I don’t know about deducing the entire mindset & toolbox of ‘Bayesian rationality,’ but knowing Bayes’ theorem is the key part of it, and I wouldn’t expect that to be too hard to reconstruct if you knew what you look to for.
Bayes’ theorem follows trivially from the definition of conditional probability, and that definition is itself quite intuitive. So in theory, once you have a feel for what probability is, it’d be quite possible to get to Bayes’ theorem. I haven’t read Huygens’ 1657 book on probability theory, but if it was any good, I bet Huygens knew enough about it to beat Bayes to Bayes’ theorem by a century.
Chapters 1 and 2 of Jaynes’ Probability Theory: The Logic of Science show how Bayes’ theorem follows necessarily from certain basic principles of plausible reasoning. In some sense all roads lead to Bayes when trying to derive a consistent mathematical procedure for manipulating degrees of plausibility.
You are quite right. I thought about mentioning the Cox-Jaynes road to Bayes’ theorem in my post, but decided that someone trying to reconstruct Bayes’ theorem would be more likely to get to it by muddling through intuitively via conditional probability.
I don’t know about deducing the entire mindset & toolbox of ‘Bayesian rationality,’ but knowing Bayes’ theorem is the key part of it, and I wouldn’t expect that to be too hard to reconstruct if you knew what you look to for.
Bayes’ theorem follows trivially from the definition of conditional probability, and that definition is itself quite intuitive. So in theory, once you have a feel for what probability is, it’d be quite possible to get to Bayes’ theorem. I haven’t read Huygens’ 1657 book on probability theory, but if it was any good, I bet Huygens knew enough about it to beat Bayes to Bayes’ theorem by a century.
Chapters 1 and 2 of Jaynes’ Probability Theory: The Logic of Science show how Bayes’ theorem follows necessarily from certain basic principles of plausible reasoning. In some sense all roads lead to Bayes when trying to derive a consistent mathematical procedure for manipulating degrees of plausibility.
You are quite right. I thought about mentioning the Cox-Jaynes road to Bayes’ theorem in my post, but decided that someone trying to reconstruct Bayes’ theorem would be more likely to get to it by muddling through intuitively via conditional probability.