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     "source": [
      "Bayesian Methods for Hackers"
     ]
    },
    {
     "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>"
     ]
    },
    {
     "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>"
     ]
    },
    {
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     "input": [
      "social()"
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        "\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",
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    {
     "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": 1,
     "metadata": {},
     "source": [
      "Chapter 1"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "The Phiosophy of Bayesian Inference"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Bayesian inference differs from more traditional statistical inference by preserving _uncertainty_. Let's start thinking Bayesian. The Bayesian view interprets probability as a measure of believability in an event, that is, how confident are we in an event occurring. This is actually the natural interpretation of probability itself.\n",
      "\n",
      "Consider an alternative interpretation of probability: _Frequentist_, known as the more classical version of statistics, assumes that probability is the long-run frequency of events. For example, the _probability_ of plane accidents under a frequentist theory is interpreted as the _long-term frequency_ of plane accidents. This makes sense, but is difficult to understand when events have no long-term frequency of occurrences, for example presidential elections, which only happen once. Frequentists get around this by creating alternate realities and saying that across all these realities, the frequency of occurrences defines the probability.\n",
      "\n",
      "Bayesians, have a more intuitive approach. They interpret a probability as a measure of belief, or confidence, of an event occurring. Simply, a probability is a summary of an opinion. An individual who assigns a belief of 0 to an event has no confidence that it will occur; conversely, assigning a belief of 1 implies that they are absolutely certain of the event occurring. Beliefs between 0 and 1 allow of weightings of other outcomes. This definition agrees with the plane accident example. For having observed the frequency of plane accidents, an individuals belief should be equal to that frequency, excluding any outside information. Under this framework it is not meaningful to speak about probabilities (beliefs) of examples like the presidential outcome: how confident are you that candidate _A_ will win?\n",
      "\n",
      "Notice that assigning belief (probability) to an individuals implies that we can have different individuals that have different beliefs of events occurring, because they possess different _information_ about the world. This is very similar to what naturally is occurring. The existence of different beliefs (probabilities) does not mean anyone is wrong. Consider these examples:\n",
      "\n",
      "* Flip a coin and two people guess the result. We would both agree that the probability of Heads is 1/2. Assume then, that I peek at the coin. Now I know for certain what the result is: I assign a probability of 1.0 to either Heads or Tails (whichever it is). Now what is the other persons belief that the coin is Heads? Unless we know for certain the result, you would still assume a 1/2 probability. Thus we assign different probabilities to the result.\n",
      "\n",
      "* Your code either has a bug in it or not, but we don't know for certain, though we have a belief about the presence or absence of a bug.\n",
      "\n",
      "* A medical patient is presenting symptoms $x$, $y$, and $z$. There are a number of diseases that could be causing all of them, but only one disease is present. A doctor has beliefs about which disease, but a second doctor may have slightly different beliefs.\n",
      "\n",
      "Treating beliefs as probabilities is natural to humans. We use it constantly as we interact with the world and only see partial truths, but we gather evidence to form beliefs. Alternatively, we have been _trained_ to think of probability like a Frequentist.\n",
      "\n",
      "In traditional probability, we denote our belief about an event _A_ as $P(A)$. This quantity is called the _prior probability_.\n",
      "\n",
      "In Bayesian theory, similar to human nature, we update out beliefs after seeing evidence, even if the evidence is counter to what was initially believed. We denote this updated belief as $P(A|X)$, interpreted as the probability of $A$ given the evidence $X$. We called the updated belief the _posterior probability_ so as to contrast it with the prior probability. For example, consider the posterior probabilities (posterior beliefs) of the above examples, after observing some evidence $X$.\n",
