The correlation coefficient ρ was then defined as the covariance normalized by the individual standard deviations of the two involved outcomes: equation(7) resourcecorrelation:ρt=covt(sqrt(hs1,t)∗sqrt(hs2,t)). In every trial the correlation coefficient was finally translated into a position on the response slider using the normative function (h2,t – covt)/(h1,t + h2,t – 2 ∗ covt), which is derived in the Supplemental Information. This relationship

(Figure S1) did not change over the entire course of the experiment (because we always used the same ratio of 1:2 between outcome σ). We kept the mean of the resource outcomes constant during each session and therefore

the optimal strategy was indeed to not update those variables once a reliable estimate had been formed during the observation phase of each block. In selleck compound fact, the best-fitting learning rate for resource values was consistently very small across Selleckchem Compound C subjects (average 0.08), confirming that, as intended by the design, subjects indeed treated the mean as a stable value after the initial observation period and adjusted their learning rate downward to reflect this steady nature (Behrens et al., 2007). We investigated whether subjects used different learning rates for variance and covariance learning or whether these processes could be described by a single parameter. We did this by comparing a model with separate parameters for variance and covariance learning with a model that used a common parameter for both learning processes. We found that the reduced model could describe learning STK38 as well as the full model if model complexity is considered (Table 1). Note that both overall mean value and variance were constant during the experiment but the best-fitting learning rate for variance was higher than for value. This suggests that, in contrast to mean outcome value, subjects continuously updated their estimate of individual risk in response to local temporal fluctuations

in the individual variances. We therefore used the reduced model with a common risk/covariance learning parameter to generate fMRI regressors. Parameter estimates were fit for every individual subject using least-squares minimization between model predicted weights and actual weights set by the subject (see below). We created several alternative models that do not require learning of covariance information. Those models are described in the Supplemental Experimental Procedures. We compared how well each model predicted subjects’ behavior by fitting the free parameters of each model such that the mean squared sum of the deviation between model predicted (wm) and subjects’ weights (ws) was minimized.