Fig 1.
Panel A shows the conceptualisation of an agent connected to the world by the sensory information it receives (u) and the actions it takes (y), as described in active inference. Beliefs about the world depend on inferences about true states (x) based on sensory input. The sensory (u) and active (y) states correspond to the ‘Markov blanket’ which connects the agent with, but also distinguishes it from, the surrounding environment [52]. Panel B shows the basic structure of the HGF. The HGF estimates the inference processes that best explain the behavioural responses of an agent given a time series of inputs [50,53]. Model parameters can be estimated by inverting the model to infer participant-specific parameters and belief trajectories [50]. The perceptual model (χ in Panel A) is described via beliefs (x) represented at multiple layers that evolve across time (k), scaled by variance parameters (ω, ϑ). In B, the variance parameter ϑ controls the rate of change of change in x3, while ω controls the rate of change in x2.
Fig 2.
Panels A-C show the results of the model fitting and comparison procedures, illustrating the log-model evidence (LME) for all models (A) and for the veridical compared to felt models (B). Panel C illustrates the probabilities of the different models in the participant population based on Bayesian model selection, where HG4 was the most likely generative structure. Panel D shows a schematic of the winning HGF4 model. Panel E shows the parameter identifiability matrix for the HGF4, which shows that no model parameters were highly correlated (i.e., one could not simply be substituted for another). Panel F shows a comparison of the log model evidence per participant between the veridical and felt versions of the HGF4, illustrating the veridical version was better for most participants.
Fig 3.
Results of the parameter comparison.
Panel A: Illustration of grip and load force on the force transducers. Panel B: The stimulus objects. Panel C: Illustration of the relationship between mass and volume in the stimuli. Panel D: Plots show individual data points with mean and 95% confidence intervals for comparisons of model parameters between autistic and neurotypical groups.
Fig 4.
Panel A shows the task environment and Panel B shows the winning HGF3 model structure. Panels C and D illustrate the log-model evidence (LME) for all models and the probabilities of the different models in the participant population as indicated by Bayesian model selection. Panel E shows the belief trajectory of the fitted model for a single participant. In the bottom section, observed outcomes are shown in green (1 = normal ball, 0 = bouncy). The inferred posterior belief about the likelihood of a normal or bouncy ball (i.e., s(μ2)) is in red and the binary distributed response variable (pitch angle: above or below median) in pink. The thin black line shows the learning rate. Mean and 95% CIs for μ2 and μ3 are shown in blue in the middle and top panels.
Fig 5.
Mean and 95% CIs of model-derived estimates.
Figures show the decision parameter, ζ, (panel A), the random walk variance parameter, ω, (panel B), posterior beliefs about x2 (ball bounciness; panel C) and x3 (environmental volatility; panel D), and learning rates at levels 2 (panel E) and 3 (panel F) of the HGF. Thicker significance bars indicate group-level effects and thinner bars indicate pair-wise differences. *p < .05, **p < .01, ***p < .001.