%0 Journal Article %A Balázs Hangya %A Joshua I. Sanders %A Adam Kepecs %T A mathematical framework for statistical decision confidence %D 2016 %R 10.1101/017400 %J bioRxiv %P 017400 %X Decision confidence is a forecast about the probability that a decision will be correct. Confidence can be framed as an objective mathematical quantity the Bayesian posterior probability, providing a formal definition of statistical decision confidence. Here we use this definition as a starting point to develop a normative statistical framework for decision confidence. We analytically prove interrelations between statistical decision confidence and other observable decision measures. Among these is a counterintuitive property of confidence that the lowest average confidence occurs when classifiers err in the presence of the strongest evidence. These results lay the foundations for a mathematically rigorous treatment of decision confidence that can lead to a common framework for understanding confidence across different research domains, from human behavior to neural representations. %U https://www.biorxiv.org/content/biorxiv/early/2016/01/01/017400.full.pdf