Other than Bayes’ world, which other worlds might we be living in?
A world with causes and effects. (Bayes’ world as described is Cassandra’s world, for the usual reasons of “prediction” not being what you want for choosing actions).
[ There was something else here, having to do with how it is hard to use causal info in a Bayesian way, but I deleted it for now in order to think about it more. You can ask me about it if interested. The moral is, it’s not so easy to just be Bayesian with arbitrary types of information. ]
Hmm. I think I know what you’re referring to — aside from prediction, you also need to be able to factor out irrelevant information, consider hypotheticals, and construct causal networks. A world where cause and effect didn’t work a good deal of the time might still be predictable, but choosing actions wouldn’t work very effectively.
(I suspect that if I’d read more of Pearl’s Causality I’d be able to express this more precisely.)
Well, when you use Bayes theorem, you are updating based on a conditioning event. But with causal info, it is not a conditioning event anymore. I don’t think it is literally impossible to be Bayesian with causal info, but it sounds hard. I am still thinking about it.
So I am not sure how practical this “be more Bayesian” advice really is. In practice we should be able to use information of the form “aspirin does not cause cancer”, right?
A world with causes and effects. (Bayes’ world as described is Cassandra’s world, for the usual reasons of “prediction” not being what you want for choosing actions).
[ There was something else here, having to do with how it is hard to use causal info in a Bayesian way, but I deleted it for now in order to think about it more. You can ask me about it if interested. The moral is, it’s not so easy to just be Bayesian with arbitrary types of information. ]
Hmm. I think I know what you’re referring to — aside from prediction, you also need to be able to factor out irrelevant information, consider hypotheticals, and construct causal networks. A world where cause and effect didn’t work a good deal of the time might still be predictable, but choosing actions wouldn’t work very effectively.
(I suspect that if I’d read more of Pearl’s Causality I’d be able to express this more precisely.)
Is that what you’re getting at, at all?
Well, when you use Bayes theorem, you are updating based on a conditioning event. But with causal info, it is not a conditioning event anymore. I don’t think it is literally impossible to be Bayesian with causal info, but it sounds hard. I am still thinking about it.
So I am not sure how practical this “be more Bayesian” advice really is. In practice we should be able to use information of the form “aspirin does not cause cancer”, right?
[ I did not downvote the parent. ]