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Combining e-values using demi-supermartingales

  • Speaker: Jiahao Ming(University of Waterloo)

  • Time: Sep 2, 2026, 10:30-11:30

  • Location: Room M714, College of Science Building

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.