R2 D2

Shiny R2-D2 app: https://solviro.shinyapps.io/R2D2_shiny/

\begin{align*}
  y_i &\sim \lognormal(\mu_i, \sigma) \\
  \mu_i &= \beta_0 + \sum_{k=1}^{16}x_{k,i}\beta_k \\
  \beta_0 &\sim p(\beta_0) \\
  \sigma &\sim p(\sigma) \\
  \beta_k &\sim \normal(0, (\frac{\sigma^2}{\sigma^2_{x_k}} \phi_k \tau^2)^{1/2}) \\
  R^2 &\sim \betadist(s_1, s_2) \\
  \phi &\sim \dirichlet(1,\dots,1) \\
  \tau^2 &= \frac{R^2}{1-R^2}
\end{align*}

$$ \begin{align*} y_i &\sim p(\mu_i, \sigma) \\ \mu_i &= \beta_0 + \sum_{k=1}^{16}x_{k,i}\beta_k \\ \beta_0 &\sim p(\beta_0) \\ \sigma &\sim p(\sigma) \\ \beta_k &\sim \normal(0, (\frac{\sigma^2}{\sigma^2_{x_k}} \phi_k \tau^2)^{1/2}) \\ R^2 &\sim \betadist(s_1, s_2) \\ \phi &\sim \dirichlet(1,\dots,1) \\ \tau^2 &= \frac{R^2}{1-R^2} \end{align*} $$