This paper discusses a counterpart of conformal prediction for e-values, conformal e-prediction. Conformal e-prediction is conceptually simpler and had been developed in the 1990s as precursor of conformal prediction. When conformal prediction emerged as result of replacing e-values by p-values, it seemed to have important advantages over conformal e-prediction without obvious disadvantages. This paper re-examines relations between conformal prediction and conformal e-prediction systematically from a modern perspective. Conformal e-prediction has advantages of its own, such as the ease of designing conditional conformal e-predictors and the guaranteed validity of cross-conformal e-predictors (whereas for cross-conformal predictors validity is only an empirical fact and can be broken with excessive randomization). Even where conformal prediction has clear advantages, conformal e-prediction can often emulate those advantages, more or less successfully.

翻译：本文讨论了保形预测在e值上的对应方法——保形e预测。保形e预测在概念上更为简单，早在20世纪90年代就已作为保形预测的前身被提出。当保形预测通过将e值替换为p值而出现时，它似乎比保形e预测具有重要优势且无明显劣势。本文从现代视角系统性地重新审视了保形预测与保形e预测之间的关系。保形e预测具有其独特优势，例如易于设计条件保形e预测器，以及交叉保形e预测器具有理论有效性保证（而交叉保形预测器的有效性仅为经验事实，且可能因过度随机化而失效）。即使在保形预测具有明显优势的领域，保形e预测通常也能或多或少成功地模拟这些优势。