Beta-Binomial prior elicitation

Live demo

Open this example in Shinylive

The app runs entirely in the browser with webR; no local R installation is required for the demo.

A Beta input provides a direct way to shape a prior over a probability.

If the prior is

$$p \sim \mathrm{Beta}(\alpha, \beta)$$

and we observe $x$ successes in $n$ Bernoulli trials, the conjugate posterior is

$$p \mid x,n \sim \mathrm{Beta}(\alpha + x, \beta + n - x).$$

The example uses bslib::page_sidebar(): the editable prior and trial controls live in the sidebar, while the prior/posterior plot is shown in a bslib::card().

The Shiny input provides the current alpha and beta values:

bslib::sidebar(
  modist_input(
    "prior",
    family = "beta",
    value = list(alpha = 2, beta = 2)
  ),
  sliderInput("n", "Trials", min = 1, max = 100, value = 20),
  sliderInput("x", "Successes", min = 0, max = 20, value = 12)
)

The prior and posterior curves need only base R’s dbeta().

Run the complete example with:

shiny::runApp(
  system.file("examples/bayes-beta-binomial", package = "shinymodist")
)