Figure 1
The expected outcomes of an event with base rate occurrence of 0.50 that are generated by learning windows of different widths.
Figure 2
Simulations using prediction error, decay rate, and learning window width as a means of estimating expected value of the outcome (see Supplementary Material A for further information). Example of how a prediction error model (panel A), a simple decay rule (panel B), and the learning window algorithm (W) (panel C) adjusts as a function of stochastic presentations of outcomes and how it adjusts to a sudden change in the base-rate of the outcome. The observed outcome (black circles) is discrete and binary with a value equal to 0 if absent and 1 if present on each trial. At the change point (0 on the x axis), the probability of the outcome shifts from 0.25 to 0.75, as indicated by the black dotted line. The blue and red lines indicate trial-by-trial expected values of the outcome when the rate of learning (panel A), or rate of decay (panel B) is fast (L/D = .5) and learning window width (panel C) is narrow (W = 4) versus when the rate of learning is slow (L/D = .05) or window width is wide (W = 32). Note that expected values on the y axis have been normalized by (1–D)/D for the purposes of illustration in panel B.
Figure 3
A simulation of the choice task reported by Budhani, Richell, and Blair (2006) using a simple learning window model. For each of two window widths (W = 9, W = 3) we ran 1000 simulated participants on the full 270 trial procedure, assuming an independent learning window for each stimulus, updated whenever the stimulus was chosen and outcome consequently presented (O = 1 when points were won; O = –1 when points were lost). (See supplementary materials B for further details of this simulation) Following Budhani et al. (2006; Figure 2) here we show the mean number of errors to reach a learning criterion of 8 consecutive correct choices, in the initial acquisition and reversal phases, for a 100:0 discrimination and 80:20 discrimination. Simulated data are shown on the right, original empirical data from Budhani et al. (2006) are recreated on the left.