A test martingale is a running evidence score that, if nothing has changed, is not expected to grow — the honest core of an e-process.
Also known as: martingale / test supermartingale
A test martingale is a running evidence score that starts at one and, under the assumption that nothing has changed, has no upward drift — it can wander, but it is not expected to climb. The underlying idea is the martingale, the mathematical shape of a fair game: whatever has happened so far, your expected next value is exactly where you stand now. So if a test martingale does climb and keeps climbing, that is genuine evidence something shifted.
This is what makes an alarm trustworthy instead of trigger-happy. Because a test martingale cannot be expected to grow when all is well, a large value is hard to produce by luck — and exactly how hard is pinned down by Ville's inequality.
Every e-process is, at heart, a test martingale (or a supermartingale, the one-sided version). It is the object that turns 'this metric feels off' into a number you can bound and act on.
ValidAnytime turns these ideas into a live alarm you can trust — valid no matter how often you look. Prove it on your own data, free.