Humans adapt rationally to approximate estimates of uncertainty.

Efficient learning requires estimation of, and adaptation to, different forms of uncertainty. If uncertainty is caused by randomness in outcomes (noise), observed events should have less influence on beliefs, whereas if uncertainty is caused by a change in the process being estimated (volatility) the influence of events should increase. Previously, we showed that humans respond appropriately to changes in volatility irrespective of outcome valence (Pulcu and Browning, 2017), but there is less evidence of a rational response to noise. Here, we test adaptation to variable levels of volatility and noise in human participants, using choice behaviour and pupillometry as a measure of the central arousal system. We find that participants adapt as expected to changes in volatility, but not to changes in noise. Using a Bayesian observer model, we demonstrate that participants are, in fact, adapting to estimated noise, but that their estimates are imprecise, leading them to misattribute it as volatility and thus to respond inappropriately.