False alarm — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
What a heavier tail actually buys
Four decays, each tuned until it is equally quiet on a stream with nothing happening, then given one burst. At a burst of three hundred they see it for 54, 63, 68 and 104 seconds — indistinguishable. At nine thousand the exact polynomial reaches 384 seconds and the exponential 156. The shape of a tail does not decide how far back a scheme can see. It decides how fast that distance grows with the size of the event, and the exchange rate is the reciprocal of the exponent.
A detector that learns its own quiet
A burst detector built from a fast decayed counter needs a threshold, and the one it was measured with came from sixty independent runs of the background — an oracle no deployed system has. Two counters and a running mean square of their difference can supply it from the stream itself, and on a stream that does not move they hit a 5% false-alarm rate at every setting tried. What they lose is the burst: a scale that learns every reading learns the burst as noise and forgets it in 20 to 40 seconds whatever its size. Holding the scale while alarmed brings the oracle's horizon back for small bursts, turns a slow drift into an alarm that will not stop, and still cannot see past the lag at which the slow counter holds more of the burst than the fast one.
Named alongside it
The objects these essays reach for when they reach for this one.
Design parameterEstimatorExponential decayHalf lifeHonest limitMeasurement designState bitsStreaming modelVarianceFittingForward decayPower law