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Equation 6 · Part 5 · Ecological Rationality: When Biases Are Adaptations

Symbol c_miss

P(D∣H)P(D∣¬H)  >  P(¬H)P(H)⋅cfacmiss\frac{P(D \mid H)}{P(D \mid \lnot H)} \; > \; \frac{P(\lnot H)}{P(H)} \cdot \frac{c_{fa}}{c_{miss}}
cmissc_{miss}

What this part means

the fitness cost of a miss, the threshold that minimizes total expected fitness cost is to infer H whenever: [displayed formula].

Its job in the formula

cmc_miss occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Where the article explains it

Where cfac_{fa} is the fitness cost of a false alarm and cmissc_{miss} is the fitness cost of a miss, the threshold that minimizes total expected fitness cost is to infer H whenever: P(D∣H)P(D∣¬H)  >  P(¬H)P(H)⋅cfacmiss\frac{P(D \mid H)}{P(D \mid \lnot H)} \; > \; \frac{P(\lnot H)}{P(H)} \cdot \frac{c_{fa}}{c_{miss}}.

The passage around this formula

…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 cfac_{fa} is the fitness cost of a false alarm and cmissc_{miss} is the fitness cost of a miss, the threshold that minimizes total expected fitness cost is to infer H whenever: P(D∣H)P(D∣¬H)  >  P(¬H)P(H)⋅cfacmiss\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…

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Sources cited in the surrounding passage

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