Logic of Statistical Inference: Reasoning with E-Values

Inference with e-values is attracting increasing attention in statistics. We show that e-values can be embedded in two recent logical frameworks for statistical inference: a dynamic epistemic framework centred on learning from observation streams, and a rejection-based framework centred on non-monotonic inference. For the former we show that e-value-based plausibility maps satisfy the key learnability conditions of [3]. For the latter, we show that a natural logarithmic transform of canonical e-values yields a rejection score in the sense of [2] and relate it directly to the plausibility scores of the dynamic framework.