Fig. 4: Computational modelling.
A shows a depiction of the Jumping Gaussian Estimation Task modelling process used in this study. This version of an extended HGF model captured learning about the mean (x) and variance (a) independently. Pentagons represent trial-by-trial inputs (yx = rover positions; ya = beam widths). Squares represent the modelling parameters, relating to learning about the mean (x) and noise (a) separately: θ refers to the constant step-size in volatility learning (µ2), ω is the equivalent on the lower-level belief and κ determines the coupling strength between levels. Parameters for u refer to the lowest level, where beliefs about noise and mean are combined for a common prediction about the mean. The decision model includes ζx and ζa for determining the decision noise or SD when drawing from a Gaussian distribution around the respective belief (µ1) about mean and noise. The β1 parameter captures how much an individual makes use of her belief about noise when adapting the beam width. Using the Volatility Block as an example, the HGF outputs are shown to demonstrate the ability of the model to capture and predict the behaviour anticipated. B shows a comparison between participant estimates, and estimates made via the model simulations, across blocks. The x axis displays the trial number for each block. The y axis shows the screen position scale. Here, 0 indicates the middle of the screen, while positive and minus figures show the right- and left-hand sides of the screen, respectively. In this way, mean estimates (rover positions) and noise estimates (beam widths) can both be displayed as positions on the screen. Median participant estimates of the mean, i.e. rover positions, are indicated by the black solid lines. Median simulated estimates of the mean based on the JGET HGF model are shown in orange. The median participant’s noise estimate (beam width) for each trial is shown using the width of the screen in black/grey. The median simulated noise estimate is shown as a width in orange. C, D show the relationship between our decision model parameter “use of noise belief” (β1) and delusional ideation scores. Plot (C) looks specifically at the Noise Block (purple) and the Volatility Block (pink), whereas plot (D) looks at the Combined Uncertainty Block (gold) and the Bivalent Combined Uncertainty Block (red). E shows the relationship between β1 values in the Combined Uncertainty Block (gold) and the Bivalent Combined Uncertainty Block (red), and scores on the psychometric schizotypy scale.
