Is there any technical difference between a conditioned and conditioning variable?
E.g. see below picture
Can I call both X and Y conditioned OR conditioning?
Thanks
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1$\begingroup$ Could you explain what you mean by "technical difference"? After all, there is an obvious prima facie difference that most people would understand as being "technical": $X$ is the conditioning variable and $Y$ is not! Please be aware, too, that this notation has at least two distinct uses (technically): they differ according to whether $(X,Y)$ is a random variable or $X$ is a parameter (and might not be random at all). Which do you have in mind? $\endgroup$– whuber ♦Mar 16, 2018 at 15:43
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I think the only difference lies in the grammar, like one is a past tense and the other is a continuous tense. So you would say "Y is conditioned on X" in this case. The word conditioning can be used in places like "You can find the expectation of Y by conditioning on X"
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$\begingroup$ Conditioning is defined without any reference to time, so "past tense" is inapplicable. "Continuous tense" makes no sense. Is there perhaps a misspelling here? $\endgroup$– whuber ♦Mar 16, 2018 at 15:43
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1$\begingroup$ Conditioning of-course is not defined with respect to time, but in English we change the tense in order to make sense. A similar case would be "Correlation" and "Correlated", we use both the words, depending on the tense, present and past respectively in this case. $\endgroup$ Mar 16, 2018 at 15:54
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$\begingroup$ I see that I misunderstood your meaning of "past tense." Thank you for clarifying. However, it isn't apparent this answers the question, which concerns some kind of (vaguely expressed) difference between $X$ and $Y$. Are you asserting the variables play equivalent roles or not? $\endgroup$– whuber ♦Mar 16, 2018 at 16:36