Live demo
Open this example in Shinylive
This example uses two interactive priors for a Normal likelihood:
\[ y_i \mid \mu, \sigma^2 \sim \mathcal{N}(\mu, \sigma^2), \]
\[ \mu \sim \mathcal{N}(m_0, s_0^2), \qquad \sigma^2 \sim \operatorname{InverseGamma}(\alpha_0, \beta_0). \]
The posterior is proportional to likelihood times priors:
\[ p(\mu, \sigma^2 \mid y) \propto p(y \mid \mu, \sigma^2)\, p(\mu)\, p(\sigma^2). \]
The app reveals observations from the real mtcars$mpg
data, evaluates the posterior on a small deterministic grid, then
integrates the joint surface numerically to obtain marginal posterior
densities for \(\mu\) and \(\sigma^2\). This keeps the example
transparent and avoids an MCMC dependency.
The two priors are ordinary modist_input() controls:
modist_input(
"mu_prior",
family = "normal",
value = list(mu = 20, sigma = 5)
)
modist_input(
"variance_prior",
family = "inversegamma",
value = list(alpha = 5, beta = 120)
)Run it locally with:
shiny::runApp(
system.file("examples/normal-priors", package = "shinymodist")
)