[SEQ RERUN] Priors as Mathematical Objects

To­day’s post, Pri­ors as Math­e­mat­i­cal Ob­jects, was origi­nally pub­lished on 12 April 2007. A sum­mary (taken from the LW wiki):

As a math­e­mat­i­cal ob­ject, a Bayesian “prior” is a prob­a­bil­ity dis­tri­bu­tion over se­quences of ob­ser­va­tions. That is, the prior as­signs a prob­a­bil­ity to ev­ery pos­si­ble se­quence of ob­ser­va­tions. In prin­ci­ple, you could then use the prior to com­pute the prob­a­bil­ity of any event by sum­ming the prob­a­bil­ities of all ob­ser­va­tion-se­quences in which that event oc­curs. For­mally, the prior is just a gi­ant look-up table. How­ever, an ac­tual Bayesian rea­soner wouldn’t liter­ally im­ple­ment a gi­ant look-up table. Nonethe­less, the for­mal defi­ni­tion of a prior is some­times con­ve­nient. For ex­am­ple, if you are un­cer­tain about which dis­tri­bu­tion to use, you can just use a weighted sum of dis­tri­bu­tions, which di­rectly gives an­other dis­tri­bu­tion.

Dis­cuss the post here (rather than in the com­ments to the origi­nal post).

This post is part of the Rerun­ning the Se­quences se­ries, where we’ll be go­ing through Eliezer Yud­kowsky’s old posts in or­der so that peo­ple who are in­ter­ested can (re-)read and dis­cuss them. The pre­vi­ous post was Marginally Zero-Sum Efforts, and you can use the se­quence_re­runs tag or rss feed to fol­low the rest of the se­ries.

Se­quence re­runs are a com­mu­nity-driven effort. You can par­ti­ci­pate by re-read­ing the se­quence post, dis­cussing it here, post­ing the next day’s se­quence re­runs post, or sum­ma­riz­ing forth­com­ing ar­ti­cles on the wiki. Go here for more de­tails, or to have meta dis­cus­sions about the Rerun­ning the Se­quences se­ries.

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