alt Hacker NewsIt’s not true that “there are always priors”. There are no priors when you calculate the area of a triangle, because priors are not a thing in geometry. Priors are not a thing in frequentist inference either.
You may do a Bayesian calculation that looks similar to a frequentist calculation but it will be conceptually different. The result is not really comparable: a frequentist confidence interval and a Bayesian credible interval are completely different things even if the numerical values of the limits coincide.
Frequentist confidence intervals as generally interpreted are not even compatible with the likelihood principle. There's really not much of a proper foundation for that interpretation of the "numerical values".