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R/misc/beta-binomial.qmd

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+---
+title: "Beta-Binomial Bayesian Model Example"
+author: "Emanuel Rodriguez"
+execute:
+    message: false
+    warning: false
+format:
+    html:
+        monofont: "Cascadia Mono"
+        highlight-style: gruvbox-dark
+        css: styles.css
+        callout-icon: false
+        callout-apperance: simple
+        toc: false
+        html-math-method: katex
+---
+
+## Introduction
+
+In this short article I will try to put together a set of notes to 
+go over the Beta-Binomial Bayesian Model. The example used here is pretty
+trivial but so is this model so :shrug: 
+
+## When to use the Beta-Binomial? 
+
+The situations it makes sense to use the Beta-Binomial Model (BBM) are
+cases where we have some conditional dependence between a random 
+variable $Y$ and a continuous parameter $\pi \in [0, 1]$. Where $Y$ is the number of successes in $n$ independent trials, each with a probability of 
+success $\pi$.
+
+For the sake of these notes, let us start by setting up an example that will
+allow us to illustrate the implementation of this model. Suppose there
+is a slot machine manufacturer who recently was accused of embedding software 
+into the hardware that would cause more losses than usual to players.
+To be allowed to continue selling machines to casinos, they must go through a 
+series of inspections. The body governing the sale of these machines has tasked 
+us to determine whether or not the software has been completely removed or if, 
+instead, the company refined the bias to make it less noticeable.  
+
+
+## What we already know
+
+The set of facts that we can put together to build a known distribution
+