hmm, what you are discussing above is typically called the formulation of the prior, not the calculation of it. And I agree that this formulation can be problem

hmm, what you are discussing above is typically called the formulation of the prior, not the calculation of it. And I agree that this formulation can be problematic. It is almost certainly the most contentious element in Bayesian inference. However, I will note that your examples are largely overstating the problem. The prior is not typically as subjective as you are implying. Furthermore, the Bayesian prediction converges to the frequential result in the limit of 'large' data. If your results are so highly sensitive to your prior that the results drastically change, then you either have: 1) insufficient data, at which point the frequentist results would also certainly have been as bad or worse (the prior acts as a regularization) 2) a misspecified prior Either way, it is absolutely required that you perform tests to ensure your results are not greatly sensitive to your choice of prior, or if so that this is clearly noted as a modeling assumption. And bayes naturally has many means to test precisely this, such as cross-validation, bayes-factors, hierarchical, etc. I also note that this is why I typically prefer Jeffreys Priors in my work. I mention this so that one can see that not all priors are 'subjective'. These are difficult to use in some fields, admittedly.