= Base-rate dependence of autonomic emotion classification
Fix a true-positive <probability> $s>0$ and false-positive <probability> $f>0$. The <positive predictive value> at <base rate> $p$ is $v(p)=sp/(sp+f(1-p))$. Differentiation gives $v'(p)=sf/[f+(s-f)p]^2>0$, while $v(p)\to0$ as $p\to0$. Thus a <classifier> can retain the same conditional performance yet become unreliable among its positive classifications when the target <emotion> is rare. This is a mathematical implication of the specified binary model, not an empirical performance estimate.
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