a target=\"_parent\" href=\"http://nbviewer.ipython.org/github/rmdk/IPython-Notebooks/blob/master/Machine%20Learning/Bayesian%202.ipynb\">Bayesian Inference 2</a>\n",
      "\n",
      "* <a target=\"_parent\" href=\"http://nbviewer.ipython.org/github/rmdk/IPython-Notebooks/blob/master/Machine%20Learning/Bayesian%203.ipynb\">Bayesian Inference 3</a>\n",
      "\n",
      "* <a target=\"_parent\" href=\"http://nbviewer.ipython.org/github/rmdk/IPython-Notebooks/blob/master/Machine%20Learning/Bayesian%20Inference%204.ipynb\">Bayesian Inference 4</a>\n",
      "\n",
      "* <a target=\"_parent\" href=\"http://rmdk.ca\">Bayesian Inference 6</a>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "social()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "    <a style='float:left; margin-right:5px;' href=\"https://twitter.com/share\" class=\"twitter-share-button\" data-text=\"Check this out\" data-via=\"Ryanmdk\">Tweet</a>\n",
        "<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n",
        "    <a style='float:left; margin-right:5px;' href=\"https://twitter.com/Ryanmdk\" class=\"twitter-follow-button\" data-show-count=\"false\">Follow @Ryanmdk</a>\n",
        "<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n",
        "    <a style='float:left; margin-right:5px;'target='_parent' href=\"http://www.reddit.com/submit\" onclick=\"window.location = 'http://www.reddit.com/submit?url=' + encodeURIComponent(window.location); return false\"> <img src=\"http://www.reddit.com/static/spreddit7.gif\" alt=\"submit to reddit\" border=\"0\" /> </a>\n",
        "<script src=\"//platform.linkedin.com/in.js\" type=\"text/javascript\">\n",
        "  lang: en_US\n",
        "</script>\n",
        "<script type=\"IN/Share\"></script>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 61,
       "text": [
        "<IPython.core.display.HTML at 0x111688990>"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "This notebook covers or includes:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* Introduction to Bayesian Methods\n",
      "* Uses Python and PyMC\n",
      "* Many Examples and Figures"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Introduction"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "PyMC is a python library dedicated for Bayesian analysis. The book I am using for these notebooks is designed to bridge the complex gaps in the documentation, and make this library and Bayesian analysis more accessible. This notebook will be focused around solving the problem introduced above in \n",
      "<a href='http://nbviewer.ipython.org/github/RMDK/IPython-Notebooks/blob/master/Machine%20Learning/Probability%20Distribution%20Review.ipynb'>Probability Distributions Review</a>.\n",
      "\n",
      "This type of programming is called _probabilistic programming_, and has previously been daunting to learn. The author provides an interesting quote that describes probabilistic programming.\n",
      "\n",
      "> Another way of thinking about this: unlike a traditional program, which only runs in forward directions, a probabilistic program is run in both forward and backward directions. It runs forward to compute the consequences of the assumptions it contains about the world, but also runs backwards from the data to constrain the possible explanations. In practice, many probabilistic programming systems will cleverly interleave these forward and backward operations to be efficiently hone in on the best explanations.\n",
      "\n",
      "PyMC code is fairly easy to read. The only new thing is the syntax, so we will go through it slowly. Remember, we will be simply representing the model's components ($\\tau, \\ \\lambda _1, \\ \\lambda _2$) as variables.\n",
      "\n",
      "First we will reload and plot the text-message data from last lesson."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from matplotlib import pyplot as plt\n",
      "\n",
      "import seaborn as sns\n",
      "# Some initial styling\n",
      "rc={'axes.labelsize': 16.0, 'font.size': 16, \n",
      "    'legend.fontsize': 16.0, 'axes.titlesize': 18,\n",
      "    'xtick.labelsize': 15.0, 'ytick.labelsize': 15.0}\n",
      "\n",
      "sns.set(context = 'poster', style = 'whitegrid', rc=rc)\n",
      "\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "\n",
      "count_data = pd.read_csv('https://raw.githubusercontent.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/data/txtdata.csv',\n",
      "    header=None, names=['msgs'])\n",
      "N = len(count_data)\n",
      "\n",
