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

Reliability diagram — where it appears

A plot of the mean probability forecast in each group against the share of that group's events that happened, with perfect calibration as the diagonal. It is a picture of a forecaster and a binning rather than of a forecaster alone, and the number read off it moves systematically as the number of bins changes.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

One forecaster, one sample, and the bins it was read in. A reliability diagram of 500 forecasts in 10 equal-count bins, drawn over the curve the same forecaster has in population. The forecaster is honest, so its population curve is the diagonal exactly and every departure the points show is sampling. The sample's reliability term reads 0.002262 and its expected calibration error 0.0358, against a true reliability of 0.000000. Both are properties of this binning as much as of this forecaster: at 5 bins and at 50 the same honest forecaster reports 0.001429 and 0.014100.

A curve that is a binning

A forecaster with no miscalibration in it at all reads 0.001429 at five bins and 0.014100 at fifty, on the same five hundred forecasts. The closed form is K/n times the forecaster's own irreducible score, and subtracting it returns zero.

calibrate · Calibration How long an honest forecaster looks broken for. The calibration error shown by a forecaster with no miscalibration in it at all, at five record lengths, drawn against one over the square root of the length so that the closed form is a straight line through the origin. It is 0.1252 at fifty forecasts and 0.0090 at ten thousand, against a closed form of √(2K/πn) times the mean root bin variance which gives 0.1257 and 0.0089. The threshold drawn across it is 0.02, a figure routinely read as evidence that something is wrong; the mean falls under it at 1976 forecasts and the 95th percentile at about 4111. Below that, an honest forecaster and a miscalibrated one are being told apart by a statistic that is mostly the sample size.

The miscalibration a perfect forecaster shows

A forecaster whose true reliability is exactly zero shows a calibration error of 0.1252 on fifty forecasts and 0.0090 on ten thousand. Every one of 1,200 blameless hundred-forecast records exceeds the 0.02 routinely read as evidence of a problem, and the mean does not fall under it until 1,976 forecasts.

calibrate · Calibration The honest curve, and the same forecaster in three coarse vocabularies. The ROC curve of the honest probability at full signal, area 0.8683, beside the same forecaster rounded to the nearest whole number, area 0.7684 — the two-valued liar — to the nearest half, area 0.8205, and to the nearest tenth, area 0.8650. A vocabulary of v values is v points on the square joined by straight segments, and tied reports count half.

A forecaster that rounds

An honest probability issued in tenths loses 0.0033 of ROC area and 0.000708 of resolution — the variance its bands average away, and 89.5% of the 0.000792 it adds to the Brier score. Two hundred records of two thousand forecasts show that loss on 189; it takes about 3,300 forecasts to put it two standard errors from zero. And 3.207 in every thousand forecasts in tenths are a 0% on an event that happened, which a logarithmic score charges without limit.

calibrate · Calibration

Named alongside it

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

Probability forecastReliability termBinningBrier scoreDebiased estimatorExpected calibration errorForecast calibrationMurphy's decompositionSampling variationBase rateCalibration testChi-square

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