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Calibration to the recorded label and to the true label cannot both hold across groups

Source: R/ledger_scan2.R
morie_calibration_flip.Rd

With symmetric recording flip rates fA, fB, the recorded rate is \(f + (1-2f)\,p_W\). Calibration to the record in both groups at score r forces true rates \((r-f_g)/(1-2f_g)\) that differ (Research.P5.DataProcessing.calibration_incompatible); calibration to the truth forces recorded rates that differ (calibration_to_W_incompatible).

Usage

morie_calibration_flip(fA, fB, r)

Arguments

fA, fB

Flip rates, not 1/2.

r

Score values.

Value

A data frame: r, true rates under record calibration (true_A, true_B), recorded rates under true calibration (recorded_A, recorded_B) and incompatible.

References

MacKay DJC (2003). Information Theory, Inference, and Learning Algorithms, Exercise 8.9. Cambridge.

Examples

morie_calibration_flip(fA = 0.05, fB = 0.2, r = c(0.3, 0.5, 0.8))
#>     r    true_A    true_B recorded_A recorded_B incompatible
#> 1 0.3 0.2777778 0.1666667       0.32       0.38         TRUE
#> 2 0.5 0.5000000 0.5000000       0.50       0.50        FALSE
#> 3 0.8 0.8333333 1.0000000       0.77       0.68         TRUE