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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 RocCurve and the other curves take, 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	NaN, replaced only if nothing is false-positive	NaN, replaced only if nothing is true-negative

The last row is the one worth knowing. A ratio is replaced only where its own count vanishes, as the reference replaces it; with no positive sample, the one that is not replaced is 0/0, NaN. Measured, with the replacement set to 1: ([0, 0], [0, 1]) gives (NaN, NaN), ([0, 0], [1, 1]) gives (NaN, 1), and a truth of all positives gives (1, 1) (#1250).

Members

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