Numerator: P(D mid H)

The passage around this formula

This is a rule about optimal thresholds, not merely an intuition, and it has a compact formal statement. A decision-maker observes ambiguous evidence D bearing on whether a state H holds — a predator is present, a partner is unfaithful, an approach signals romantic interest — against the alternative that it does not. Where $c_{fa}$ is the fitness cost of a false alarm and $c_{miss}$ is the fitness cost of a miss, the threshold that minimizes total expected fitness cost is to infer H whenever: $\frac{P(D \mid H)}{P(D \mid \lnot H)} \; > \; \frac{P(\lnot H)}{P(H)} \cdot \frac{c_{fa}}{c_{miss}}$. When the two error costs are equal, the cost ratio on the right collapses to one, and the rule reduces to the ordinary Bayesian classifier that a norm blind to consequences would…

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