Ahhh… that makes a lot of sense -Thank you! A couple of things that I still find a bit confusing:
‘It’s easy to get tripped up here, because authors are describing uniformly-dense spherical objects, but calling them “elephants” to make it sound more accessible.’ - So what is the difference between objective Bayesianism and subjective Bayesianism? And do you have any references to show that what you describe is the view of the objective Bayesian school of thought? Although your explanation makes a lot of sense, it does seems to contradict the obvious meaning of the text that I quoted above, which is the bible of objective Bayesianism, so I would appreciate some references that show that the author is actually ‘describing uniformly-dense spherical objects, but calling them “elephants” to make it sound more accessible.’
Professor Jaynes says “It is ‘objectivity’ in this sense that is needed for a scientifically respectable theory of inference.”—How can scientists make claims like “everyone should prefer hypothesis 1 over hypothesis 2 because of the evidence” when they can only talk about the plausibility of the hypotheses given the information that they have which is obviously different to the information that everyone else has? Does every individual have to verify the claims of scientists independently given their own information?
‘Hypotheses about universal common priors are pretty shaky.’ - Are you saying that “a priori” probability distributions don’t exist? This seems to contradict the objective Bayesian viewpoint (please see the quotation below ⬇️ from the Wikipedia page on Uninformative priors)
Some attempts have been made at finding a priori probabilities, i.e. probability distributions in some sense logically required by the nature of one’s state of uncertainty; these are a subject of philosophical controversy, with Bayesians being roughly divided into two schools: “objective Bayesians”, who believe such priors exist in many useful situations, and “subjective Bayesians” who believe that in practice priors usually represent subjective judgements of opinion that cannot be rigorously justified (Williamson 2010). Perhaps the strongest arguments for objective Bayesianism were given by Edwin T. Jaynes, based mainly on the consequences of symmetries and on the principle of maximum entropy.
I should probably have stated earlier that I’m more interested in practical and human-level (and medium-term artificial agents, with far more calculating power than humans, but still each a tiny subset of the actual universe), than in academic or theoretical distinctions.
I am not well-positioned to explain or defend the idea of “objective” probability. There may be such a thing in toy situations, but I haven’t seen any path from micro to macro that makes me believe it’s feasible for anything real.
I see… Thanks a lot for your help anyway. Much appreciated. I’m actually quite new to this forum so I would really appreciate it if someone could point me to the seasoned objective Bayesians here
Ahhh… that makes a lot of sense -Thank you! A couple of things that I still find a bit confusing:
‘It’s easy to get tripped up here, because authors are describing uniformly-dense spherical objects, but calling them “elephants” to make it sound more accessible.’ - So what is the difference between objective Bayesianism and subjective Bayesianism? And do you have any references to show that what you describe is the view of the objective Bayesian school of thought? Although your explanation makes a lot of sense, it does seems to contradict the obvious meaning of the text that I quoted above, which is the bible of objective Bayesianism, so I would appreciate some references that show that the author is actually ‘describing uniformly-dense spherical objects, but calling them “elephants” to make it sound more accessible.’
Professor Jaynes says “It is ‘objectivity’ in this sense that is needed for a scientifically respectable theory of inference.”—How can scientists make claims like “everyone should prefer hypothesis 1 over hypothesis 2 because of the evidence” when they can only talk about the plausibility of the hypotheses given the information that they have which is obviously different to the information that everyone else has? Does every individual have to verify the claims of scientists independently given their own information?
‘Hypotheses about universal common priors are pretty shaky.’ - Are you saying that “a priori” probability distributions don’t exist? This seems to contradict the objective Bayesian viewpoint (please see the quotation below ⬇️ from the Wikipedia page on Uninformative priors)
I should probably have stated earlier that I’m more interested in practical and human-level (and medium-term artificial agents, with far more calculating power than humans, but still each a tiny subset of the actual universe), than in academic or theoretical distinctions.
I am not well-positioned to explain or defend the idea of “objective” probability. There may be such a thing in toy situations, but I haven’t seen any path from micro to macro that makes me believe it’s feasible for anything real.
I see… Thanks a lot for your help anyway. Much appreciated. I’m actually quite new to this forum so I would really appreciate it if someone could point me to the seasoned objective Bayesians here