If I understand the math correctly (this is always in doubt) — In order to be better than Bayes, it would have to be not equivalent to Bayes; and therefore to violate one of Cox’s postulates.
That said, it’s not hard to imagine an implementation of Bayes substantially better than explicit, conscious, language-based, numerical reasoning augmented with kludgy workarounds for discovered biases.
I expect to find that random methods, which approach Bayes’s Theorem in the limit of infinite computing resources but are different in finite cases, are superior for finite computing resources. Enough special cases of this are found to have speedups and nicer properties that a general-case proof seems to be true in the same way that P != NP seems to be true (though with lower confidence).
If I understand the math correctly (this is always in doubt) — In order to be better than Bayes, it would have to be not equivalent to Bayes; and therefore to violate one of Cox’s postulates.
That said, it’s not hard to imagine an implementation of Bayes substantially better than explicit, conscious, language-based, numerical reasoning augmented with kludgy workarounds for discovered biases.
I expect to find that random methods, which approach Bayes’s Theorem in the limit of infinite computing resources but are different in finite cases, are superior for finite computing resources. Enough special cases of this are found to have speedups and nicer properties that a general-case proof seems to be true in the same way that P != NP seems to be true (though with lower confidence).