I would be interested to see Eliezer’s response to Judea Pearl’s paper “Why I am only a half-Bayesian.”
I believe I saw that at some point, actually—I think I’m thinking of this comment and the associated thread, which unfortunately doesn’t have much in a way of a response.
Hm, the context there wasn’t originally about causality, which seems to come in as an aside. As far as I can judge from it, Eliezer is saying that causal models are things you can have probability distributions over, to be updated by evidence, just like every other sort of model of reality. They are not a separate magisterium from probability, and there is no need to be only half a Bayesian. That causality is not a statistical concept is of no more significance than that velocity is not a statistical concept.
It’s not clear to me what he intended by mentioning Pearl’s paper. As far as I know, Pearl nowhere considers probability distributions over causal models. He considers them only from the point of view of answering two-valued questions such as “Are these data consistent with this causal model?” or “Given this causal model, do these observations of some of its variables allow estimation of the magnitude of these causal effects?” He does not study questions such as “what causal model is most likely, given these data?” Some do, although as yet that seems to be limited to one group of researchers in neuroscience.
I believe I saw that at some point, actually—I think I’m thinking of this comment and the associated thread, which unfortunately doesn’t have much in a way of a response.
Hm, the context there wasn’t originally about causality, which seems to come in as an aside. As far as I can judge from it, Eliezer is saying that causal models are things you can have probability distributions over, to be updated by evidence, just like every other sort of model of reality. They are not a separate magisterium from probability, and there is no need to be only half a Bayesian. That causality is not a statistical concept is of no more significance than that velocity is not a statistical concept.
It’s not clear to me what he intended by mentioning Pearl’s paper. As far as I know, Pearl nowhere considers probability distributions over causal models. He considers them only from the point of view of answering two-valued questions such as “Are these data consistent with this causal model?” or “Given this causal model, do these observations of some of its variables allow estimation of the magnitude of these causal effects?” He does not study questions such as “what causal model is most likely, given these data?” Some do, although as yet that seems to be limited to one group of researchers in neuroscience.