From the perspective of Bayesian cognition, it seems rather reasonable to separate the ways we update beliefs into two categories (i) actual experiences, captured by the dataset $D$ and its induced posterior $\pi(\theta\mid D)$, versus (ii) “what-if?” queries, captured by the hypothetical member $X_N$ and the posterior distribution over $X_{N,1}$ given $\lbrace X_{[N,2]} = r \rbrace$, where $\theta$ is held at its posterior from actual observations $D$.

From the statistical perspective, no standard taxonomy exists that can differentiate between cases (i) and (ii). Borrowing terminology from Tenenbaum, I think these type of questions are characteristic of the Bayesian theme of “learning as inference”. Directly applying the Bayes Rule makes it easy to conflate “structure learning” with “strength” or “parameter estimation”. The question in this post can then be reduced into (i) taxonomizing the *type* of observations a Bayesian reasoner can encounter, and (ii) deciding what parts of the hierarchy (structure/parameter/etc) are updated in light of the different observation types.