Limitations of proposed signatures of Bayesian confidence

Abstract

The Bayesian model of confidence posits that confidence is the observer’s posterior probability that the decision is correct. It has been proposed that researchers can gain evidence in favor of the Bayesian model by deriving qualitative signatures of Bayesian confidence, i.e., patterns that one would expect to see if an observer was Bayesian, and looking for those signatures in human or animal data. We examine two proposed qualitative 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 for trials with neutral evidence. This signature only holds when class-conditioned stimulus distributions do not overlap and internal noise is very low. Another signature is that, as stimulus magnitude increases, confidence increases on correct trials but decreases on incorrect trials. This signature is also dependent on stimulus distribution type. There is an alternative form of this signature that has been applied in the literature; we find no indication that it is expected under Bayesian confidence, which resolves an ostensible discrepancy. We conclude that, to determine the nature of the computations underlying confidence reports, there may be no shortcut to quantitative model comparison.