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. From a practical viewpoint, computability and the availability of software may restrict your choice of prior in any case. See: * http://en.wikipedia.org/wiki/Conjugate_prior * http://en.wikipedia.org/wiki/Uniform_prior * http://en.wikipedia.org/wiki/Jeffreys_prior