After looking again into some singular draws from the prior predictive, I have to add a question.
I now recreated the model with 1000 observations. Prior is still a normal with mean 0 and sigma 2.
When I now to plot_ppc, the following is the result:
Let us pull out one of these draws, which contains 1000 samples:
Seeing, this, I realized that these cannot be 1000 independent samples of a Normal(0, 2).
It somehow looks like the sampler “got stuck” in the area of a mean = 5 Normal. I still don’t understand how this can happen.