Is the probability theory used in frequentist and bayesian statistics the same? I know that the interpretation of the concept of probability is different under both approaches, but is it the case too with the mathematical formulation of probability theory (same set of axioms, etc)?
$\begingroup$ If it were different, then for at least one of the approaches it would be incorrect to call it "probability." $\endgroup$– whuber ♦Aug 31, 2022 at 22:28
1$\begingroup$ Yes it's the exact same. The difference is in what things we are giving probabilities: the Bayesian puts probabilities over "population unknowns", like what the average height of male americans over 30 years old is, which is/was "controversial" because there is in fact at a given point in time a single correct such height. $\endgroup$– John MaddenAug 31, 2022 at 22:47