"One downside of Bayesian statistics is that it requires prior information — and often scientists need to start with a guess or estimate. Assigning numbers to subjective judgments is “like fingernails on a chalkboard,” said physicist Kyle Cranmer, who helped develop a frequentist technique to identify the latest new subatomic particle — the Higgs boson.It's actually worse than that. It is a favorite of ideological hacks who place their ideology into the equation up front, thereby getting the results they want rather than objective knowledge. Bayesian calculations are an open invitation to pretend that circular arguments are justified statistically.
Others say that in confronting the so-called replication crisis, the best cure for misleading findings is not Bayesian statistics, but good frequentist ones. It was frequentist statistics that allowed people to uncover all the problems with irreproducible research in the first place, said Deborah Mayo, a philosopher of science at Virginia Tech. The technique was developed to distinguish real effects from chance, and to prevent scientists from fooling themselves.
Uri Simonsohn, a psychologist at the University of Pennsylvania, agrees. Several years ago, he published a paper that exposed common statistical shenanigans in his field — logical leaps, unjustified conclusions, and various forms of unconscious and conscious cheating.
He said he had looked into Bayesian statistics and concluded that if people misused or misunderstood one system, they would do just as badly with the other. Bayesian statistics, in short, can’t save us from bad science."
That's not to say that with legitimate use of non-biased input, Bayes calculations can't be valuable, as in the case of the fisherman rescued by the Coast Guard which used Bayes to anticipate the location of the drifting man. But that uses known information, regarding physical data which is not ideological as an input to the calculation. That is far different from trying to calculate, say, the existence of a deity, where any input is prejudiced by definition.
Whenever Bayes is used, the calculations must ALWAYS be scrutinized for bias, because in some venues they always will be. And that is, indeed, like fingernails on a chalkboard.