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LikelihoodRatios

How much a prediction should move a belief — and, unlike every other classification metric here, independently of how common the class is.

A positive prediction multiplies the prior odds by Positive and a negative one by Negative. That is what makes the pair worth reporting on a rare class: Precision falls as the class gets rarer even though the classifier has not changed, and these do not. A test asserts exactly that — holding sensitivity and specificity fixed while adding negatives leaves both ratios where they were and moves precision.

Two numbers, so a small type of its own

class_likelihood_ratios returns a pair, and the two are not interchangeable: LR+ above 1 says a positive prediction is evidence for the class, LR- below 1 says a negative prediction is evidence against it. A tuple would have carried no names and no documentation, so this is a sealed class with two named properties — the shape the curve-shape rule settled for the curves, applied to two scalars instead of three arrays.

Four ways a ratio has no value, and they do not answer alike

what is missing	Positive	Negative
nothing false-positive — specificity is 1	undefined	a value
nothing true-negative — specificity is 0	a value	undefined
no negative sample in the truth	undefined	undefined
no positive sample in the truth	undefined, and not replaceable	the same

The last row is the one worth knowing. undefinedPositive and undefinedNegative substitute for the first three; on the fourth the reference returns nan regardless of what was asked for, and this reproduces that. Measured: with the replacement set to 1, a truth of all negatives gives (nan, nan) and a truth of all positives gives (1, 1). Nothing in the reference's signature says so.

Members

Member	What it does
LikelihoodRatios.Compute	Both ratios, from labels.