Epidemiology visualized: the prosecutor's fallacy

Abstract

The "prosecutor's fallacy" (the assumption that Pr [probability] (A|B) = Pr (B|A)) arises often in epidemiology but is often unrecognized as such, in part because investigators do not have strong intuitions about what the fallacy means. Here, we help inform such intuitions and remind investigators of this fallacy by using visualizations. In figures, we demonstrate the prosecutor's fallacy, as well as show conditions under which Pr (A|B) can be assumed to be equal to Pr (B|A). Visualizations can help build intuition around statistical concepts such as the prosecutor's fallacy and should be more widely considered as teaching tools.

Keywords: Bayes' rule; Bayes' theorem; logical fallacies; prevention paradox; probability; prosecutor's fallacy; statistics.