The other is frequentism, which could be simplified (strawmanned?) as “the situation must happen many times, and then ‘probability’ is the frequency of this specific outcome given the situation”.
That definition has the advantage of defining probability as something that’s objective while the Bayesian definition depends on the prior beliefs of a particular person and is subjective.
Sometimes the subjectivity comes back in the form of choosing the proper reference class.
If I flip a coin, should our calculation include all coins that were ever flipped, or only coins that were flipped by me, or perhaps only the coins that I flipped on the same day of week...?
Intuitively, sometimes the narrower definitions are better (maybe a specific type of coin produces unusual outcomes), but the more specific you get, the fewer examples you find.
That’s important. Bayes and Frequentism are not just different ways of doing calculations, they also make different implications about what probability is.
That definition has the advantage of defining probability as something that’s objective while the Bayesian definition depends on the prior beliefs of a particular person and is subjective.
Sometimes the subjectivity comes back in the form of choosing the proper reference class.
If I flip a coin, should our calculation include all coins that were ever flipped, or only coins that were flipped by me, or perhaps only the coins that I flipped on the same day of week...?
Intuitively, sometimes the narrower definitions are better (maybe a specific type of coin produces unusual outcomes), but the more specific you get, the fewer examples you find.
That’s important. Bayes and Frequentism are not just different ways of doing calculations, they also make different implications about what probability is.