[A]ctually a 95% confidence interval is an interval generated by a process, where the process has a 95% chance of generating a confidence interval that contains the true mean.
Is it incorrect for a Bayesian to gloss this as follow?
Given (only) that this CI was generated by process X with input 0.95, this CI has a 95% chance of containing the true mean.
I could imagine a frequentist being uncomfortable with talk of the “chance” that the true mean (a certain fixed number) is between two other fixed numbers. “The true mean either is or is not in the CI. There’s no chance about it.” But is there a deeper reason why a Bayesian would also object to that formulation?
Is it incorrect for a Bayesian to gloss this as follow?
I could imagine a frequentist being uncomfortable with talk of the “chance” that the true mean (a certain fixed number) is between two other fixed numbers. “The true mean either is or is not in the CI. There’s no chance about it.” But is there a deeper reason why a Bayesian would also object to that formulation?