Confidence sequence

A confidence sequence is a whole ribbon of confidence intervals — one for every moment — that are all valid at the same time. A normal confidence interval, by contrast, is a one-shot promise: it is only valid if you fix the sample size up front and look exactly once. With a confidence sequence you can watch the interval tighten as data arrives and stop the instant it tells you what you need.

For monitoring, this means you can track an estimate live — a conversion rate, a model's accuracy, an average score — and act the moment the interval excludes the value you cared about, without the usual penalty for looking early or often.

Confidence sequences are the interval-shaped sibling of e-processes: the same anytime-valid machinery, expressed as a range you can trust rather than a single alarm.