Normal Distribution
nothing is called 95% until it has been counted
Concept

Decision theory — where it appears

The framework that chooses an action by its expected consequences, averaging each outcome's stated cost over what is uncertain. Conventional significance levels and decision thresholds are the answers it gives for particular costs, usually unstated.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

How often the split is taken, and by which rule. Over 400 draws on each of five laws. The first two rows have no break in them at all, the last two have one at row 60, and the middle one is a moving average. A criterion that counts a fitted two-regime model's parameters and nothing else takes the split on 99% of draws where there is no break. Counting the break point as one more parameter brings that to 67%. Charging what the search actually manufactures — 5.16 units, measured on a law with no break — brings it to 16%, and still takes the split on 61% of draws where there is one.

Choosing whether to break

Charging what the search manufactures takes a rule from splitting a stationary sample on 99% of draws to 16%. It also costs regret, because the two mistakes a rule can make are not the same size.

charged · Break point Expected loss of three upper limits against the level each is set at, fifteen exponential observations, penalty 20. A failure costs 20 standard deviations of margin. At the conventional 97.5% the t limit's loss is 2.143, Hall's 1.922 and the fitted family's 1.530. Each at its own best level: the t limit 1.263 at 99.95%, Hall's 1.862 at 98.50%, the family 1.308 at 99.25%. The best fixed multiple of the standard error costs 1.255.

The level a limit should be set at

When a failure costs twenty times a standard deviation of margin, a t limit on fifteen exponential observations set at the conventional 97.5% has an expected loss of 2.143. Set at 99.95%, the same formula's loss is 1.263 — within 1% of the best any fixed multiple of s/√n can do, and ahead of both Hall's transformation and the fitted gamma family at their own best levels. Hall's is the worst at every level on every source. Choosing the level does more than choosing the construction, and the correction that reads the sample is the one no level rescues.

tails · Student

Named alongside it

The objects these essays reach for when they reach for this one.

Change pointCoverageError rateExpected lossIdentificationInformation criterionLoss differentialModel selectionOptimismRegretRisk setSample size

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