Figure 10.

Decisions and movement. This graph illustrates how beliefs about categorical variables may influence those about continuous variables (message 1) and vice versa (message 2). The upper part of the graph is the same as that from Figure 5, while the lower part is that from the right of Figure 2. The additional η factor represents the empirical prior for a hidden cause, v, that determines the dynamics of x, much as the policies at the higher level determine the dynamics of state transitions. The equations below show that we can treat the descending message as a Bayesian model average, incorporating posterior predictive beliefs about outcomes under policies, averaged over policies. The ascending message is the free energy integrated over time for each outcome. This effectively treats each outcome as an alternative hypothesis for the continuous dynamics at the lower level.