Hierarchical Bayesian inference in Michael Rescorla's realist cognitive science presupposes more than local Bayesian success. Perception and cognition may involve causally relevant credal states that are updated sequentially and reused in later inference and decision-making, but such reuse also requires that the locally Bayesian stages be integrable into a single global evidential space. Drawing on a local/global distinction developed elsewhere under the headings of local Bayes charts, descent, and obstruction, we argue that local Bayesian coherence does not by itself guarantee global Bayesian integration. In hierarchical settings, the local quotients that make Bayesian updating well behaved may fail to descend to a common public structure. When that happens, the system need not be non-Bayesian or irrational; it may instead exhibit a coherent but globally non-affine evidential order. The payoff is twofold: we make explicit a no-obstruction assumption built into many hierarchical Bayesian models, and we show that approximate Bayes can sometimes reflect structural compression rather than only computational shortfall, noise, or resource limitation.
Lorand Bruhacs (Wed,) studied this question.