The 2015 Q4 issue of SIAM Review will carry an article by Houman Owhadi, Clint Scovel, and myself on the brittle dependency of Bayesian posteriors as a function of the prior. This is an abbreviated presentation of results given in full earlier this year in Elec. J. Stat. The PDF is available for free under the terms of the Creative Commons 4.0 licence.
H. Owhadi, C. Scovel & T. J. Sullivan. “On the Brittleness of Bayesian Inference” SIAM Review 57(4):566–582, 2015. doi:10.1137/130938633