      "plt.bar(np.arange(N), count_data['msgs'], color=\"#9b59b6\", alpha=0.8)\n",
      "plt.xlabel('Time (days)')\n",
      "plt.ylabel('count of msgs received')\n",
      "plt.title('Did the texting habits change over time?')\n",
      "plt.xlim(0, N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "(0, 74)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAwcAAAI5CAYAAAD0X0YmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f8f9a90>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "\n",
      "alpha = 1.0 / count_data.mean() # 'count_data' holds text message counts\n",
      "\n",
      "lambda_1 = pm.Exponential('lambda_1', alpha)\n",
      "lambda_2 = pm.Exponential('lambda_2', alpha)\n",
      "tau = pm.DiscreteUniform('tau', lower=0, upper=N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this code we create PyMC variables for the model components that we need. We assign them to PyMC's _stochastic variables_, so-called because they are treated by the back end as random number generatiors. We can demonstrate this fact by calling their built-in `random()` methods."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('Random Output:', tau.random(), tau.random(), tau.random())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "('Random Output:', array(42), array(62), array(29))\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@pm.deterministic\n",
      "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n",
      "    out = np.zeros(N)\n",
      "    out[:tau] = lambda_1 # lambda before tau is lambda_1\n",
      "    out[tau:] = lambda_2 # lambda after (and including) tau is lambda_2\n",
      "    return out"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This code creates a new function `lambda_`, but we can just think of it as a random variable: the random variable $\\lambda$. Note that because `lambda_1`, `lambda_2`, and `tau` are random, `lambda_` will be random. No variables are fixed yet.\n",
      "\n",
      "`@pm.deterministic` is a decorator that tells PyMC this is a deterministic function. Thus if the arguments were deterministic (they are not), the output would be deterministic as well."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "observation = pm.Poisson('obs', lambda_, value=count_data, observed=True)\n",
      "model = pm.Model([observation, lambda_1, lambda_2, tau])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The variable `observation` combines out data, `count_data`, without our proposed data-generation scheme, given by the variable `lambda_`, through the `value` keyword. We set `observed = True` to tell PyMC that this should stay fixed in our analysis. Finally, PyMC wants us to collect all the variables of interest and create a `model` instance out of them. This makes our life easier when we retrieve the results.\n",
      "\n",
      "The code below will be fully explained later, but we show it here to see where the results come from. One can think of it as a _learning_ step. The model employed here is a _Markov Chain Monte Carlo_ (MCMC), which is also explained later. This technique returns thousands of random variables from the posterior distributions of $\\lambda _1$, $\\lambda _2$ , and $\\tau$. We can plot a histogram of the random variables to see what the posterior distributions look like. Below we collect the samples (called _traces_ in the MCMC literature) into histograms."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Code to be explained later\n",
      "mcmc = pm.MCMC(model)\n",
      "mcmc.sample(40000, 10000, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 3424 of 40000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------           17%                  ] 6809 of 40000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        25%                  ] 10145 of 40000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     32%                  ] 12934 of 40000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------------   39%                  ] 15770 of 40000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------46%                  ] 18575 of 40000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------53%                  ] 21390 of 40000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------60%---               ] 24232 of 40000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------67%-----             ] 27060 of 40000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------74%--------          ] 29951 of 40000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------82%-----------       ] 32854 of 40000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------89%-------------     ] 35658 of 40000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------96%----------------  ] 38536 of 40000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 40000 of 40000 complete in 6.8 sec"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lambda_1_samples = mcmc.trace('lambda_1')[:]\n",
