Figure 8.

Precision and uncertainty. This figure shows the graph of Figure 5, but supplemented with precision parameters and prior factors over these precisions. These encode confidence in policies (γ), transitions (ω), and likelihoods (ζ). The priors for these are the factors Γ, Ω, and Z, respectively. Note that the messages required to update beliefs about the hidden states are almost identical to those of Figure 3, but are now averaged over beliefs about the precision. Messages from the past (1) and future (2) are contextualized by the transition precision, while those from sensory input (3) are modulated by the likelihood precision. As in Figure 3, we provide the form of the variational and belief propagation messages implied by this model to illustrate the commonalities between their forms. Again, this is due to the structure of the Markov blankets of each state, which now includes precision parameters.