Referring to Pattern Recognition and Machine Learning by Bishop(Page 367, Section 8.1):
Such models have particularly nice properties if we choose the relationship between each parent-child pair in a directed graph to be conjugate, and ...
As a newcomer to Bayesian statistics, I'm a little confused about the concept of conjugate relationship here. The wiki of conjugate prior states that:
In Bayesian probability theory, if the posterior distributions p(θ | x) are in the same probability distribution family as the prior probability distribution p(θ), the prior and posterior are then called conjugate distributions
My question is: are the two conjugations here same? In other words, does the quotation from Bishop book entail that all the parent-child pairs are in the same probability distribution family?