Log-optimal anytime-valid E-values

We consider the problem of measuring statistical evidence against a composite null hypothesis. base our approach on concept an E-value, which measures by multiplication factor achieved engaging in bets that are fair under null. adopt log-optimality criterion for choosing among all possible E-values, was considered earlier fixed sample size. extend these ideas to sequential testing optional stopping, revisiting anytime-valid E-values. Our main contribution is formulation criterion. study its properties, and work out examples analytically computationally.