I applied completely orthodox frequentist probability.
I had predicted your objection would be that expected value is an application of Bayes’ theorem, but I was prepared to argue that orthodox probability does include Bayes’ theorem. It is one of the pillars of any introductory probability textbook.
A problem isn’t “Bayesian” or “frequentist”. The approach is. Frequentists take the priors as given assumptions. The assumptions are incorporated at the beginning as part of the context of the problem, and we know the objective solution depends upon (and is defined within) a given context. A Bayesian in contrast, has a different perspective and doesn’t require formalizing the priors as given assumptions. Apparently they are comfortable with asserting that the priors are “subjective”. As a frequentist, I would have to say that the problem is ill-posed (or under-determined) to the extent that the priors/assumptions are really subjective.
Suppose that I tell you I am going to pick up a card randomly and will ask you the probability of whether it is the ace of hearts. Your correct answer would be 1⁄52, even if I look at the card myself and know with probability 0 or 1 that the card is the ace of hearts. Frequentists have no problem with this “subjectivity”, they understand it as different probabilities for different contexts. This is mainly a response to this comment, but is relevant here.
Yet again, the misunderstanding has arisen because of not understanding what is meant by the probability is “in” the cards. In this way, Bayesian’s interpret the frequentist’s language too literally. But what does a frequentist actually mean? Just that the probability is objective? But the objectivity results from the preferred way of framing the problem … I’m willing to consider and have suggested the possibility that this “Platonic probability” is an artifact of a thought process that the frequentist experiences empirically (but mentally).
I applied completely orthodox frequentist probability.
I had predicted your objection would be that expected value is an application of Bayes’ theorem, but I was prepared to argue that orthodox probability does include Bayes’ theorem. It is one of the pillars of any introductory probability textbook.
A problem isn’t “Bayesian” or “frequentist”. The approach is. Frequentists take the priors as given assumptions. The assumptions are incorporated at the beginning as part of the context of the problem, and we know the objective solution depends upon (and is defined within) a given context. A Bayesian in contrast, has a different perspective and doesn’t require formalizing the priors as given assumptions. Apparently they are comfortable with asserting that the priors are “subjective”. As a frequentist, I would have to say that the problem is ill-posed (or under-determined) to the extent that the priors/assumptions are really subjective.
Suppose that I tell you I am going to pick up a card randomly and will ask you the probability of whether it is the ace of hearts. Your correct answer would be 1⁄52, even if I look at the card myself and know with probability 0 or 1 that the card is the ace of hearts. Frequentists have no problem with this “subjectivity”, they understand it as different probabilities for different contexts. This is mainly a response to this comment, but is relevant here.
Yet again, the misunderstanding has arisen because of not understanding what is meant by the probability is “in” the cards. In this way, Bayesian’s interpret the frequentist’s language too literally. But what does a frequentist actually mean? Just that the probability is objective? But the objectivity results from the preferred way of framing the problem … I’m willing to consider and have suggested the possibility that this “Platonic probability” is an artifact of a thought process that the frequentist experiences empirically (but mentally).