It has been emphasized (Behrens et al., 2007 and Yu and Dayan, 2005) that uncertainty may be used to the advantage of learners, allowing them to optimally weigh new data against old when updating their beliefs. One approach, which could be regarded as a form of novelty detection, suggests that learners quantify at each time point the likelihood that the statistics underlying the environment have changed based on the current sample (Nassar

et al., 2010, Payzan-LeNestour PD 332991 and Bossaerts, 2011 and Yu and Dayan, 2005). This quantity, termed unexpected uncertainty, can be used to flexibly modulate the weight given to new data as evidence for such a change varies. The computation of unexpected uncertainty is nontrivial, because improbable data samples may be attributed to a change in the statistics underlying the environment, or alternatively to the known unreliability of predictive relationships, dubbed expected uncertainty (Yu and Dayan, 2005). Importantly, the

definition of unexpected uncertainty does not imply that the agent is unaware that his environment is subject to change. Instead, selleck products a data sample with high unexpected uncertainty indicates that it is surprising given the cue-outcome association acquired through sampling, even when expected uncertainty, or the known, learned unreliability of this association, is accounted for. One form of expected uncertainty is risk, or the inherent stochasticity

of the environment that remains even when Phosphatidylinositol diacylglycerol-lyase the contingencies are fully known. For example, when sampling from an environment in which reward is delivered 50% of the time versus one in which reward is delivered 95% of the time, risk is higher in the former case. The perceptions of risk and unexpected uncertainty are antagonistic (Yu and Dayan, 2005) in the sense that when risk is high, as in the former case, changes in the environment are hard to detect and hence, unexpected uncertainty is low, whereas when risk remains low, as in the latter example, changes in the environment lead to strong increases in unexpected uncertainty. Unexpected uncertainty is also influenced by estimation uncertainty or the imprecision of the learner’s current beliefs about the environment (Chumbley et al., 2012, Frank et al., 2009, Payzan-LeNestour and Bossaerts, 2011, Prévost et al., 2011 and Yoshida and Ishii, 2006), which is also referred to as second-order uncertainty (Bach et al., 2011). If beliefs are acquired through learning as opposed to instruction, this quantity decreases with sampling. When estimation uncertainty is high, improbable samples may be partially attributed to the agent’s inaccurate beliefs about the structure of the environment, rather than to a change in that structure. Recent behavioral work suggests that subjects’ choices may indeed reflect a learning scheme that makes use of unexpected uncertainty (Nassar et al.