Bayesian inference with incomplete knowledge explains perceptual confidence and its deviations from accuracy.

In perceptual decisions, subjects infer hidden states of the environment based on noisy sensory information. Here we show that both choice and its associated confidence are explained by a Bayesian framework based on partially observable Markov decision processes (POMDPs). We test our model on monkeys performing a direction-discrimination task with post-decision wagering, demonstrating that the model explains objective accuracy and predicts subjective confidence. Further, we show that the model replicates well-known discrepancies of confidence and accuracy, including the hard-easy effect, opposing effects of stimulus variability on confidence and accuracy, dependence of confidence ratings on simultaneous or sequential reports of choice and confidence, apparent difference between choice and confidence sensitivity, and seemingly disproportionate influence of choice-congruent evidence on confidence. These effects may not be signatures of sub-optimal inference or discrepant computational processes for choice and confidence. Rather, they arise in Bayesian inference with incomplete knowledge of the environment.