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Those chapters show that any consistent (in some sense) statistical reasoning system must result in the same answers as a Bayesian system. They don't show that
by rfergie 13y ago
Those chapters show that any consistent (in some sense) statistical reasoning system must result in the same answers as a Bayesian system.
They don't show that the frequentist approach is wrong. If both methods result in the same answer and frequentist methods are easier to use then what is the problem?
- loup-vaillant 13y agoNo problem of course. But that's a big if. And how are you going to evaluate whether both methods do in fact deliver the same answer? Also, the Frequentist approach is not wrong. It's inaccurate, to the extent its results differ from the Bayesian ones. This inaccuracy tend to go down as we gather more data. Which is a good thing, or else science itself wouldn't work. One more thing. You said "in some sense". Are you seriously suggesting that the assumptions behind Cox's Theorem can reasonably be challenged?
- thebooktocome 13y ago> Are you seriously suggesting that the assumptions behind Cox's Theorem can reasonably be challenged? Sure: probability is continuous.
- loup-vaillant 13y agoYou mean, "it is not totally obvious that probability is continuous". Well… To me, it is obvious.
- rfergie 13y agoI'm ashamed to say that I said "in some sense" to be deliberately vague about what I meant by consistency - I didn't want to overstate the strength of Cox's theorem or end up arguing about Godel.
- loup-vaillant 13y agoActually, I was accusing you of understating the strength of Cox's theorem.