I don't really see the problem in the first place: we're just writing less by assuming that the subscript is identical to the argument (except maybe for capitalization) - and if it's not, people usually disambiguate by adding the subscripts back in.
You would have to be a twisted soul to write P(x|y) if x is drawn from r.v. Y and y from r.v. X and P[Y|X] is the distribution in question.
> You would have to be a twisted soul to write P(x|y) if x is drawn from r.v. Y and y from r.v. X and P[Y|X] is the distribution in question.
Sure, that would be perverse. What I was referring to was more the fact that capital X and lowercase x look similar on the page and (more importantly) sound similar in my head.
Pedagogically I've found that saying "X takes on the value x" confuses a LOT of undergraduates.
Also, at least for me, if I start slinging around RVs and need to get closed form solutions, it can start to be very important to distinguish between X and the value it takes on as k or u, particularly when trying to do conditional expectations or get explicit distributions on functions of multiple RVs. It's sort of an aural Hungarian notation.
Sorry to re-open this so late, but I thought about this discussion today as I was reading a paper which had a typo in the subscript specifying a distribution: http://dx.doi.org/10.1103/PhysRevLett.103.138101 (it never ceases to amaze me that people get away with publishing glaring errors like that one).
In eq. (4), they specify P_{k|v}[x|v]. Thankfully, here, it's easy to spot the typo, because k is discrete and x is continuous. But this made me realize that my objection to these subscripts is really akin to wanting to write DRY, self-commenting code.
The fundamental information is already there in the equation. Adding extra subscripts is then like adding unnecessary comments to code - if they're right, they just add redundancy but maybe help the uninitiated; but if they're wrong, they're infinitely worse than having put nothing at all (someone who didn't know that PRL lets all kinds of crap fly could really be thrown for a loop figuring out how equ. 4 is possible).
> Pedagogically I've found that saying "X takes on the value x" confuses a LOT of undergraduates.
I haven't taught this to anyone, so your experience is more valuable than mine here. Nonetheless - I noticed in my undergraduate statistics class that programmers (i.e. people who are accustomed to obtuse rules regarding case sensitivity) had no problem with this, while other people accustomed to playing fast and loose with notation (economists and physicists in particular) were somewhat put off.
You would have to be a twisted soul to write P(x|y) if x is drawn from r.v. Y and y from r.v. X and P[Y|X] is the distribution in question.