Talk:Conditional expectation

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This page needs substantial reworking.

  • Motivation involving finite probability spaces
  • Intuitive generalizations
  • CLear statements of abstract framework general theorems and the general probability framework
  • Cond Exp as factorization (important for defining sufficient statististics)
  • References.

If nobody objects, I'll do it in the next few hours CSTAR 15:45, 9 May 2004 (UTC)

Go for it. Charles Matthews 15:58, 9 May 2004 (UTC)


I'm still working on it. But I'd like to get some stuff out so I can ponder more on this. If I've screwed things up, please tell me. CSTAR 21:31, 9 May 2004 (UTC)

This article is terrible. It's fairly well written for an article addressed to mathematicians who know a bit of measure theory and have a bit of intuition for probability. Therefore, it's terrible. Obviously the main ideas can be stated simply in a way that can be understood by someone who knows only as much probability as can be understood without knowing even calculus. Well, it's not as much of an Augean stable as some things on Wikipedia, so maybe I'll do something with it at some point. Michael Hardy 01:55, 8 Oct 2004 (UTC)

I'm perfectly willing to believe the article is terrible...but does your argument really establish that it's terrible? Too abstract yes, not enough intuition yes etc etc. Please be more specific about what you think should be done with it, whether the abstract stuff should be removed etc. I'd be somewhat unhappy if conditioning as projection were to be removed, since without this it is hard to talk about martingales etc., but hey I won't lose any sleep over it. But simply concluding in an abrupt non-sequitur that it's terrible isn't very helpful!CSTAR 02:19, 8 Oct 2004 (UTC)

I would not remove the abstract stuff, but I would attempt to make the article comprehensible to everyone who understands the basic definition of conditional probability, not just to mathematicians who know, e.g., the Radon-Nikodym theorem. Even the definition of E(X | Y) for continuous random variables X and Y can be clearly stated in such terms if you don't require examination of the sort of issues addressed only in measure theory. Mathematical rigor is important in its place, but so is communication. I'll return to this when I've got some time. Michael Hardy 20:29, 8 Oct 2004 (UTC)

I have to say - the 'intuitive' explanation always went right by me. Charles Matthews 21:15, 8 Oct 2004 (UTC)

OK, here's something from another Wikipedia article:

The conditional expected value E( X | Y ) is a random variable in its own right, whose value depends on the value of Y. Notice that the conditional expected value of X given the event Y = y is a function of y (this is where adherence to the conventional rigidly case-sensitive notation of probability theory becomes important!). If we write E( X | Y = y) = g(y) then the random variable E( X | Y ) is just g(Y). Similar comments apply to the conditional variance.

Charles, is that the intuitive explanation that went by you? Michael Hardy 00:01, 9 Oct 2004 (UTC)

Is the previous paragraph an example of a clear explanation? Is it too impolitic to say it doesn't seem to me to be hardly an improvement? I'm also curious as to what you would point to as being more of an Augean stable in wikipedia, though I do agree that there are many, many articles which I think fit this bill.CSTAR 00:28, 9 Oct 2004 (UTC)

Guys, I think everyone's ambitions here are compatible, at least. Charles Matthews 08:52, 9 Oct 2004 (UTC)

[edit] 1_{...}

What does the 1 in the E(X 1_{...}) notation stand for?

1_A is the indicator function of A. --CSTAR 17:38, 14 Apr 2005 (UTC)
..., and, in the context of probability theory, 1A can be defined as a random variable that is equal to 1 if the event A occurs and is equal to 0 if the event A fails to occur. Michael Hardy 18:23, 14 Apr 2005 (UTC)
But what does E(X f) mean, f being a function? Does it mean the E of the function composition of X and f? (http://www.stats.uwo.ca/courses/ss357a/handouts/cond-expec.pdf uses a completely different formula)

[edit] Split into sections?

Does anybody else feel as if the table of contents is too down in the article, and some more splitting in sections could be done at the top? I don't know what is a good way of splitting it myself. Oleg Alexandrov 20:07, 14 Apr 2005 (UTC)

Yeah I agree; but don't look at me for changes..CSTAR 20:44, 14 Apr 2005 (UTC)
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