Talk:Conditional independence

Redundant Intro

The first paragraph of this article says the same thing, three times. I am not sure what is the best way to simplify it, but it is confusing enough already. —Preceding unsigned comment added by 72.29.211.19 (talk) 01:06, 11 May 2011 (UTC)

Good Examples Link

http://www.dcs.qmul.ac.uk/~norman/BBNs/Independence_and_conditional_independence.htm Davyzhu (talk) 06:05, 27 February 2008 (UTC)

Conditional Dependence links to the butterfly effect? That seems kind of absurd! That article hardly discusses conditional dependence and is totally different. I think we should have this page discuss both conditional dependence and independence. I changed the link to link here, and renamed the link to the butterfly effect.Epachamo 00:16, 20 April 2007 (UTC)

Graphic of Squares

I cannot verify that P(AUB|not C) in the first figure is equal to P(A|C)*P(B|C). I count that P(AUB|not C) is 4/37, P(A|notC) is 12/37, and P(B|notC) is 12/37. That doesn't work out. Did I miss something? 76.8.64.166 (talk) 20:51, 16 January 2008 (UTC)

Agree, the graphic is incorrect. It would be valid if the grid were 6x8 instead of 7x7, with other areas unchanged, then fractions are 12/36 x 12/36 = 4/36 167.136.242.40 (talk) 22:57, 18 February 2008 (UTC)dfry

Yeah, the graphic is incorrect !!!

Make that 4 unconditionally independent votes for incorrect.

5!!!!! —Preceding unsigned comment added by 195.219.143.2 (talk) 08:27, 20 April 2009 (UTC)

—Preceding unsigned comment added by 58.161.42.51 (talk) 00:54, 8 May 2008 (UTC)

Actually the link to the jpg (figure named CondicionalmenteIndependientes.JPG‎) IS correct... I do not know why it is shown this wrong one... —Preceding unsigned comment added by 193.204.89.132 (talk) 07:48, 28 May 2009 (UTC)

I no not know if this is the correct place to say this, but I have modified the current SVG figure to make it again correct ( like in the original picture, where the first figure grid is 6x7 ). Unfortunally, I have tried to upload the figure as a replacement of the actual one but I have only been able to upload it as a new picture. As I do not want that the history of the actual file gets lost, I have not finished the uploading. I think that I can not modify it because I have not written enough in wikipedia and I do not have permissions. Could someone help me? Cesarth (talk) 08:02, 10 April 2015 (UTC)

Independence

I have been told that two variables can be indendant, but not conditionally independant. For example, if a variable Z is dependant on two variables X and Y, and X and Y are independant, then X and Y are *not* (or may not be) independant given Z. Is this true? If it is it should be explained in this article. Fresheneesz 01:55, 1 December 2007 (UTC)

Example proving that two variables may not be conditionally independant even if they are unconditionally independant:

X – 0 or 1 (random coin flip)

Y – 0 or 1 (random coin flip)

Z – sum of X and Y (can be 0, 1, or 2)

X and Y are obviously independant. P(Z==0)=0.25, P(Z==1)=0.5, P(Z==2)=0.25 . Knowing what Z is will enable you to know something about what X is if you know what Y is - in some cases allowing you to know exactly what X is. Thus X and Y aren't conditionally independant given Z. Fresheneesz 03:30, 1 December 2007 (UTC)

Unclear Baysian networks

The section on Baysian networks is exteremly unclear, and poorly constructed. It is always a bad idea to begin with an example. The addition of the "frequentist" further confuses the section. Fresheneesz 02:11, 1 December 2007 (UTC)

I disagree -- it is always a GOOD idea to begin with an example! People are pretty good at generalising from a few worked examples, but most (even those of us with PhDs) find it difficult to understand things expressed as generalities. When I was teaching at a university I always started with an example and then went on to the general theory, and the students definitely approved of this technique. Unfortunately most textbooks do the opposite. 88.110.89.8 (talk) 18:34, 11 January 2010 (UTC)

Incorrect definition

"Two random variables X and Y are conditionally independent given a third random variable W if for any measurable set S of possible values of W, X and Y are conditionally independent given the event [W ∈ S]." — This is incorrect. Boris Tsirelson (talk) 14:07, 7 December 2008 (UTC)

I've fixed it. I'm not sure if we've got a good account of conditioning on a sigma-algebra. There's a section in the article titled conditional expectation that treats the topic, but it's fairly terse and does not mention the role of the Radon–Nikodym theorem. Michael Hardy (talk) 14:47, 7 December 2008 (UTC)

And please remove the obsolete "measurable set S of possible values of W". Yes, I know that such conditioning is not an easy matter; in fact, this is why I've created the Conditioning (probability) page. Boris Tsirelson (talk) 15:03, 7 December 2008 (UTC)

