Measuring Evidence against Exchangeability and Group Invariance with E-values

Understand

We study e-values for quantifying evidence against exchangeability and general invariance of a random variable under a compact group.

• We start by characterizing such e-values, and explaining how they nest traditional group invariance tests as a special case.
• We show they can be easily designed for an arbitrary test statistic, and computed through Monte Carlo sampling.
• We prove a result that characterizes optimal e-values for group invariance against optimality targets that satisfy a mild orbit-wise decomposition property.