Fig. 1: Overview of the task and theoretical model of belief updating (McGuire et al., 2014).
From: Functional brain network reconfiguration during learning in a dynamic environment
a Sequence of the task. At the start of each trial, participants predict where a bag will drop from an occluded helicopter by positioning a bucket on the screen. After participants submit their prediction, the bag drops and any rewarded coins that fall in the bucket are added to the participant’s score. The location of the last prediction and the last bag drop are noted on the next trial. b An example sequence of trials. Each data point represents the location of a bag on each trial (yellow for rewarded coins, gray for neutral coins). The dashed line represents the true generative mean. The mean changes occasionally. The cyan line represents the prediction from a normative model of belief updating. The inset equation shows how the model updates beliefs (Bt = belief, Xt = observed outcome, αt = learning rate on trial t). The vertical dashed line represents the boundary of the noise conditions: high-noise (left) and low-noise condition (right). Noise refers to the variance of the generative distribution. c Two learning components from the normative model. Change-point probability (CPP) reflects the likelihood that a change-point happens, which is increased when there is an unexpectedly large prediction error. Relative uncertainty (RU) reflects the uncertainty about the generative mean relative to the environmental noise, which is increased after high CPP trials and decays slowly as more precise estimates of the generative mean are possible. The inset formula shows how CPP and RU contribute to single trial estimates of learning rates.
