yannickeich
commented
7 months ago Probably there is no error in the textbook and what I describe is similar to the Gaussian case, where the local factors do have the form of Gaussian distributions, but do not require to have the positive definite covariance matrices.
In Chapter 10.7 Expectation Propagation after equation (10.193), the book says:
This division operation can be implemented by subtracting the natural parameters, as explained in Section 2.3.3.2.
However this holds not for all members of the exponential family. The product of two Poisson distributions is for example not Poisson distributed. Similar reasoning does therefore not allow to exchange the division of distributions by subtraction of their natural parameters.