      "lambda_2_samples = mcmc.trace('lambda_2')[:]\n",
      "tau_samples = mcmc.trace('tau')[:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Histogram of samples\n",
      "\n",
      "ax = plt.subplot(311)\n",
      "ax.set_autoscaley_on(False)\n",
      "\n",
      "plt.hist(lambda_1_samples, histtype='stepfilled', bins=30, alpha=0.85,\n",
      "         label='posterior of $\\lambda _1$', color='#9b59b6', normed=True)\n",
      "plt.legend(loc='upper right')\n",
      "plt.title(r'''Posterior distributions of the variables $\\lambda _1, \\ \\lambda _2, \\ \\tau$''')\n",
      "plt.xlim([15, 30])\n",
      "plt.xlabel('$\\lambda _1$ value')\n",
      "\n",
      "ax = plt.subplot(312)\n",
      "ax.set_autoscaley_on(False)\n",
      "plt.hist(lambda_2_samples, histtype='stepfilled', bins=30, alpha=0.85,\n",
      "         label='posterior of $\\lambda _2$', color='#3498db', normed=True)\n",
      "plt.legend(loc='upper right')\n",
      "plt.xlim([15, 30])\n",
      "plt.xlabel('$\\lambda _2$ value')\n",
      "\n",
      "plt.subplot(313)\n",
      "w = 1.0 / tau_samples.shape[0] * np.ones_like(tau_samples)\n",
      "plt.hist(tau_samples, bins=N, alpha = 1,\n",
      "         label=r'posterior of $\\tau$',\n",
      "         color='#A60628', weights=w, rwidth=2.)\n",
      "plt.xticks(np.arange(N))\n",
      "\n",
      "plt.legend(loc='upper left')\n",
      "plt.ylim([0, 0.75])\n",
      "plt.xlim([35, len(count_data) - 20])\n",
      "plt.xlabel(r'$\\tau$ (in days)')\n",
      "plt.ylabel('probability')\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "<matplotlib.text.Text at 0x1125e1ed0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAxMAAAI/CAYAAAAMQ4SpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1114cb750>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Interpretation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Recall that Bayesian methodology returns a _distribution_. Hence we now have distributions to describe the unknown $\\lambda$s and $\\tau$. What have we gained? Immediately, we can see the uncertainty in our estimates: the wider distribution, the less certain out posterior belief should be. We can also see what the plausible values for the parameters are: $\\lambda _1$ is around 18 and $\\lambda _2$ is around 23. The posterior distributions of the two lambdas are clearly distinct, indicating that it is indeed likely that there was a change in the users text message behaviour.\n",
      "\n",
      "Notice that the posterior distributions for the $\\lambda$s do not look like exponential distributions, even though our priors for these were exponential. In fact, the posterior distributions are not really of any form that we recognize from the original model. But that's OK! This is one of the benefits of a Bayesian point of view. If we had instead used a mathematical approaches, we would be stuck with a messy result.\n",
      "\n",
      "Our analysis also returned a distribution for $\\tau$. Its posterior distribution looks different from the other two because it is a discrete random variable, so it does assign probabilities to intervals. We can see that near day 45, there was a 50% chance that the user's behaviour changed. Had no change occurred, or had the change been gradual over time, the posterior distribution of $\\tau$ would have been more spread out, reflecting that many days were plausible candidates for $\\tau$. However, the actual results show that only three of four days make any sense as potential transition points."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Why would I want sampes from the posterior, anyways?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will deal with this question for the remainder of the book, and it is an understatement to say that it will lead us to some amazing results. For now, let's end this chapter with one last example.\n",
      "\n",
      "We will use the posterior samples to answer the following question: what is the expect number of texts at day $t$, $ 0 <= t <= 70$? Recall that the expected value of a Poisson variable is equal to its parameter $\\lambda$. Therefore, the question is equivalent to _what is the expected value of $\\lambda$ at time $t$_?\n",
