学术时间轴

Combining e-values using demi-supermartingales

Abstract
E-values provide a flexible way to quantify evidence in sequential testing, composite-null testing, and post-hoc significance decisions. In this talk, I will present a new method for combining multiple e-values. Under co-validity, a dependence condition weaker than independence, the normalized elementary symmetric polynomials of the e-values form a nonnegative demi-supermartingale. A Ville-type maximal inequality then validates the SymPol test and data-dependent optimization over a betting fraction, resolving conjectures of Wang—Zhao and Gaffke. I will explain the underlying stochastic-process argument and discuss applications to bounded-mean confidence intervals, exact fixed-sample KL-inf concentration, heterogeneous means and compound e-values.