45 lines
1.6 KiB
Plaintext
45 lines
1.6 KiB
Plaintext
---
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title: "Beta-Binomial Bayesian Model Example"
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author: "Emanuel Rodriguez"
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---
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## Introduction
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In this short article I will try to put together a set of notes to
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go over the Beta-Binomial Bayesian Model. The example used here is pretty
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trivial but so is this model so :shrug:
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## When to use the Beta-Binomial?
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The situations it makes sense to use the Beta-Binomial Model (BBM) are
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cases where we have some conditional dependence between a random
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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
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success $\pi$.
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For the sake of these notes, let us start by setting up an example that will
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allow us to illustrate the implementation of this model. Suppose there
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is a slot machine manufacturer who recently was accused of embedding software
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into the hardware that would cause more losses than usual to players.
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To be allowed to continue selling machines to casinos, they must go through a
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series of inspections. The body governing the sale of these machines has tasked
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us to determine whether or not the software has been completely removed or if,
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instead, the company refined the bias to make it less noticeable.
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## What we already know
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The set of facts that we can put together to build a known distribution
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