Figure 1.

Bayesian network representation of the POMDP generative model. Squares represent priors, likelihoods, or ‘factors’ that relate random variables to one another, and circles represent random variables (stochastic nodes). Different hidden state factors are represented as state variables and the different modality-specific $A^{\left(m\right)}$ arrays of the observation model shown are side by side, since they lead independently to the observations generated in that modality, but are conjunctively dependent on hidden state factors. Note that the $\mathbf{B}$ array can be similarly decomposed into different sub-arrays, one per hidden state factor, but it is shown as a single square here for simplicity. The prior over policies is parameterised by $\mathcal{E}$, which has separate prior over control states (${\mathcal{E}}^{\mathbf{Who}}$ and ${\mathcal{E}}^{\mathbf{T}}$) for each control state factor. The box at the top right contains mathematical descriptions of each component in the generative mode. Note that while it is included in the graphical model, we left out the $\mathbf{C}$ vector since it is not relevant for the current model.