Gelman, Yao - Holes in Bayesian Statistics
> Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm, (2) flat or weak priors lead to terrible inferences about things we care about, (3) subjective priors are incoherent, (4) Bayes factors fail in the presence of flat or weak priors, (5) for Cantorian reasons we need to check our models, but this destroys the coherence of Bayesian inference.
In particular, you may appreciate the example and discussion in section 2:
> Probability theory isn’t true (quantum physics)
http://www.stat.columbia.edu/~gelman/research/unpublished/ba...