Rina Foygel Barber et al. 2023 introduces methods for conformal prediction that do not rely on this assumption and defines the coverage gap to quantify loss in quality relative to when this assumption is met. For 10 points each:
[10m] Name this property of a sequence of random variables whose joint distribution is invariant under their permutation. This property is notably possessed by Pólya urn models and sampling without replacement.
ANSWER: exchangeability [accept word forms; prompt on word forms interchangeable]
[10e] Two answers required. Exchangeability is similar to, and implied by, these two commonly assumed properties of observations. You can give the three-letter acronym for these two properties that is often written above a tilde.
ANSWER: independent AND identically distributed [or i·i·d]
[10h] Exchangeability is justified as an assumption for many statistical models by this statement. By this statement, random variables are exchangeable if and only if they are conditionally independent with respect to a latent variable.
ANSWER: de Finetti’s representation theorem [prompt on representation theorem]
<David Bass, Other Science - Mathematics>