Shiny
Lecture 18
Shiny
Shiny is an R package that makes it easy to build interactive web apps straight from R. You can host standalone apps on a webpage or embed them in R Markdown documents or build dashboards. You can also extend your Shiny apps with CSS themes, htmlwidgets, and JavaScript actions.
Shiny App
Server
+
⇄
Client / Browser
+ +
Anatomy of an App
Sidebar layout
Multi-row layout
Other layouts
Tabsets
- see
tabsetPanel()
- see
Navbars and navlists
See
navlistPanel()and
navbarPage()
Dashboards
Shiny Widgets Gallery
A brief widget tour
App background
I’ve brought a coin with me to class and I’m claiming that it is fair (equally likely to come up heads or tails).
I flip the coin 10 times and we observe 7 heads and 3 tails, should you believe me that the coin is fair? Or more generally what should you believe about the coin’s fairness now?
Model
Let \(y\) be the number of successes (heads) in \(n\) trials then,
Likelihood: \[ \begin{aligned} y|n,p &\sim \text{Binom}(n,p) \\ f(y|n,p) &= {n \choose y} p^y(1-p)^{n-y} \\ &= \frac{n!}{y!(n-y)!} p^y(1-p)^{n-y} \end{aligned} \]
Prior: \[ \begin{aligned} p &\sim \text{Beta}(a,b) \\ \pi(p|a,b) &= \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} p^{a-1} (1-p)^{b-1} \end{aligned} \]
Posterior
From the definition of Bayes’ rule:
\[ \begin{aligned} f(p|y,n,a,b) &= \frac{f(y|n,p)}{\int^\infty_{-\infty} f(y|n,p) \, dp} \pi(p|a,b) \\ &\propto f(y|n,p) \, \pi(p|a,b) \\ \end{aligned} \]
We then plug in the likelihood and prior and then simplify by dropping any terms not involving \(p\),
\[ \begin{aligned} f(p|y,n,a,b) &\propto \left( \frac{n!}{y!(n-y)!} p^y(1-p)^{n-y} \right) \left(\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} p^{a-1} (1-p)^{b-1}\right) \\ &\propto \Big( p^y(1-p)^{n-y} \Big) \Big( p^{a-1} (1-p)^{b-1}\Big) \\ &\propto p^{y+a-1} (1-p)^{n-y + b-1} \end{aligned} \]
Posterior distribution
Based on the form of the density we can see that the posterior of \(p\) must also be a Beta distribution with parameters,
\[ p|y,n,a,b \sim \text{Beta}(y+a, n-y + b) \]
Sta 523 - Fall 2023