Odds are not easier

Epistemic sta­tus: just a re­view of a well known math the­o­rem and a brief rant about ter­minol­ogy.

Yes­ter­day I saw an­other ex­am­ple of this: is just a nor­mal­iz­ing con­stant for the pos­te­rior prob­a­bil­ity, and it’s re­ally hard (im­pos­si­ble?) to calcu­late, so let’s switch to log odd prob­a­bil­ities, which are eas­ier and the pesky term is can­celed.

Ex­cept it’s not: , the sec­ond term is ex­actly what you need to get the prob­a­bil­ity in odd form, and if you have it you can very well calcu­late the prior for the data.

So please, what­ever you write, stop say­ing that odds are eas­ier. They are pos­si­bly more in­tu­itive to ma­nipu­late, but they need ex­actly the same amount of in­for­ma­tion.