The relationship between PID, PED, and GID.

Each of the three information decompositions (the PID, PED, and GID) can be related to each-other in terms of how one is constructed from another. The PID is a special case of the GID (when the prior is the product of the marginals of the posterior), the PED is a special case of the PID (when the target is the joint-state of all the inputs), and the GID is constructed from the (local) PED. None of the three are fundamentally “prior” to any other, and this relationship forms the beginning of a unified theory of multivariate information decomposition.