Equation 6 · Part 4 · Ecological Rationality: When Biases Are Adaptations

Symbol c_fa

\frac{P(D \mid H)}{P(D \mid \lnot H)} \; > \; \frac{P(\lnot H)}{P(H)} \cdot \frac{c_{fa}}{c_{miss}}

c_{fa}

What this part means

the fitness cost of a false alarm.

Its job in the formula

$c_f$ a occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Full expressionSymbol c_faArticle meaning

Where the article explains it

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: $\frac{P(D \mid H)}{P(D \mid \lnot H)} \; > \; \frac{P(\lnot H)}{P(H)} \cdot \frac{c_{fa}}{c_{miss}}$ .

The passage around this formula

…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…

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