New preprint on model/algorithm validation with SBC - It is stronger than you thought!

Me along with @hyunji.moon, @Dashadower, @paul.buerkner, @nhuurre, Kateřina Faltejsková, @andrewgelman and @avehtari have a new preprint on SBC: Simulation-Based Calibration Checking for Bayesian Computation: The Choice of Test Quantities Shapes Sensitivity.

For those, who are unaware, simulation-based calibration checking (SBC) is a method where you use simulated datasets to verify that you implemented you model correctly and/or that your sampling algorithm work. It has been known and used for a while, but was considered to have a few shortcomings, which we try to address. See the preprint or the documentation for the SBC package for a precise description of how that works.

The gist of our preprint is that strength of SBC depends on the choice of “test quantities” for which you compute ranks. The default approach is to take all individual parameter values. This is already a very useful check, but it leaves a big class of bugs you can’t detect (e.g. when posterior is just the prior distribution). However, when you add derived test quantities, combining the parameters with the simulated data, you can (in theory) detect any problem! (Yaaaay!) But in theory you may need infinitely many quantities :-(.

In practice, it seems to be quite sufficient to add just a few additional test quantities beyond the default. In particular, our experience as well as theoretical considerations indicate that the model likelihood is very sensitive. The power of SBC is still limited by the number of simulated datasets you can reasonably fit which primarily limits how big discrepancies can go undetected.

More generally, we provide a firmly grounded theoretical analysis of SBC which will hopefully help others to build better intuition on how and why it works in practice. Notably, we make it clear that SBC does not check whether “data-averaged posterior equals the prior” as is sometimes claimed in the literature (and as I also was convinced just a couple months ago :-D )

The SBC package supports all of the ideas discussed in the preprint. I personally now use SBC for almost all my Stan work from the get go - although there is some extra work to setup SBC, you end up detecting bugs early and thus save time in the long run. If you want to see an example of simulation-driven model development workflow, check out the Small model implementation workflow

Looking forward to you feedback on the preprint (as well as the package).