Bayesian update rules for learning. Model parameters are initially estimated as prior distributions (black). When outcomes are observed, distribution means are shifted by the product of learning rate, α, and prediction error, δ, while variances change based on the estimated rate of environmental change (left). When the estimated rate of environmental change is low (red), both mean updates and uncertainty (proportional to variance) are likewise small. When change is rapid (blue), means are updated rapidly, but uncertainty remains high.