There needs to be a post specifically devoted to arguments of the form “It’s okay to do things wrong, because doing them right would be hard”. I’ve seen this so many times, in so many places, in so many subjects, that I have to conclude that people just don’t see what is wrong with it.
(No, I’m not talking about making simplifying assumptions or idealizations in models. More like presenting a collection of sometimes-useful ad-hoc tricks as a competing theory, which is then argued for as a theory against its competitors on the basis of its being “easier to apply”.)
Bayes’ Theorem says that P(H|E) = P(H)P(E|H)/P(E). That’s, like, the law. You don’t get to take P(E|H) out of the equation, or pretend it isn’t there, just because it’s difficult to estimate. As I’ve said elsewhere, if you have a belief, then you’ve done a Bayesian update—which means you have some assumption about each of those quantities appearing in the formula, whether you choose to confront these assumptions or not.
As a matter of fact, if you find P(E|H) overly difficult to estimate, that means your H isn’t paying its rent.
There needs to be a post specifically devoted to arguments of the form “It’s okay to do things wrong, because doing them right would be hard”. I’ve seen this so many times, in so many places, in so many subjects, that I have to conclude that people just don’t see what is wrong with it.
(No, I’m not talking about making simplifying assumptions or idealizations in models. More like presenting a collection of sometimes-useful ad-hoc tricks as a competing theory, which is then argued for as a theory against its competitors on the basis of its being “easier to apply”.)
Bayes’ Theorem says that P(H|E) = P(H)P(E|H)/P(E). That’s, like, the law. You don’t get to take P(E|H) out of the equation, or pretend it isn’t there, just because it’s difficult to estimate. As I’ve said elsewhere, if you have a belief, then you’ve done a Bayesian update—which means you have some assumption about each of those quantities appearing in the formula, whether you choose to confront these assumptions or not.
As a matter of fact, if you find P(E|H) overly difficult to estimate, that means your H isn’t paying its rent.