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You can maybe gain some sense, but I'm not sure if it can exactly tell you how you're going wrong (except possibly to say, "if you believe these things, it make

You can maybe gain some sense, but I'm not sure if it can exactly tell you how you're going wrong (except possibly to say, "if you believe these things, it makes no sense to also believe this other thing"; where a thing is a probability value assignment -- the danger is in believing that such analysis can give you positive knowledge [for instance, "I believe these things, so this other things must be the case"). I believe you need a total ordering, not just a finite, partial ordering. Maybe you can say wedding is good, funeral is bad, but how would you incorporate something like the birth of a child, the taste of some food, etc? Basically, you have to reduce all aspects of subjectivity to an integer, which could very well be impossible (making the activity of trying to turn subjectivity into integers highly suspect). I understand that economic games sometimes use degree of belief, but in the example of a roulette wheel, we can actually count up all of the possibilities and assign numbers based on that. I don't think we can count all of the possible subjective states. >How do you get an infinite, uncountable number of experiences? I experience this all the time (though I can't say they are infinite, it is certainly more than I can count).

bordercases 11y ago
I lost my reply because the site went down! I'll give a brief one here. > integers Or a matrix. Or with some dimension but not others. A total ranking is implausible and lossy, but partial rankings for some traits is tractable: you just have to be careful. If motivated by a decision the use of probability becomes more clear, since you can declare what kinds of errors you can handle and what you can't, relative to the information that you specifically want from an event. > positive information This is a problem with statistics, not Bayes. Null hypothesis testing with its p-values and t-tests can only reject a known distribution, not telling you the real distribution without testing for all of them. At that point it can be as prone to GIGO as Bayesian methods are. There are some statisticians who dissolve the whole Bayes vs Not debate by focusing on the optimisation of loss functions. Although it lacks the philosophical pyrotechnics of subjective probability, in practice it's probably the most reasonable approach: do what works.

bordercases 11y ago

I lost my reply because the site went down! I'll give a brief one here. > integers Or a matrix. Or with some dimension but not others. A total ranking is implausible and lossy, but partial rankings for some traits is tractable: you just have to be careful. If motivated by a decision the use of probability becomes more clear, since you can declare what kinds of errors you can handle and what you can't, relative to the information that you specifically want from an event. > positive information This is a problem with statistics, not Bayes. Null hypothesis testing with its p-values and t-tests can only reject a known distribution, not telling you the real distribution without testing for all of them. At that point it can be as prone to GIGO as Bayesian methods are. There are some statisticians who dissolve the whole Bayes vs Not debate by focusing on the optimisation of loss functions. Although it lacks the philosophical pyrotechnics of subjective probability, in practice it's probably the most reasonable approach: do what works.