source: Bayesians are frequentists. | Statistical Modeling, Causal Inference, and Social Science
Some take aways:
Bayesians are frequentists. The Bayesian prior distribution corresponds to the frequentist sample space: it’s the set of problems for which a particular statistical model or procedure will be applied.
Bayesian and frequentist inference are both about averaging over possible problems to which a method might be applied.
any Bayesian interpretation of probability has to have some frequentist underpinning to be useful. And, conversely, any frequentist sample space corresponds to some set of problems to be averaged over.
good Bayesian inference and good frequentist inference are both about having a modeled population (also called a prior distribution, or frequency distribution, or reference set) that is a good match to the applied question being asked.
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