My understanding of post-modernism is ropey, but as I understand it there's a fundamental inoompatability between Bayesian Statistics and Post-modernism. Chiefly that in order to use Bayes theorem you need to start with the premise of a coherent underlying reality even if it's one you can't necessarily reach. Therefore you iterate and zero in on the points you can reach and update your models accordingly. Post-modernism on the other hand would in many cases (there are many things that fit under the heading of post-modernism) call this a priveleged viewpoint and reject even the hard synthesis of understandings that Bayesian approaches would come up with.

Or to put things another way, Postmodernism is about embracing ambiguity, the unknown, and multiple viewpoints, Bayesian Statistics are about resolving them.