You said: “Since there’s an “unusually high” probability for P(Z1Y2) - defined as a probability higher than the marginal probabilities would indicate by default—it follows that observing Z1 is evidence which increases the probability of Y2. And by a symmetrical argument, observing Y2 must favor Z1.”
But I think what you meant was “Since there’s an “unusually high” probability for P(Z1Y2) - defined as a probability higher than the marginal probabilities would indicate by default—it follows that observing Y2 is evidence which increases the probability of Z1. And by a symmetrical argument, observing Z1 must favor Y2.”
Nothing you said was untrue, but the implication of what you wrote doesn’t match up with the example you actually gave just above that text.
I believe you made a slight typo, Eli.
You said: “Since there’s an “unusually high” probability for P(Z1Y2) - defined as a probability higher than the marginal probabilities would indicate by default—it follows that observing Z1 is evidence which increases the probability of Y2. And by a symmetrical argument, observing Y2 must favor Z1.”
But I think what you meant was “Since there’s an “unusually high” probability for P(Z1Y2) - defined as a probability higher than the marginal probabilities would indicate by default—it follows that observing Y2 is evidence which increases the probability of Z1. And by a symmetrical argument, observing Z1 must favor Y2.”
Nothing you said was untrue, but the implication of what you wrote doesn’t match up with the example you actually gave just above that text.