I have a question about the interpretation of the posterior predictive checks implemented in the bayesplot package for R, especially the ppc_dens_overlay function. I understand the idea of just simulating data according the posterior predictive density using S posterior parameter draws. However, I do not fully understand what the difference between this approach and computing in-sample predictions is. In my opinion it is exactly the same, right? Therefore, using the ppc_dens_overlay function you basically plot the empirical density of the in-sample predictions for each of the S draws, right? Or am I confusing something right now? My last question then is why there is no scale at the y-axis using ppc_dens_overlay, see https://cran.r-project.org/web/packages/bayesplot/vignettes/graphical-ppcs.html. Can someone explain this to me?
Yes, in most situations, PPCs are just a plot of the in-sample prediction vs. observed value. Note that you can make predictions also for functions of observed data (e.g. maximum or even more complex stuff), so PPCs are not necessarily only for the actual predictions.
While I cannot speak for the developers of the package, I’d guess it is because it does not contain any useful information - we care whether the observed density is similar to the predicted, not about actual density estimates, so removing the numbers is less clutter.
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Sorry for the slow reply. As the developer of that function I can confirm that @martinmodrak is indeed correct!
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