With an eye on uncertainty: Modelling pupillary responses to environmental volatility
Fig 1
This is a form of graphical notation that expresses the conditional dependencies in the generative model. Random variables are shown in circles, with arrows indicating causal influences. The progression from one state (sτ) to the next (sτ+1) is affected by the precision (ω) of the transition matrix. This stochasticity results in randomness in the observed outcomes (oτ). The panel below specifies the parameterisation of this model. Notably, in addition to (likelihood) beliefs about how states generate data (A), and beliefs about state transitions (B), we need prior beliefs about the precision of these transitions. These take the form of a gamma distribution, P(ω) ∝ βe−β·ω, where the current prior belief (ω) is a function of the most recent posterior beliefs (β). This has the convenient property that the expectation of the prior beliefs as we update them are the value of the most recent posterior beliefs [22].