Now I did it myself. Boris Tsirelson (talk) 11:38, 16 December 2008 (UTC)

returning to these comments, as they look rather old: are these the basis of the "factual accuracy is disputed" tag on "Decomposition"? to be honest, i am unclear on what exactly is being disputed in the text that appears in the article, as the proofs ( as far as i can tell ) seem to be correct. the properties themselves are stated in Judea Pearl's "Causality", which is already cited in the sources. propose that we remove the "dispute" tag. ( it seems consensus might be complicated by the fact that one of the original posters here is deceased )Benjamin Schulz (talk) 06:54, 14 March 2021 (UTC)

Properties are rubbish

Practically all rules of conditional independence are rubbish and meaningless (unless a definition is added, what it means, when to the left or right of the relation symbol two sets show up and are seperated by a comma). —Preceding unsigned comment added by 93.207.223.32 (talk) 15:36, 7 May 2010 (UTC)

And now, after the edit by Ninjagecko of 21 October 2010, they are even more rubbish and meaningless than before. Boris Tsirelson (talk) 19:35, 21 October 2010 (UTC)

Inadequate diagram

I think the diagram is inadequate -- it's impossible to tell by looking at it which squares do or do not contain blue, or red. I can figure it out by referring to the footnote and using my prior knowledge of how this works, but that's no good for a reader who doesn't already know the material. To me it seems that the only way to fix this would be to redo the diagram with each square labeled with one or more color abbreviations R, B, etc., ideally with the letter R itself appearing in red, the letter B itself appearing in blue, etc., with a white background. Duoduoduo (talk) 15:35, 18 February 2011 (UTC)

I agree. -AlanUS (talk) 13:27, 21 April 2011 (UTC)

Too technical

Can somebody please explain the mathematical notation used in this article? 71.178.164.165 (talk) 19:05, 16 January 2014 (UTC)

i think this has been addressed in subsequent versions of the article Benjamin Schulz (talk) 03:18, 16 March 2021 (UTC)

Lead

The lead needs to be rewritten, examples and discussion belong into the article body. Please refer to WP:LEAD. Paradoctor (talk) 00:44, 17 January 2014 (UTC)

introduction has been subsequently rewritten; would be curious to get additional opinion on whether it is any closer to satisfactory Benjamin Schulz (talk) 03:19, 16 March 2021 (UTC)

Proposal to merge conditional dependence into conditional independence

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

No consensus, however you may perform the merge per WP:BOLD and take accountability for it. MorningThoughts (talk) 16:27, 21 November 2019 (UTC)

---

Conditional dependence is merely the absence of conditional independence. It makes as little sense to have a separate article on it as it would to have a separate article on linear dependence in addition to the one on linear independence. The article on conditional dependence was created relatively late, in 2012, after two previous submissions had been declined (see the revision history). The misguided thinking that led to the creation of the article is summarized in the last sentence of the initial version of the article: "Conditional dependence is different from conditional independence. In conditional independence two events which are initially dependent become independent given the occurrence of a third event."

The current content of the article on conditional dependence adds little to what we have at conditional independence, and some of it looks like original research. In my view, most of it could simply be deleted, but suggestions on what to keep and how to integrate it into conditional independence are of course welcome.

Joriki (talk) 07:07, 1 July 2018 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Unification with "Independence (probability theory)", especially the definition section

This article should be unified (but not merged) with Independence (probability theory), and an expert is needed for that. What I mean is that the parts of Conditional independence that parallel Independence (probability theory) should be re-written to be as similar as possible. The main reason is that the current article is of lower quality. In particular, the current version claims that the two definitions are equivalent:

$P(A\mid B,C)=P(A\mid C)$

and

$P(A,B|C)=P(A|C)P(B|C)$

which is incorrect. The definitions are only equivalent when all the conditional probabilities are well-defined. Also, the proof of the claimed equivalence is wrong because of the division by $P(B,C)$, which may be zero. In Independence (probability theory), this problem is somewhat mitigated by a remark that follows a similarly incorrect proof. — Preceding unsigned comment added by AVM2019 (talk • contribs) 16:39, 27 November 2021 (UTC)

Incorrect phrasing

Under the section "Examples" and there under "Proximity and Delays" it says "Let events A and B be defined as the probability that person A and person B will be home in time...". The way it sounds it reads as if the events A and B are probabilities. However, events are not probabilities! Events are sets, they are subsets of the sample space. Events have a probability (as long as they are elements of the underlying sigma algebra) but they aren't probabilities themselves. It would be more accurate to say "Let events A and B be defined as the fact that person A and person B will be home in time...". 2A01:C23:C46F:7E00:1805:A74B:9E63:F331 (talk) 20:20, 13 November 2022 (UTC)