Limitations of proposed signatures of Bayesian confidence

The Bayesian model of confidence posits that confidence reflects the observer's posterior probability that the decision is correct. Hangya, Sanders, and Kepecs (2016) have proposed that researchers can test the Bayesian model by deriving qualitative signatures of Bayesian confidence (i.e., patterns that one would expect to see if an observer were Bayesian) and looking for those signatures in human or animal data.We examine two proposed signatures, showing that their derivations contain hidden assumptions that limit their applicability and that they are neither necessary nor sufficient conditions for Bayesian confidence. One signature is an average confidence of 0.75 on trials with neutral evidence. This signature holds only when class-conditioned stimulus distributions do not overlap and when internal noise is very low. Another signature is that as stimulus magnitude increases, confidence increases on correct trials but decreases on incorrect trials. This divergence signature holds only when stimulus distributions do not overlap or when noise is high. Navajas et al. (2017) have proposed an alternative form of this signature; we find no indication that this alternative form is expected under Bayesian confidence. Our observations give us pause about the usefulness of the qualitative signatures of Bayesian confidence. To determine the nature of the computations underlying confidence reports, there may be no shortcut to quantitative model comparison.