Scott has always had a problem grasping Bayesian probability. When he says that it’s a problem to have two different probabilities from the same situation, he doesn’t realize that it’s a problem for Bayesian only if the two calculations starts from the same prior information. Bayesians have no qualms at all with having two different probabilities for the same situation, provided that they start from different information.
On the other hand, it’s even more of a problem for frequentists, for whom probabilities are objective physical properties of a situation.
Exactly one of you (so far as I know) has proven a theorem extending Aumann’s agreement theorem. I wouldn’t be so hasty to charge that he doesn’t understand basic probability.
Besides, your critique is irrelevant to this scenario, unless you have an argument for why each way of calculating is using different implicit priors.
People have come up with theorems about frequentist probability for almost three centuries and still failed to grasp the Bayesian (Laplacian?) framework. It is also commendable that you equate Bayesian with basic, but that’s not the reality in the average mathematical education. Surely Scott understand basic probability enough, but he is demonstrably not aware of the foundations of probability as extended logic.
My critique surely is irrlevant to the scenario, indeed it was a commentary on the sentence
If you’re a Bayesian, then this kind of seems like a problem
found in the book, which so totally misses the point to be almost backwards.
When he says that it’s a problem to have two different probabilities from the same situation, he doesn’t realize that it’s a problem for Bayesian only if the two calculations starts from the same prior information.
It’s kind of impossible to prove theorems about when Bayesians should agree without knowing that.
And I don’t see the problem with the sentence you quoted, unless you claim that each way encodes different priors (and even so, that would be an answer to the problem, not a reason to say the problem doesn’t deserve a response).
Scott has always had a problem grasping Bayesian probability.
When he says that it’s a problem to have two different probabilities from the same situation, he doesn’t realize that it’s a problem for Bayesian only if the two calculations starts from the same prior information. Bayesians have no qualms at all with having two different probabilities for the same situation, provided that they start from different information. On the other hand, it’s even more of a problem for frequentists, for whom probabilities are objective physical properties of a situation.
Exactly one of you (so far as I know) has proven a theorem extending Aumann’s agreement theorem. I wouldn’t be so hasty to charge that he doesn’t understand basic probability.
Besides, your critique is irrelevant to this scenario, unless you have an argument for why each way of calculating is using different implicit priors.
People have come up with theorems about frequentist probability for almost three centuries and still failed to grasp the Bayesian (Laplacian?) framework.
It is also commendable that you equate Bayesian with basic, but that’s not the reality in the average mathematical education. Surely Scott understand basic probability enough, but he is demonstrably not aware of the foundations of probability as extended logic.
My critique surely is irrlevant to the scenario, indeed it was a commentary on the sentence
found in the book, which so totally misses the point to be almost backwards.
It’s kind of impossible to prove theorems about when Bayesians should agree without knowing that.
And I don’t see the problem with the sentence you quoted, unless you claim that each way encodes different priors (and even so, that would be an answer to the problem, not a reason to say the problem doesn’t deserve a response).