trees

book/_build/html/Homework05lab.html

@@ -190,6 +190,7 @@
 <li class="toctree-l1"><a class="reference internal" href="correlation.html">Correlation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="regression.html">Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="probability.html">Probability</a></li>
+<li class="toctree-l1"><a class="reference internal" href="bayes.html">Probability II</a></li>
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book/_build/html/Rbasics.html

@@ -76,7 +76,7 @@
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
     <link rel="next" title="Selected Solutions" href="solutions.html" />
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@@ -191,8 +191,16 @@
 <li class="toctree-l1"><a class="reference internal" href="normal.html">Normal Distribution</a></li>
 <li class="toctree-l1"><a class="reference internal" href="correlation.html">Correlation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="regression.html">Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="probability.html">Probability</a></li>
+<li class="toctree-l1"><a class="reference internal" href="bayes.html">Probability II</a></li>
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Google Sheets (optional)</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="gsheets.html">Overview</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="gregression.html">Regression</a></li>
+</ul>
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@@ -202,12 +210,6 @@
 
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@@ -674,7 +676,7 @@ <h1>Comments<a class="headerlink" href="#comments" title="Permalink to this head
 
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book/_build/html/StatwrapRegression.html

@@ -194,6 +194,7 @@
 <li class="toctree-l1"><a class="reference internal" href="correlation.html">Correlation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="regression.html">Regression</a></li>
 <li class="toctree-l1"><a class="reference internal" href="probability.html">Probability</a></li>
+<li class="toctree-l1"><a class="reference internal" href="bayes.html">Probability II</a></li>
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book/_build/html/_sources/bayes.md

@@ -0,0 +1,37 @@
+(bayes)=
+# Probability II
+
+```{admonition} Important Readings
+:class: seealso
+- {cite}`tijms2012understanding`, Chapter 6
+- {cite}`strogatz2010chances`
+```
+
+In this section, we leave the main textbook to learn Bayes' Theorem. This helps provide a foundation for further coursework in Bayesian statistics or just help you interact with nerdy people who talk about "Bayesian updating" in response to new information. Bayes' Theorem helps solve for a conditional probability $\mathbb{P}(A \mid B)$ given some other information. This involves "updating" because after observing $B$, the probability of $A$ changes from $\mathbb{P}(A)$ to $\mathbb{P}(A \mid B)$. The unconditional is a prior belief and the conditional probability is a posterior belief. Bayesian probabilities and statistics are important in any kind of environment where information is gathered. For example, medical doctors use Bayes' Theorem to assess the chance of a disease ($A$) given a particular test result ($B$). 
+
+Nothing in this section will require events to be independent. 
+
+
+## Chance Trees
+
+A probability tree helps organize information regarding conditional probabilities or almost anything that involves the general multiplication rule. 
+
+
+```{figure} images/tikz/generaltree.svg
+---
+width: 80%
+name: generaltree
+---
+A generic chance tree.
+```
+
+And here is something more concrete. For English words of Latin or French origin, the letter Q is always followed by a U. This means if we know that such a word starts with Q, the conditional probability of the second letter being U is <span style="color: #006400;">1</span> (100%). However, if the first letter is not Q, a U isn't very likely. If second letters are drawn randomly for non-Q words, this probability would be <span style="color: #0000CD;">1/26</span>. We'll also assume, for simplicity, that there is a <span style="color: #FFA500;">1/26</span> probability that a word starts with Q.
+
+
+```{figure} images/tikz/Qwordtree.svg
+---
+width: 80%
+name: Qwordtree
+---
+Trees are especially helpful when the probability of a second event (like the letter U) depends on the first event (the previous letter being Q or not Q).
+```

book/_build/html/_sources/probability.md

@@ -3,7 +3,7 @@
 
 ```{admonition} Important Readings
 :class: seealso
-- {cite}`freedman2007statistics`, Chapter 13, 14
+- {cite}`freedman2007statistics`, Chapters 13, 14, 15
 ```
 
 ## Probabilities