Tutorial for Posterior Predictive Check

[LouisRouillard]

As a quick and easy inference diagnosis, a tutorial showing how the existing sbi plotting capabilities can be used to perform a Posterior Predictive Check (PPC).

[LouisRouillard]

Is there any formal reference for a PPC I should be using ?

[LouisRouillard]

I wonder if shifting x_o in the end instead of simulating a bad x_PP is not confusing, I can change it easily if it is the case.

[janfb]

great, thanks for this PR @LouisRouillard !

I think this looks good already! A couple of comments:

• in pair plot you can pass upper="scatter" and scatter_offdiag=dict(...) for scatter kwargs to show posterior samples as scatter plot, which could be more intuitive here.
• you can also pass the style for the points marker with, e.g., points_offdiag=dict(marker='+', ms=10),
• in general, there are tons of options for pair plot, you find a overview in the default here.
• just a small thing: I would prefer lower-case variance name, e.g., x_pp instead of x_PP

[janfb]

I think the error case is good to show and it's fine to manipulate x directly instead of constructing a misspecified one. At this point, and as a general remark at the end you could say that one would check for this failure mode by running prior predictive checks.

[LouisRouillard]

Should be ready for merge

[michaeldeistler]

Thanks a lot!