I guess what I’m really trying to say is that x may only have a causal influence on y if a bunch of other factors are present,
Which can be represented in a straightforward fashion in Jaynes’s notation.
f(y | x0, x1=C… xN=C2)
If x “is a cause” of y when x1...xN, then this conditional will accurately predict y without ever saying “cause”. The causal talk seems to me superfluous mathematically—it’s just describing limiting cases of conditionals.
If you literally think that conditional probabilities describe causation, then you should water your grass to make it rain (because p(rain | grass-is-wet) is higher than p(rain | grass-is-dry)). Causation is not about prediction.
Which can be represented in a straightforward fashion in Jaynes’s notation.
f(y | x0, x1=C… xN=C2)
If x “is a cause” of y when x1...xN, then this conditional will accurately predict y without ever saying “cause”. The causal talk seems to me superfluous mathematically—it’s just describing limiting cases of conditionals.
If you literally think that conditional probabilities describe causation, then you should water your grass to make it rain (because p(rain | grass-is-wet) is higher than p(rain | grass-is-dry)). Causation is not about prediction.