Anytime-Valid Inference

Anytime-valid inference studies how to make trustworthy statistical decisions when data are inspected repeatedly and the time to stop is chosen based on what has been observed. It replaces fixed-horizon tests with tools such as e-values and e-processes, betting martingales, and confidence sequences that control false alarms or maintain coverage at every time. These methods are used for sequential audits, model and leaderboard evaluation, selective prediction, streaming decisions, and performance certification, often aiming to save samples or computation through early stopping. A central challenge is balancing power and efficiency with guarantees whose assumptions—such as exchangeability, predictable sampling, or valid dependence models—may not hold in real adaptive systems.