Posterior predictive check question

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Hi @cluhmann ,

I would like to ask one additional question in the context of the above discussion.

As we have seen above, there are actuelly three sources of uncertainty when generating the plot for the posterior predictive check:

  1. The estimated mu is drawn from the posterior.
  2. With this mu, a predictive sample is drawn from the likelihood.
  3. The number of these draws is limited to the number of observations that was given to the likelihood for sampling of the posterior.

What I now asked myself: 1) and 3) are both strongly dependend on the number of observations. When the number of observations is low (like 10 in your example), the spread of the posterior for mu should be much wider then, say, the spread in case of 10000 observations.

So, the uncertainty that comes from the low number of observations is actually already represented in the posterior.

Isn’t then the additional limitation to 10 samples for generating one kde in the ppc_plot again emphasizing this uncertainty which is already represented, leading to an exaggeration of this uncertainty? Or is this justified by some well grounded considerations?

Best regards
Matthias