      "\n",
      "1. $P(A)$ : The coin has a 50% chance of being Heads. $P(A|X)$: You look at the coin, observe heads has landed, denote this information $X$, and assign a probability 1.0 to Heads and 0.0 to Tails.\n",
      "\n",
      "2. $P(A)$ : This big, but complex code likely has a big in it. $P(A|X)$ The code passed all $X$ tests; there still might be a big, but its presence is less likely now.\n",
      "\n",
      "3. $P(A)$ : The patient could have any number of diseases. $(PA|X)$ : Performing a blood test generated evidence $X$, ruling out some of the possible diseases from consideration.\n",
      "\n",
      "In each example we did not completely discard the prior belief (probability) after seeing new evidence $X$, but we _re-weighted the prior_ to incorporate the new evidence.\n",
      "\n",
      "By introducing prior uncertainty about events, we are already admitting that any guess we make is potentially very wrong. After observing data, or other evidence, we update out beliefs, and our guess becomes less wrong. This is the flip side of the prediction coint, where we typically try to be _more right_ than _less wrong_."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Bayesian Inference In Practice"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If a Frequentist and Bayesian inference were programming functions, with inputs being statistical problems, then the two would be different in what they return. The frequentist function would return a number representing an estimate (typically a summary statistical like te sample average), whereas the Bayesian function would return _probabilities_. \n",
      "\n",
      "For example, in our debugging problem above: calling the frequentist function with the argument \"My code passed all $X$ tests; is my code bug-free?\" would return a _YES_. On the other hand, the Bayesian function would test: \"My code often has bugs. My code passed all $X$ tests; is my code bug-free?\" would return probabilities of _YES_ and _NO_. For example:\n",
      "\n",
      "> _YES_, with probability 0.8; _NO_, with probability 0.2\n",
      "\n",
      "Note the Bayesian function accepted an additonal argument: \"Often my code has bugs\". This parameter is the _prior_. By including the prior parameter, we are telling the funcion to include out belief about the situation. Technically this parameter in the Bayesian function is optional, but we will see excluding it has its own consequences.\n",
      "\n",
      "__Incorperating Evidence__\n",
      "\n",
      "As we acquire more and more evidence, our prior belief is slowly replaced by the new evidence. For example, if your prior belief is something rediculous, like \"I expect the sun to explode today\", and each day you are proved wrong, you would hope that any inference would correct you. Bayesian inference will correct this belief.\n",
      "\n",
      "Denote $N$ as the number of instances of evidence we possess. As we gather an _infinite_ amount of evidence, say as $N$ --> inifinity, out Bayesian results (0ften) align with frequentist results. Hence for large $N$, statistical inference is more or less objective. On the other hand, for small $N$, inference is much more _unstable_ frequentist estimates have more variance and larger confidence intervals. This is where Bayesian analysy excels. By introducing _uncertainty_ that reflects the instability of statistical inference of a small $N$ dataset.\n",
      "\n",
      "One may believe that for large $N$, one can be indifferent between the two techniques since they offere similar inference, and might lean towards the simpler frequentist methods. In this position, the authors offer a quote from Andrew Gelman (2005) <a href=''[1]></a>.\n",
      "\n",
      "> Sample sizes are never large. If $N$ is too small the get a sufficiently-precise estimate, you need to get more data (or make more assumptions). But once $N$ is 'large enough', you can start subdividing the data to learn more. For example: in a public opinion poll, once you have a good estimate for an entire country, you can estimate among men and women, and different age groups. $N$ is never enough because if it were \"enough\" you'd already be onto the next problem for which you need more data.\n",
      "\n",
      "__Are frequentist methods incorrect then? No.__\n",
      "\n",
