I’m not really sure what frequentism is, though...Can you spell out what you think the coherent frequentist position is?
I’m not sure either, as I’ve confessed before, but here’s how it seems to me: whereas Bayesians view beliefs as “thermometer readings” that go up and down as new information comes in, frequentists view beliefs as “certificates” that have to be “earned” through specific rituals, and are subject to periodic renewal.
Since (in view of results such as Cox’s theorem) one can’t really deny that probability theory is the appropriate mathematical model for belief if there is any appropriate model at all, it seems that what frequentists actually object to, deep down, is the idea of personal belief as the object of formalization. They are only comfortable with (“official”) belief-formation as a social process. In their view (so I propose), you are only allowed to make probabilistic claims after you perform a well-defined experiment of some kind (specifically, of the kind in which relative frequencies of the events you’re interested in can be observed).
Frequentists don’t have a defined view of beliefs, they have a defined view of probability, namely that probability statements about events are statements about the limit of that event’s frequency in an arbitrary number of trials. The Bayesian position is that probability can be understood as degree of belief. The Bayesian epistemological position is that all beliefs ought to be understood as probability statements. There is no Frequentist epistemology, a frequentist could hold any epistemology they wanted more or less.
I understand that this is the standard story, but don’t find it satisfactory; hence was presenting my own “deeper” explanation (which I still regard as tentative).
After all, based only on what you’ve said, a frequentist could also be a Bayesian! This doesn’t seem right, or at least doesn’t seem to account for the fact that there seems to be a controversy between “frequentists” on the one hand, and “Bayesians” on the other.
I don’t see how a frequentist could Bayesian, to hold a Bayesian epistemology one would also have to adhere to a Bayesian theory of probability. Since frequentists don’t hold such a theory that can not hold Bayesian epistemology.
As per my original comment, someone could agree that probabilities represent beliefs but also hold that the content of (“legitimate”) beliefs consists only of statements about frequencies. This would allow them to simultaneously hold a frequentist interpretation of probability and a Bayesian epistemology. (As you said, “There is no Frequentist epistemology, a frequentist could hold any epistemology they wanted more or less.”)
I’m not sure either, as I’ve confessed before, but here’s how it seems to me: whereas Bayesians view beliefs as “thermometer readings” that go up and down as new information comes in, frequentists view beliefs as “certificates” that have to be “earned” through specific rituals, and are subject to periodic renewal.
Since (in view of results such as Cox’s theorem) one can’t really deny that probability theory is the appropriate mathematical model for belief if there is any appropriate model at all, it seems that what frequentists actually object to, deep down, is the idea of personal belief as the object of formalization. They are only comfortable with (“official”) belief-formation as a social process. In their view (so I propose), you are only allowed to make probabilistic claims after you perform a well-defined experiment of some kind (specifically, of the kind in which relative frequencies of the events you’re interested in can be observed).
See Science Doesn’t Trust Your Rationality.
Frequentists don’t have a defined view of beliefs, they have a defined view of probability, namely that probability statements about events are statements about the limit of that event’s frequency in an arbitrary number of trials. The Bayesian position is that probability can be understood as degree of belief. The Bayesian epistemological position is that all beliefs ought to be understood as probability statements. There is no Frequentist epistemology, a frequentist could hold any epistemology they wanted more or less.
I understand that this is the standard story, but don’t find it satisfactory; hence was presenting my own “deeper” explanation (which I still regard as tentative).
After all, based only on what you’ve said, a frequentist could also be a Bayesian! This doesn’t seem right, or at least doesn’t seem to account for the fact that there seems to be a controversy between “frequentists” on the one hand, and “Bayesians” on the other.
I don’t see how a frequentist could Bayesian, to hold a Bayesian epistemology one would also have to adhere to a Bayesian theory of probability. Since frequentists don’t hold such a theory that can not hold Bayesian epistemology.
As per my original comment, someone could agree that probabilities represent beliefs but also hold that the content of (“legitimate”) beliefs consists only of statements about frequencies. This would allow them to simultaneously hold a frequentist interpretation of probability and a Bayesian epistemology. (As you said, “There is no Frequentist epistemology, a frequentist could hold any epistemology they wanted more or less.”)