Bayesianism for Humans

Re­cently, I com­pleted my first sys­tem­atic read-through of the se­quences. One of the biggest effects this had on me was con­sid­er­ably warm­ing my at­ti­tude to­wards Bayesi­anism. Not long ago, if you’d asked me my opinion of Bayesi­anism, I’d prob­a­bly have said some­thing like, “Bayes’ the­o­rem is all well and good when you know what num­bers to plug in, but all too of­ten you don’t.”

Now I re­al­ize that that ob­jec­tion is based on a mi­s­un­der­stand­ing of Bayesi­anism, or at least Bayesi­anism-as-ad­vo­cated-by-Eliezer-Yud­kowsky. “When (Not) To Use Prob­a­bil­ities” is all about this is­sue, but a cleaner ex­pres­sion of Eliezer’s true view may be this quote from “Beau­tiful Prob­a­bil­ity”:

No, you can’t always do the ex­act Bayesian calcu­la­tion for a prob­lem. Some­times you must seek an ap­prox­i­ma­tion; of­ten, in­deed. This doesn’t mean that prob­a­bil­ity the­ory has ceased to ap­ply, any more than your in­abil­ity to calcu­late the aero­dy­nam­ics of a 747 on an atom-by-atom ba­sis im­plies that the 747 is not made out of atoms. What­ever ap­prox­i­ma­tion you use, it works to the ex­tent that it ap­prox­i­mates the ideal Bayesian calcu­la­tion—and fails to the ex­tent that it de­parts.

The prac­ti­cal up­shot of see­ing Bayesi­anism as an ideal to be ap­prox­i­mated, I think, is this: you should avoid en­gag­ing in any rea­son­ing that’s demon­stra­bly non­sen­si­cal in Bayesian terms. Fur­ther­more, Bayesian rea­son­ing can be fruit­fully mined for heuris­tics that are use­ful in the real world. That’s an idea that ac­tu­ally has real-world ap­pli­ca­tions for hu­man be­ings, hence the ti­tle of this post, “Bayesi­anism for Hu­mans.”

Here’s my at­tempt to make an ini­tial list of more di­rectly ap­pli­ca­ble corol­laries to Bayesi­anism. Many of these corol­laries are non-ob­vi­ous, yet em­i­nently sen­si­ble once you think about them, which I think makes for a far bet­ter ar­gu­ment for Bayesi­anism than Dutch Book-type ar­gu­ments with lit­tle real-world rele­vance. Most (but not all) of the links are to posts within the se­quences, which hope­fully will al­low this post to dou­ble as a de­cent in­tro­duc­tory guide to the parts of the se­quences that ex­plain Bayesi­anism.