Check again: if I take sample values and plug them directly into Bayes' Theorem, by itself, then I will NOT also have a confidence interval. More must be done than "just plug into Bayes' Theorem". The 'Rationalist' community persistently makes that error, plugging numbers into Bayes' Theorem alone. Notice how I keep pointing to "Bayes' Theorem by itself" is out-dated? Because we have important improvements. The 'Rationalist' community is NOT using up-to-date methods. That is NOT an argument against Bayesian Inference; you misunderstood, because they are both named after the same guy. Bayes' THEOREM, used in isolation, is an error. Do you see that?