[zozbot234]

There's always priors, they're just "flat", uniform priors (for maximum likelihood methods). But what "flat" means is determined by the parameterization you pick for your model. which is more or less arbitrary. Bayesians would call this an uninformative prior. And you can most likely account for stronger, more informative priors within frequentist statistics by resorting to so-called "robust" methods.

[_alternator_]

First, there is not such thing as a ‘uninformative’ prior; it’s a misnomer. They can change drastically based on your paramerization (cf change of variables in integration).

Second, I think the nod to robust methods is what’s often called regularization in frequentist statistics. There are cases where regularization and priors lead to the same methodology (cf L1 regularized fits and exponential priors) but the interpretation of the results is different. Bayesian claim they get stronger results but that’s because they make what are ultimately unjustified assumptions. My point is that if they were fully justified, they have to use frequentist methods.

[kgwgk]

One standard way to get uninformative priors is to make them invariant under the transformation groups which are relevant given the symmetries in the problem.

[kgwgk]

It’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.

[zozbot234]

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".

[kgwgk]

What does “as generally interpreted” mean? There is one valid way to interpret confidence intervals. The point is that it’s not based on a posterior probability and there is no prior probability there either.