      "Frequentist methods are still useful or state-of-the-art in many areas. Tools such as least squares linear regression, LASSO regression, and expectation-maximization algorithms are all powerful and fast. Bayesian methods compliment these techniques by solving problems that these approaches cannot, or supplimenting existing methods with more flexible models."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "A more formal definition of the Bayesian framework"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We are interested in beliefs, which can be interpreted as probabilities if we are thinking Bayesian. We have a _prior_ belief in event $A$, beliefs formed by previous information.\n",
      "\n",
      "Next, we observe our evidence. To continue the buggy-code example: if out code passes $X$ tests, we want to update our belief to incorporate this. We call the new updated belief the _posterior_ probability. Updating the belief is done via the following equation, known as Bayes Theorem, discovered by Thomas Bayes.\n",
      "\n",
      "$$ P(A|X) = \\frac{P(X|A) P(A)}{ P(X)} $$\n",
      "\n",
      "$$\\propto P(X|A)(P(A)$$\n",
      "\n",
      "This formula is not unique to Bayesian inference, but it is used in this context to connect prior probabilities $P(A)$ with an update posterior probability $P(A|X)$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example: Coin Flip"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Suppose, naively, that you are unsure about the probability of $heads$ in a coin flip. You believe that there is some true underlying ration, call it $p$, but have no prior opinion on what $p$ might be.\n",
      "\n",
      "We begin to flip a coin, and record the observations: either $H$ or $T$. This is our observed data. How does our inference change as we observe more and more data? More specifically, what do our posterior probabilities look like when we have little data, versus when we have lots of data.\n",
      "\n",
      "Below we plot this sequence of updating posterior probabilities as we observe increasing amount of data (coin flips)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\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': 14.0, 'axes.titlesize': 18,\n",
      "    'xtick.labelsize': 12.0, 'ytick.labelsize': 12.0}\n",
      "\n",
      "sns.set(context = 'poster', style = 'whitegrid', rc=rc)\n",
      "\n",
      "import scipy.stats as stats"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 170
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create some data\n",
      "dist = stats.beta\n",
      "n_trials = [0,1,2,3,4,5,8,15,50,500]\n",
      "data = stats.bernoulli.rvs(0.5, size = n_trials[-1])\n",
      "x = np.linspace(0,1,100)\n",
      "\n",
      "# Plot the data\n",
      "\n",
      "for k, N in enumerate(n_trials):\n",
      "    sx = plt.subplot(len(n_trials) / 2, 2, k+1)\n",
      "    plt.xlabel(\"$p$, probability of heads\") \\\n",
      "        if k in [0, len(n_trials) - 1] else None\n",
      "    heads = data[:N].sum()\n",
      "    y = dist.pdf(x, 1 + heads, 1 + N - heads)\n",
      "    plt.plot(x, y, label='observed %d tosses, \\n %d heads' % (N, heads))\n",
      "    plt.fill_between(x, 0, y, color='blue', alpha=0.4)\n",
      "    plt.vlines(0.5, 0, 4, color='k', linestyles='--', lw=1)\n",
      "    \n",
      "    leg = plt.legend()\n",
      "    leg.get_frame().set_alpha(0.4)\n",
      "    plt.subplots_adjust(wspace=None, hspace=0.4)\n",
      "    \n",
      "plt.suptitle('Bayesian updating of posterior probabilities',\n",
      "             y = 1.02)\n"
     ],
     "language": "python",
     "metadata": {},
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paVQTfMmoCXWlmuBLqM++c+5R59yxwU78POfcBudctnMucgKVhc65LOdcb+fc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\nL6nh5W9/dnX09Ro9U/pdRJA+6MKO68akWufruuue6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4AugIv6TSOzMpOU4l+xOWxU11p4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\nuf/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j5+l/X+2ga4fmNG9W9bGfQtQn28JaV7k6HUJURW5+IUm2OPj+XgF4uldvpduKuLu5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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x14bee1b10>"
       ]
      }
     ],
     "prompt_number": 171
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The posterior probabilities are represented by the curves, and our uncertainty is proportional to the width of the curve. Eventually as we observe more data, our probabilities will tighten closer and closer to the true value of $p = 0.5$ (marked by the dashed line).\n",
      "\n",
      "Note that at the start of these iterations the plots are not peaked at 0.5. There is no reason it should be, since we did not have a prior opinion of what $p$ was."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example: Bug, or just an unintended feature?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let $A$ denote the event that out code has __no bugs__ in it. Let $X$ denote the event that the code passes all debugging tests. For now, we leave the prior probability of no bugs as a variable, $P(A) = p$.\n",
