Other Bayesians such as De Finetti come to many of the same conclusions easier using gambling and the principle of indifference.
Wait, what? IIRC he used some expected utility based arguements for determining P(A and B) and P(A or B). Did I hallucinate that? Looks at the Logic of Science. Why yes, it looks like I did. Huh. Thank you for correcting my mistaken belief.
I imagine I got Jaynes’ presentation mixed up with other presentations when I was looking at foundations of probability theory and arguements for strong Bayesianism a while back. Admittedly, the Dutch booking arguements are a heck of a lot simpler than Jaynes inscrutable maths. But they suffer from, you know, relying on utilities. A big problem if your impetus for utilities relies on probabilities! You want Savage’s theorem IIRC to get probability theory and utilities at once, instead of one relying on the other.
Jaynes’s version of (Bayesian) statistics is grounded in information theory instead of gambling, and epistemologically it is much easier to ask the question “how does this information change my beliefs”, rather than: “If I was a betting man applying the principle of indifference to the outcomes, what odds would I then put on my prior beliefs so nobody can Dutch book me?”
From what I understand the Dutch book/decision motivated arguements are used for agent foundations purposes and to provide evidence that powerful AI systems will be goal-directed. I don’t know if that’s a role that can be played by informaiton theoretic principles.
I am not aware of Savage much apart from both Bayesian and Frequentists not liking him. And I did not follow Jaynes math fully and there are some papers going back and forth on some of his assumptions, so the mathematical underpinnings may not be as strong as we would like.
I don’t know, Intuitively you should be able to ground the agent stuff in information theory, because the rules they put forwards are the same, Jaynes also has a chapter on decision theory where he makes the wonderful point that the utility function is way more arbitrary than a prior, so you might as well be Bayesian if you are into inventing ad hoc functions anyway.
Wait, what? IIRC he used some expected utility based arguements for determining P(A and B) and P(A or B). Did I hallucinate that? Looks at the Logic of Science. Why yes, it looks like I did. Huh. Thank you for correcting my mistaken belief.
I imagine I got Jaynes’ presentation mixed up with other presentations when I was looking at foundations of probability theory and arguements for strong Bayesianism a while back. Admittedly, the Dutch booking arguements are a heck of a lot simpler than Jaynes inscrutable maths. But they suffer from, you know, relying on utilities. A big problem if your impetus for utilities relies on probabilities! You want Savage’s theorem IIRC to get probability theory and utilities at once, instead of one relying on the other.
From what I understand the Dutch book/decision motivated arguements are used for agent foundations purposes and to provide evidence that powerful AI systems will be goal-directed. I don’t know if that’s a role that can be played by informaiton theoretic principles.
I am not aware of Savage much apart from both Bayesian and Frequentists not liking him. And I did not follow Jaynes math fully and there are some papers going back and forth on some of his assumptions, so the mathematical underpinnings may not be as strong as we would like.
I don’t know, Intuitively you should be able to ground the agent stuff in information theory, because the rules they put forwards are the same, Jaynes also has a chapter on decision theory where he makes the wonderful point that the utility function is way more arbitrary than a prior, so you might as well be Bayesian if you are into inventing ad hoc functions anyway.