      "\n",
      "In the code below, let $i$ inded samples from the posterior distributions. Given a dat $t$, we average over all possible $\\lambda _i$ for that dat $t$, using $\\lambda _i = \\lambda  _{1, i} \\ \\  if \\ \\ t < \\tau _i$, else we use $\\lambda _i = \\lambda _{2, i}$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "NN = tau_samples.shape[0]\n",
      "expected_texts_per_day = np.zeros(N)\n",
      "for day in range(0, N):\n",
      "    #ix is a bool index of all tau samples corresponding to\n",
      "    # the switchpoint occurring prior to value of 'day'\n",
      "    ix = day < tau_samples\n",
      "    # Each posterior sample corresponds to a value for tau.\n",
      "    # for each day, that value of tau indicates whether we are 'before'\n",
      "    # in the lambda_1 regime, or 'after' the switchpoint in the lambda_2 regime.\n",
      "    # By taking the posterior sample of lambda1/2 accordingly, we can \n",
      "    # average over all samples to get an expect value for lambda on that day.\n",
      "    # The message count random variable is Poisson distributed,\n",
      "    # therefore lambda (the Poisson parameter) is the expected value of\n",
      "    # message count.\n",
      "    expected_texts_per_day[day] = (lambda_1_samples[ix].sum()+\n",
      "                                   lambda_2_samples[~ix].sum()) / NN\n",
      "    \n",
      "plt.plot(range(N), expected_texts_per_day, color='#9b59b6', lw=4,\n",
      "         label='Predicted number of texts')\n",
      "             \n",
      "plt.xlim(0, N)\n",
      "plt.xlabel('Day')\n",
      "plt.ylabel('Expected # of texts')\n",
      "plt.title('Expected number of texts received')\n",
      "\n",
      "plt.bar(np.arange(len(count_data)), count_data['msgs'], color=\"#3498db\", alpha=0.65,\n",
      "    label=\"observed texts per day\")\n",
      "plt.legend(loc='upper left')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 53,
       "text": [
        "<matplotlib.legend.Legend at 0x11c3c1d50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAwcAAAI5CAYAAAD0X0YmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJEmSJEmSJEmSJEmSJEmSJEmSJEnS+P5/yAb8vEZ43dQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11b33d410>"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our analysis thus far shows strong support for believing the user's behaviour did chance ($\\lambda _1$ would have been close in value to $\\lambda _2$ had this not been true), and that change was sudden rather than gradual, as denoted by $\\tau$'s strong peaked posterior distribution. We can speculate what might have caused this: a cheaper text-message rage, recent text subscription, or maybe a new relationship. In reality, the text message increase corresponds to a trip the user took for work, leading to an increase of messages to a girlfriend."
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "<a target=\"_parent\" href=\"http://nbviewer.ipython.org/github/rmdk/IPython-Notebooks/blob/master/Machine%20Learning/Bayesian%203.ipynb\">Up Next: Bayesian Methodology 3</a>\n",
      "\n",
      "<hr>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.core.display import HTML\n",
      "\n",
      "\n",
      "def css_styling():\n",
      "    styles = open(\"/users/ryankelly/desktop/custom_notebook2.css\", \"r\").read()\n",
      "\n",
      "    return HTML(styles)\n",
      "css_styling()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<style>\n",
        "\n",
        "/*\n",
        "\n",
        "    Name:       Base16 Ashes Light\n",
        "    Author:     Jannik Siebert (https://github.com/janniks)\n",
        "\n",
        "    CodeMirror template adapted for IPython Notebook by Nikhil Sonnad (https://github.com/nsonnad/base16-ipython-notebook)\n",
        "    CodeMirror template by Jan T. Sott (https://github.com/idleberg/base16-chrome-devtools)\n",
        "    Original Base16 color scheme by Chris Kempson (https://github.com/chriskempson/base16)\n",
        "\n",
        "*/\n",
        "\n",
        " /*Uncomment to use a custom font*/\n",
        "/*div#notebook, div.CodeMirror, div.output_area pre, div.output_wrapper, div.prompt {\n",
        "  font-family: 'Computer Modern', \"Helvetica Neue\", Arial, monospace !important;\n",
        "}*/\n",
        "\n",
        "\n",
        "/* GLOBALS */\n",
        "body {background-color: #F3F4F5;}\n",
        "a {color: #AE95C7;}\n",
        "h1 {text-align: center;}\n",
        "/* INTRO PAGE */\n",
