When reading about the Bayesian approach to statistics, priors are an important component of the whole methodology.

Yet, it seems like priors are chosen without any specific theoretical motivation. There is the theory of conjugate priors, which is motivated mostly computationally, I believe, but still, I haven't seen a result in the line of "the choice of a certain prior will lead to faster convergence rate" or something similar to that.

Is there a good reference that analyzes the choice of a prior somehow, instead of always assuming that it is given, and assuming that it is completely the modeler's choice?