Sequential statistics by trading: e-processes and coordinated traders

The goal of sequential statistics is to draw inference from data that is gathered gradually through time. E-processes (`E’ for `Evidence’) form the basis of a recent approach to this problem that simultaneously produces strong statistical error bounds and high statistical power. This method has an interesting connection with mathematical finance: it admits an equivalent description in terms of coordinated traders in a fictitious financial market, each of whom attempts to profit from the view that certain statistical (null) hypotheses are false while other (alternative) hypotheses are true. I will discuss some problems where this perspective leads to new procedures for sequential testing. This talk is based on work with Philippe Casgrain, Wouter Koolen, Aaditya Ramdas, Johannes Ruf, and Johanna Ziegel.