        ".toolbar_info, .list-container {color: #393F45;}\n",
        "\n",
        "/* NOTEBOOK */\n",
        "\n",
        "/* comment out this line to bring the toolbar back */\n",
        "/*div#maintoolbar, div#header {display: none !important;}*/\n",
        "\n",
        "div#notebook {border-top: none;}\n",
        "\n",
        "div.input_prompt {color: #C795AE;}\n",
        "div.output_prompt {color: #C79595;}\n",
        "div.input_area {\n",
        "  border-radius: 0px;\n",
        "  border: 1px solid #C7CCD1;\n",
        "}\n",
        "div.output_area pre {font-weight: normal; color: #565E65;}\n",
        "div.output_subarea {font-weight: normal; color: #565E65;}\n",
        "\n",
        ".rendered_html table, .rendered_html th, .rendered_html tr, .rendered_html td {\n",
        "  border: 1px  #747C84 solid;\n",
        "  color: #747C84;\n",
        "}\n",
        "div.output_html { font-family: 'Computer Modern', \"Helvetica Neue\", Arial, sans-serif; }\n",
        "table.dataframe tr {border: 1px #565E65;}\n",
        "\n",
        "div.cell.selected {border-radius: 0px;}\n",
        "div.cell.edit_mode {border-radius: 0px; border: thin solid #C79595;}\n",
        "div.text_cell_render, div.output_html {color: #565E65;}\n",
        "\n",
        "span.ansiblack {color: #393F45;}\n",
        "span.ansiblue {color: #95AEC7;}\n",
        "span.ansigray {color: #ADB3BA;}\n",
        "span.ansigreen {color: #95C7AE;}\n",
        "span.ansipurple {color: #C795AE;}\n",
        "span.ansired {color: #C7AE95;}\n",
        "span.ansiyellow {color: #AEC795;}\n",
        "\n",
        "div.output_stderr {background-color: #C7AE95;}\n",
        "div.output_stderr pre {color: #DFE2E5;}\n",
        "\n",
        ".cm-s-ipython.CodeMirror {background: #F3F4F5; color: #393F45;}\n",
        ".cm-s-ipython div.CodeMirror-selected {background: #DFE2E5 !important;}\n",
        ".cm-s-ipython .CodeMirror-gutters {background: #F3F4F5; border-right: 0px;}\n",
        ".cm-s-ipython .CodeMirror-linenumber {color: #ADB3BA;}\n",
        ".cm-s-ipython .CodeMirror-cursor {border-left: 1px solid #747C84 !important;}\n",
        "\n",
        ".cm-s-ipython span.cm-comment {color: #C79595;}\n",
        ".cm-s-ipython span.cm-atom {color: #C795AE;}\n",
        ".cm-s-ipython span.cm-number {color: #C795AE;}\n",
        "\n",
        ".cm-s-ipython span.cm-property, .cm-s-ipython span.cm-attribute {color: #95C7AE;}\n",
        ".cm-s-ipython span.cm-keyword {color: #C7AE95;}\n",
        ".cm-s-ipython span.cm-string {color: #AEC795;}\n",
        ".cm-s-ipython span.cm-operator {color: #C79595;}\n",
        ".cm-s-ipython span.cm-builtin {color: #C795AE;}\n",
        "\n",
        ".cm-s-ipython span.cm-variable {color: #95C7AE;}\n",
        ".cm-s-ipython span.cm-variable-2 {color: #AE95C7;}\n",
        ".cm-s-ipython span.cm-def {color: #C7C795;}\n",
        ".cm-s-ipython span.cm-error {background: #C7AE95; color: #747C84;}\n",
        ".cm-s-ipython span.cm-bracket {color: #565E65;}\n",
        ".cm-s-ipython span.cm-tag {color: #C7AE95;}\n",
        ".cm-s-ipython span.cm-link {color: #C795AE;}\n",
        "\n",
        ".cm-s-ipython .CodeMirror-matchingbracket { text-decoration: underline; color: #393F45 !important;}\n",
        "</style>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "<IPython.core.display.HTML at 0x112018fd0>"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def social():\n",
      "    code = \"\"\"\n",
      "    <a style='float:left; margin-right:5px;' href=\"https://twitter.com/share\" class=\"twitter-share-button\" data-text=\"Check this out\" data-via=\"Ryanmdk\">Tweet</a>\n",
      "<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n",
      "    <a style='float:left; margin-right:5px;' href=\"https://twitter.com/Ryanmdk\" class=\"twitter-follow-button\" data-show-count=\"false\">Follow @Ryanmdk</a>\n",
      "<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n",
      "    <a style='float:left; margin-right:5px;'target='_parent' href=\"http://www.reddit.com/submit\" onclick=\"window.location = 'http://www.reddit.com/submit?url=' + encodeURIComponent(window.location); return false\"> <img src=\"http://www.reddit.com/static/spreddit7.gif\" alt=\"submit to reddit\" border=\"0\" /> </a>\n",
      "<script src=\"//platform.linkedin.com/in.js\" type=\"text/javascript\">\n",
      "  lang: en_US\n",
      "</script>\n",
      "<script type=\"IN/Share\"></script>\n",
      "\"\"\"\n",
      "    return HTML(code)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}