Shiny

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# Shiny
### Colin Rundel
### 2019-11-25

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<img src="imgs/hex-shiny.png" width="50%" style="display: block; margin: auto;" />
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## Shiny

- is a framework for writing web apps in R

- easiest way to create interactive tools using R

- can be run locally in RStudio, hosted on RStudio's shinyapps.io or your own server, or even embedded in RMarkdown documents.

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## Shiny Resources

All of these can be found at RStudio's Shiny [homepage](https://shiny.rstudio.com/):

- Shiny Gallery - https://shiny.rstudio.com/gallery/

- Shiny Articles - https://shiny.rstudio.com/articles/

- Function Reference - https://shiny.rstudio.com/reference/shiny/1.4.0/

- Mastering Shiny [WIP] - https://mastering-shiny.org/

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## A "Fair" Coin and the Beta-Binomial model

Let's imagine a situation where I have a coin that I claim is fair, you are less certain - you can ask me to flip the coin `$n$` times and we will record the number of "heads" as `$x$`. After this experiment what should you believe about the fairness of my coin?

<br/>

We can model this using the conjugate beta-binomial model,

$$
`\begin{aligned}
\pi(p) &\sim \text{Beta}(\alpha, \beta) \\
x \,|\, p &\sim \text{Binom}(p, n)\\
\end{aligned}`
$$
it then follows that
$$
p\,|\,x \sim \text{Beta}(\alpha+x, \beta+N - x)
$$

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## Live Demo

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## Approximate Bayesian Computation (ABC)

Offered without any theory or proof, consider the following algorithm:

1. Sample `$m$` values from each of the given prior distribution(s), `$\boldsymbol{\theta}^{(m)}$`.

2. For each of the `$m$` draws, simulate the data from the assumed data generative process, `$\boldsymbol{x}^{(m)}$`.

3. If the simulated data is sufficient close to the observed data, keep `$\boldsymbol{\theta}^{(m)}$`.

4. The distribution of the kept `$\boldsymbol{\theta}^{(m)}$`s will approximate the posterior  distribution `$\boldsymbol{\theta}|\boldsymbol{x}$`.

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## Beta-Binomial ABC

Our particular use case provides a straight forward application of this method,

1. Draw from the prior:
```r
p = rbeta(m, alpha, beta)
```

2. Simulate the data: 
```r
x_sim = rbinom(m, n, p)
```

3. Keep the matches:
```r
abc_post = p[x_sim == x]
```

.center[
**Why do we care?**
]