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<h1 class="title">Chapter 2 Notes</h1>
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<p>Emanuel Rodriguez </p>
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<p>In this chapter we step through an example of “fake” vs “real” news to build a framework to determine the probability of real vs fake of a new news article titled “The President has a secret!”</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co"># libraries</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(bayesrules)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(dplyr)</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(fake_news)</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a>fake_news <span class="ot">&lt;-</span> tibble<span class="sc">::</span><span class="fu">as_tibble</span>(fake_news)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<p>What is the proportion of news articles that were labeled fake vs real.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>fake_news <span class="sc">|&gt;</span> <span class="fu">glimpse</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>Rows: 150
Columns: 30
$ title &lt;chr&gt; "Clinton's Exploited Haiti Earthquake ‘to Stea…
$ text &lt;chr&gt; "0 SHARES Facebook Twitter\n\nBernard Sansaric…
$ url &lt;chr&gt; "http://freedomdaily.com/former-haitian-senate…
$ authors &lt;chr&gt; NA, NA, "Sierra Marlee", "Jack Shafer,Nolan D"…
$ type &lt;fct&gt; fake, real, fake, real, fake, real, fake, fake…
$ title_words &lt;int&gt; 17, 18, 16, 11, 9, 12, 11, 18, 10, 13, 10, 11,…
$ text_words &lt;int&gt; 219, 509, 494, 268, 479, 220, 184, 500, 677, 4…
$ title_char &lt;int&gt; 110, 95, 96, 60, 54, 66, 86, 104, 66, 81, 59, …
$ text_char &lt;int&gt; 1444, 3016, 2881, 1674, 2813, 1351, 1128, 3112…
$ title_caps &lt;int&gt; 0, 0, 1, 0, 0, 1, 0, 2, 1, 1, 0, 1, 0, 0, 0, 0…
$ text_caps &lt;int&gt; 1, 1, 3, 3, 0, 0, 0, 12, 12, 1, 2, 5, 1, 1, 6,…
$ title_caps_percent &lt;dbl&gt; 0.000000, 0.000000, 6.250000, 0.000000, 0.0000…
$ text_caps_percent &lt;dbl&gt; 0.4566210, 0.1964637, 0.6072874, 1.1194030, 0.…
$ title_excl &lt;int&gt; 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0…
$ text_excl &lt;int&gt; 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0…
$ title_excl_percent &lt;dbl&gt; 0.0000000, 0.0000000, 2.0833333, 0.0000000, 0.…
$ text_excl_percent &lt;dbl&gt; 0.00000000, 0.00000000, 0.06942034, 0.00000000…
$ title_has_excl &lt;lgl&gt; FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE…
$ anger &lt;dbl&gt; 4.24, 2.28, 1.18, 4.66, 0.82, 1.29, 2.56, 3.47…
$ anticipation &lt;dbl&gt; 2.12, 1.71, 2.16, 1.79, 1.23, 0.43, 2.05, 1.74…
$ disgust &lt;dbl&gt; 2.54, 1.90, 0.98, 1.79, 0.41, 1.72, 2.05, 1.35…
$ fear &lt;dbl&gt; 3.81, 1.90, 1.57, 4.30, 0.82, 0.43, 5.13, 4.25…
$ joy &lt;dbl&gt; 1.27, 1.71, 1.96, 0.36, 1.23, 0.86, 1.54, 1.35…
$ sadness &lt;dbl&gt; 4.66, 1.33, 0.78, 1.79, 0.82, 0.86, 2.05, 1.93…
$ surprise &lt;dbl&gt; 2.12, 1.14, 1.18, 1.79, 0.82, 0.86, 1.03, 1.35…
$ trust &lt;dbl&gt; 2.97, 4.17, 3.73, 2.51, 2.46, 2.16, 5.13, 3.86…
$ negative &lt;dbl&gt; 8.47, 4.74, 3.33, 6.09, 2.66, 3.02, 4.10, 4.63…
$ positive &lt;dbl&gt; 3.81, 4.93, 5.49, 2.15, 4.30, 2.16, 4.10, 4.25…
$ text_syllables &lt;int&gt; 395, 845, 806, 461, 761, 376, 326, 891, 1133, …
$ text_syllables_per_word &lt;dbl&gt; 1.803653, 1.660118, 1.631579, 1.720149, 1.5887…</code></pre>
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<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>fake_news <span class="sc">|&gt;</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(type) <span class="sc">|&gt;</span> </span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">summarise</span>(</span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a> <span class="at">total =</span> <span class="fu">n</span>(),</span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a> <span class="at">prop =</span> total <span class="sc">/</span> <span class="fu">nrow</span>(fake_news)</span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a> ) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code># A tibble: 2 × 3
type total prop
&lt;fct&gt; &lt;int&gt; &lt;dbl&gt;
1 fake 60 0.4
2 real 90 0.6</code></pre>
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<p>If we let <span class="math inline">\(B\)</span> be the event that a news article is “fake” news, and <span class="math inline">\(B^c\)</span> be the event that a news article is “real”, we can write the following:</p>
<p><span class="math display">\[P(B) = .4\]</span> <span class="math display">\[P(B^c) = .6\]</span></p>
<p>This is the first “clue” or set of data that we have to build into our framework. Namely, majority of articles are “real”, therefore we could simply predict that the new article is “real”. This updated sense or reality now becomes our priors.</p>
<p>Getting additional data, and updating our priors, based on additional data.</p>
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