MMP.13:6 - Bias-Annotation
The worked laws are simple enough for exact calculations. Real records can have selection, dependence, weak identification or model mismatch that a convenient binomial or normal family conceals. The resulting uncertainty is conditional on the assumptions represented; it does not automatically include an omitted mechanism.
Bayesian and frequentist results are compared by the conclusions they support. A narrower interval alone cannot rank different probability meanings. The choice of prior, coverage domain and receiving target is part of the inference, even when software supplies defaults.