Covariate shift assumption — untestability motivates retreat to → Partially specified models

The paper treats these as successive fallback positions, not parallel options. Covariate shift buys reusable training data and retrained models cheaply, but only by assuming p(y|x) is identical across training and test — an assumption the paper flags as "very strong and also untestable," which it calls "particularly problematic from a safety perspective, since it could lead to silent failures" (concrete-problems, §"Well-specified models: covariate shift and marginal likelihood.", p. 17). Partially specified models respond directly to that untestability, not to a performance shortfall: rather than committing to one exact invariant across the whole distribution and hoping it holds, they commit to assumptions about only some aspects of the distribution, of the analyst's choosing, so what must be checked is smaller and more explicit. The move trades the scope of the guarantee for the ability to know, in principle, whether the assumption underlying it actually held.