Wikipedia:Articles for deletion/Delusions in probability theory and statistics

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result of the debate was delete. Ezeu 00:14, 7 June 2006 (UTC)[reply]

Common misconceptions in probability and statistics

Original research. It never becomes clear what the point is the essay attempts to make; there is supposed to be a "widespread delusion" but no connection between the vaguely described delusion and what follows. An earlier prod tag was removed by the author. Lambiam ^Talk 22:24, 28 May 2006 (UTC)[reply]

Delete I don't think it comes close to an encylopedic entry. Yanksox 22:30, 28 May 2006 (UTC)[reply]
Delete per nom as original research. The title "delusions" sounds pretty bad as well.--Jersey Devil 22:34, 28 May 2006 (UTC)[reply]
Delete. Original research. Even the title is strange. Something like Common misconceptions might have been better. Keep under better title or Merge. --CSTAR 23:27, 28 May 2006 (UTC)[reply]

Hmm. Now that it's been rewritten maybe a title chage: Causality and stochastic independence?--CSTAR 05:24, 29 May 2006 (UTC)[reply]

Merge anything useful with probability theory, then delete, no redirect. —Viriditas | Talk 23:39, 28 May 2006 (UTC)[reply]
Delete, nothing I can see that is worth merging. Cedars 00:40, 29 May 2006 (UTC)[reply]
Comment. The original article was so badly written that I don't think it was possible to make a neutral judgment about it. I've rewritten it well, to bring out the point the author was trying to make. Perhaps it will still be delete-worthy, but I hope now the debate is better-informed. People should go back and read it again now that it's comprehensible. Ryan Reich 01:15, 29 May 2006 (UTC)[reply]
Delete, Yes, I agree, it is “original research”. Though attempts to explain definition of independence of events by means of “knowledge” and “information” are widely widespread in the probability literature but while I did not manage to find publications on the theme of these delusion. Only the simple Stoyanov's example where it is shown, that except for probability nothing operates independence of events. Thank you for help and editing:) Excuse me. - Helgus 01:26, 29 May 2006 (UTC)[reply]
Note. Helgus is the author of the original essay. --Lambiam ^Talk 01:36, 29 May 2006 (UTC)[reply]

I should apologize for my wording; I wasn't trying to be mean. It just needed cleaning up. Ryan Reich 01:41, 29 May 2006 (UTC)[reply]
~~Keep~~ Keep or merge with statistical independence. After thinking about the article while rewriting it (and reading a comment Helgus makes on his talk page), I've come to realize that it's not especially different from a page like An infinitely differentiable function that is not analytic, or any of the other paradox pages we have. Although those have names like Sleeping beauty paradox. I haven't read the book Helgus quotes, but if the example is indeed from there it is not original research. Perhaps the article should simply be emphasized as a paradox of statistical dependence. Ryan Reich 01:55, 29 May 2006
It appears that there's some support for merging, and I don't want to split the vote if it comes to that. I think the content belongs, wherever it may land. Ryan Reich 03:01, 29 May 2006 (UTC)[reply]
Keep. I'd merge it with statistical independence unless another "delusion" is added, but that is not important for the AfD debate. Many thanks to Ryan for teasing the meaning out of the original text and rewriting it. -- Jitse Niesen (talk) 02:24, 29 May 2006 (UTC)[reply]
- PS: I realize that I haven't explained why it should be kept. Firstly, the reference casts doubts on the OR claim. Secondly, the point that statistical independence does not always agree with the intuitive understanding of (causal) independence is important and should be noted somewhere, but I wouldn't find it yet mentioned in Wikipedia. -- Jitse Niesen (talk) 02:35, 29 May 2006 (UTC)[reply]
As explained by Helgus, the lead paragraph is OR, but he took the example from the reference. Only, it is not clear what it is an example of. In Helgus words: "it is shown, that except for probability nothing operates independence of events". Maybe Ryan Reich can translate this for us. I don't discern any delusion or paradox in the example. See also Helgus' comment below. I've written something on the talk page of this page, where I propose to take any more technical discussion. --Lambiam ^Talk 11:11, 29 May 2006 (UTC)[reply]
Why split the discussion? An AfD debate is a discussion in itself; no reason to have part of the discussion on the talk page.

Anyway, I don't understand your remark on the talk page at all. The article does not talk about information after Ryan's rewrite. Perhaps you could cut out the sarcasm if you want a technical discussion?