      "\n",
      "We are interested in $P(A|X)$, i.e. the probability of no bugs, given our debugging tests $X$. To do this we need to compute some quantities.\n",
      "\n",
      "what is $P(X|A)$ : The probability that the code passes $X$ tests given there are no bugs? For a code with no bugs, this is equal to 1 since it will pass all tests.\n",
      "\n",
      "$P(X)$ is a bit trickier: The event $X$ can be divided into two possibilities, event $X$ occurring even though are code indeed _has_ bugs (denoted ~ $A$, spoken _not_ $A$), or even $X$ without bugs ($A$). $P(X)$ can be represented as:\n",
      "\n",
      "$$P(X) = P(X and A) + P(X and ~ A)$$\n",
      "\n",
      "$$=P(X|A)(P(A) + P(X | ~A)P(~A)$$\n",
      "$$=P(X|A)p + P(X | ~A)(1 - p)$$\n",
      "\n",
      "We have computed $P(X|A) above, yet not $P(X|~A), which is subjective: out code can pass tests but still have a bug in it, though the probability there is a bug present is reduced. This is dependent on the number of tests performed, the degree of complication in the tests, ect. We can be conservative and assign $P(X|~A) = 0.5. Then\n",
      "\n",
      "$$P(A|X) = \\frac{1p}{1p+0.5(1-p)}$$\n",
      "\n",
      "$$= \\frac{2p}{1+p}$$\n",
      "\n",
      "This is the posterior probability, What does it look like as a function of our prior?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p = np.linspace(0, 1, 50)\n",
      "plt.plot(p, 2 * p / (1 + p))\n",
      "plt.scatter(0.2, (2*0.2) / 1.2, s=140)\n",
      "plt.xlim(0, 1)\n",
      "plt.ylim(0, 1)\n",
      "plt.xlabel('Prior, $P(A) = p$')\n",
      "plt.ylabel('Posterior, $P(A|X)$, with $P(A) = p$')\n",
      "plt.title('Are there bugs in my code?')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 172,
       "text": [
        "<matplotlib.text.Text at 0x14c5a6f50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CREREmkyZ18fyTQd4c6El6+DJgLoeXdtxx+QBTBiZRES4VrUWaS5CJqEwxlwH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\nDnspPIAZoQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x13ce13710>"
       ]
      }
     ],
     "prompt_number": 172
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we see the gains in posterior probability when our prior probability, $p$, is low. If we set a prior probability at 0.2, that means there is a 20% chance that the written code is bug-free. Though, it would be more realistic to scale this value by the size of the code. Therefore, the updated belief (posterior probability after running the debugging script) is that my code is bug-free 0.33 or 33% of the time.\n",
      "\n",
      "We can chart this another way, since our prior $p$, is the probability that there are _no bugs_, $ 1 - p$ is the probability that there _are bugs_. Similarly, our posterior probability $P(A|X)$ is the probability that there is no bug _given we saw all the tests pass_, thus $1 - P(A|X)$ is the probability that there is a bug _given all tests passed_."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "color = [\"#9b59b6\", \"#3498db\"]\n",
      "prior = [0.2, 0.8]\n",
      "posterior = [1. /3, 2./3]\n",
      "plt.bar([0, 0.7], prior, alpha=0.7, width=0.25,\n",
      "        label='prior distribution', color=color[0])\n",
      "\n",
      "plt.bar([0 + 0.25, 0.7 + 0.25], posterior, alpha=0.7,\n",
      "        width=0.25, label='posterior distribution',\n",
      "        color=color[1])\n",
      "\n",
      "plt.xticks([0.2, 0.95], ['Bugs Absent', 'Bugs Present'])\n",
      "plt.ylabel('Probability')\n",
      "plt.legend(loc='upper left')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 183,
       "text": [
        "<matplotlib.legend.Legend at 0x14d7bd5d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/ZmmPHOTUsn9LpcdtgBOAO2OMh1O+9uCREEKbxi5OkiRJasnSHjlYDQystN0F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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x14d193810>"
       ]
      }
     ],
     "prompt_number": 183
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that after we observe $X$ occur, the probability of bugs being absernt increased. By increasing the number of tests, we can approach confidence (probability 1) that there are no bugs present."
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "<a target=\"_parent\" href=\"http://nbviewer.ipython.org/github/RMDK/IPython-Notebooks/blob/master/Machine%20Learning/Probability%20Distribution%20Review.ipynb\">Up Next: Review of Probability Distributions</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": 191,
       "text": [
        "<IPython.core.display.HTML at 0x14e49bc90>"
       ]
      }
     ],
     "prompt_number": 191
    },
    {
     "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": 3
    }
   ],
   "metadata": {}
  }
 ]
}