54 lines
1.6 KiB
Plaintext
54 lines
1.6 KiB
Plaintext
---
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title: "Chapter 3 Beta-Binomial Bayesian Model Notes"
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author: "Emanuel Rodriguez"
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monofont: "Cascadia Mono"
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css: styles.css
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---
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```{r}
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library(bayesrules)
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library(tidyverse)
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```
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The chapter is set up with an example of polling results. We are put into
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the scenario where we are managig the campaing for a candidate. We know
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that on average her support based on recent polls is around 45%. In the
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next few sections we'll work through our Bayesian framework and incorporate
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a new tool the **Beta-Binomial** model. This model will take develop a
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continuous prior, as opposed to the discrete one's we've been working with
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so far.
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## The Beta prior
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:::{.callout-note}
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## Probability Density Function
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Let $\pi$ be a continuous random variable with probability density
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function (pdf) $f(\pi)$. Then $f(\pi)$ has the following properties:
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1. $f(\pi) \geq 0$
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2. $\int_{\pi}f(\pi)d\pi = 1$ (this is analogous to $\sum$ in the case of pmfs)
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3. $P(a < \pi < b) = \int_a^bf(\pi)d\pi$ when $a\leq b$
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:::
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:::{.callout-tip icon="true"}
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a quick note on (1) above. Note that it does not place a restriction on
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$f(\pi)$ being less than 1. This means that we can't interpret values of
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$f$ as probabilities, we can however use to interpret plausability of
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two different events, the greater the value of $f$ the more plausible.
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To calculate probabilities using $f$ we must determine the area under the
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curve it defines, as shown in (3).
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:::
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