TITLE: what can be said about the choice of a prior in Bayesian statistics?
QUESTION [11 upvotes]: 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?

REPLY [3 votes]: The key point is to show that your analysis does not depend much on the prior in the first place.  
You could try 

a conjugate prior (if one exists)
a (possibly improper) uniform prior and  
a Jeffreys prior (justified by its invariance under re-parameterization) 

and if you get answers that are reasonably close then that should provide some support that your analysis does not depend on arbitrary choice of prior.
BUGS and similar systems give quite a bit of flexibility regarding the prior but otherwise, from a practical viewpoint, easy computability and the availability of software may restrict your choice of prior.
See:

http://en.wikipedia.org/wiki/Conjugate_prior
http://en.wikipedia.org/wiki/Uniform_prior
http://en.wikipedia.org/wiki/Jeffreys_prior