(marginal) PPD plots

[mattansb]

Currently, the ppd_* functions are essentially the ppc_* functions without the y (observed data).
However, this isn't "the" (marginal) PPD - it shows individual replications:

library(bayesplot)
library(ggplot2)

set.seed(20260225)
mu_posterior <- rnorm(100, mean = 3, sd = 1)
sigma_posterior <- rgamma(100, shape = 2, rate = 1)

ypred <- t(mapply(rnorm, mu_posterior, sigma_posterior, n = 50))

ppd_dens_overlay(ypred) + 
  ggtitle("Replications of the posterior predictive distribution")

ppd_dens_overlay(ypred) +
  geom_density(aes(group = NA), linewidth = 1) +
  ggtitle("Replications of the posterior predictive distribution + marginal PPD")

^{Created on 2026-02-25 with reprex v2.1.1}

It would be useful to allow the ppd_* functions to show the PPD (in addition to or instead of the individual replications).

E.g., this last plot (IMO) provides a good visualization of the epistemic vs aleatoric uncertainty in the PPD.

[jgabry]

Thanks for opening the issue. I agree this would be useful. What do you think about a show_marginal argument that defaults to FALSE in order to not change the default behavior that has been there for a while?

[tjmahr]

What about something like

ppd_dens_overlay(ypred) + 
  geom_density(
    aes(group = y_id), 
    color = bayesplot::color_scheme_get(i = 5)[["dark"]]
  )

ypred is s draws by n observations. We have one light density blue per draw (row). What I added here is one dark blue per column which is the posterior predictive distribution for a single observation.

[tjmahr]

My plot might be more of "something to put in the examples".