I recently went through a video which said that in the relation x->W<-Y, X does not influence y.X has causal relationship to W and W has evidential relationship to Y .So will X not affect Y ?
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I recently went through a video which said that in the relation x->W<-Y, X does not influence y.X has causal relationship to W and W has evidential relationship to Y .So will X not affect Y ?
Let’s let W represent “The Lawn is Wet,” X represent “It rained recently,” and Y represent “The automatic sprinklers were on recently.”
Clearly, X influences W: If it rained recently, it is likely that the lawn is wet.
Clearly, Y influences W: If the sprinklers were on recently, it is likely that the lawn is wet.
Clearly, knowing W, we can make inferences about X and Y.
But, does X directly influence Y?
Put differently, does the fact of recent rain (or not) influence whether the automatic sprinklers were on recently?
No. If we know nothing about the state of the lawn, because we didn’t look outside, the chance of recent rain is independent of the chance of recent sprinkler activity.
Once we look outside, though, and determine the state of the lawn, then we can draw inferences between rain and sprinkler activity.