When you say ‘algorithm’, surely you don’t just mean HMC, ADVI, or INLA? My impression was that SBC is also an important part of model development, that is, “a critical part of a robust Bayesian workflow.” I took this phrase to mean that we should use SBC when developing models. Certainly SBC should work if the data generating process matches the model specification. If it doesn’t then there is a bug in the model specification. However, the use of SBC seems to extend beyond this narrow situation.
Here’s an example. My interpretation is that SBC verified that a subset of the parameter space is well calibrated.
Given that there are situations where the data generating process is somewhat different from the parameter recovery model, SBC seems like a useful procedure to investigate whether the posterior will be accurate or not. Why would SBC not help here?
Posterior predictive checks and loo are great once you actually have real data, but SBC seems like a useful procedure to validate your model before you have data.