Säilynoja et al. (2026)

The big idea¶

Prior SBC (Talts et al. (2018)) checks that an inference algorithm is calibrated across the whole prior. But the prior can place most of its mass where inference is easy while a small problematic region — the one that actually matters for a specific observed dataset — is washed out in the prior average (their Fig. 1: two canceling biases that prior SBC cannot see). Posterior SBC conditions the whole calibration check on the observed data y_obs: it draws ground truths from the posterior π(θ|y_obs), generates data from them, refits, and tests the PIT values for uniformity. Using the sequential-Bayesian-update view (their Eq. 3), this is the right check when you care about trusting the inference on the dataset you actually have, and it remains valid under model misspecification. It is operationalized for both MCMC and amortized (neural) Bayesian inference, where it serves as a cheap default trustworthiness diagnostic.

Use in progenax¶

Not yet used — recorded as a future direction. The current gravoturb AC18 is prior SBC (calibration over the BM19 prior); its documented honest-scope caveat (“validates the engine under the model, averaged over the prior”) is exactly the limitation posterior SBC addresses. A natural follow-up beyond workstream ① would add a posterior-SBC check conditioned on a specific mock cluster’s data — more honest for “trust the inferred (ℳ, α, β) for this cluster.” This paper uses the Säilynoja et al. (2022) ECDF-difference graphical test (via bayesplot); it does not re-derive the simultaneous-band construction, so the F2.5 figure is grounded in the 2022 paper, not this one.

Notes¶

• Code for the paper’s experiments: github.com/TeemuSailynoja/posterior-sbc (R / bayesplot; cross-check only — the gravoturb figures use the arviz array layer).

• Posterior SBC is still embarrassingly parallel (independent refits) and inherits SBC’s honest scope: it certifies self-consistency of the inference, not that the generative model matches reality.