But the background knowledge part is highly not-constraining (just given your math). When a math algorithm gives constrained output, but you have wide scope for choice of input, it's not so good. you need to do stuff to constrain the inputs.

it seems to me you just dump all the hard parts of thinking into the priors and then say the rest follows. but the hard parts are still there. we still need to work out good explanations to use as input for the last step of not doing stuff that violates math/logic.