The point of the example is that the events A and B are independent in the sense of probability theory, if p = 1/2. However, they are not independent in the usual sense of the word, as both depend on the throws of the coin. -- Jitse Niesen (talk) 14:34, 29 May 2006 (UTC)[reply]

As I understood it when I did the rewrite, the phrase "it is shown, that except for probability nothing operates independence of events" was intended to mean that in a mathematical (as opposed to physical) probabilistic experiment, events are "shallow": the only pieces of information are the descriptions of the events and the probabilities of each outcome, which are independent of the events themselves. This is the (or one of the) sentence which led me to believe that Helgus was talking about lack of causality and hidden information. Ryan Reich 14:42, 29 May 2006 (UTC)[reply]
The article states that the terminology "independent events" has the unfortunate side effect of implying that "non-independent events appear to embody some kind of information one about the other", and this is then presumably a form of the misconception of the title. I tried to show by a very simple example that this is not a misconception but that indeed they do. The article also states as another form of the "misconception": "both [independent events] are constrained by a third, underlying variable". In the example of the article, both A and B are constrained by the same triple of outcomes of other events. It is almost as if the example was produced to illustrate that the presumed misconception is in fact not a misconception. The article was originally written with the purpose of showing that the lead paragraph of Statistical independence was based on a delusion. This was later reiterated by the author on the talk page of Statistical independence. I assume the example given is indeed from Stoyanov's book. If it is not a counterexample to the "misconception" identified in the article, then what is it a counterexample to? I can only guess, but my best guess is that it is a counterexample to the following false claim, which is precisely the converse of the alleged misconception: "If two events are statistically independent, they are also independent in the sense that they are not constrained by a third, underlying variable". That this claim is indeed false is shown by Stoyanov's example for the case p = 1/2. I don't know if this is a common misconception, and I don't know whether Stoyanov claims it is one, but in any case it is not the misconception from the article. If the example is merged into Statistical independence purely as an example of showing how you can compute for this case whether the events A and B are independent, that's fine (although as an example for that it is needlessly complicated and not particularly appealing). If it is incoporated as a counterexample, we'd better find out from Stolyanov's book (which I don't have) what it is a counterexample to. The "misconception" from the article is unverifiable "original research" as far as I'm concerned. --Lambiam ^Talk 19:25, 29 May 2006 (UTC)[reply]
I don't agree that the concept is original research, just as any example in mathematics, appropriately accompanying the theory it's a part of, is not original research (up to a point). It is not unencyclopedic to give examples of what something is not as part of describing what it is. This content should go in statistical independence in this capacity. The example is not worthless either, as it illustrates part of the irrelevance of causality to statistical independence. Would it be original research to provide one or two more as illustrations of the rest? Ryan Reich 20:14, 29 May 2006 (UTC)[reply]
The above sentence contains a switcheroo from "concept" to "example". The example is not OR. The concept is. The concept is not the example. You write: "appropriately accompanying the theory it's a part of" — but that's at least a big part of what is at issue. The example is not an example of what is described in the lead paragraph. What is described in the lead paragraph is not illustrated by an example contained in this article. But even if it were an appropriate example, is the theory it is supposed to accompany and be a part of (presumably that which is described in the lead paragraph, or else what) a notable concept in probability theory, or is it just someone's misguided pet peeve? How do we know without reliable source? I can write an article about the common pitfall of making a copying error, replacing a "2" for a "z" in a formula, and illustrate with a valid example how that leads to an incorrect result. Is that then not original research because there is an example accompanying it, even though it cannot be properly sourced as per WP:V? --Lambiam ^Talk 01:07, 30 May 2006 (UTC)[reply]
There is a huge difference between swapping 2 and z, and swapping causal and statistical independence: the first one has nothing to do with anything more general, but the second one is an important part of understanding probability. To be clear: I think the "concept" is that of statistical independence, and I think that the allegedly original idea in this article is a clarification, similar to a statement like "In number theory, (a,b) refers to the greatest common divisor of a and b rather than their inner product or their ordered pair". It's a necessary clarification because when people conceptualize dependent events they think of causality, just as in the previous sentence, it would be necessary to clarify for an analyst that a commonly used symbol does not have the accustomed meaning. Before we enter another round of this, please indicate whether you think that such a clarification is necessarily OR. Ryan Reich 03:14, 30 May 2006 (UTC)[reply]
Personally I don't think it is necessary to state that statistical independence is not implied by causal independence. I'm not even sure what that means and if it is true. If you feel it is a welcome addition to the article Statistical independence, please edit it, citing your source for this claim, of course; we don't need this deletion debate for that. If you then further wish to claim that this is a common misconception among non-mathematicians, please cite your source for that as well. And if you go on to provide an example, laudable by itself, please find an example that indeed illustrates the issue. --Lambiam ^Talk 09:35, 30 May 2006 (UTC)[reply]
Well, then we disagree on how mathematics is to be taught, but that has nothing to do with this debate, so I'm through. Ryan Reich 14:31, 30 May 2006 (UTC)[reply]
Merge with Statistical independence, and delete redirect as unintuitive. (I apologoize for the possibility that this will mean a history merge by the closer; but this does seem the thing to do.) Septentrionalis 02:52, 29 May 2006 (UTC)[reply]
Comment. I have read the Stoyanov’s book. He speaks nothing about “delusions”. I have used his academic example only by way of illustration the main idea of considered page about “delusions”. I continue to insist, that the main idea of this page (“delusion”) is OR and consequently page should be deleted:) - Helgus 05:51, 29 May 2006 (UTC)[reply]
- It seems from your explanation that, now the "delusion" bit (and what you call the main idea) is removed, the article is not OR. -- Jitse Niesen (talk) 14:34, 29 May 2006 (UTC)[reply]
  - A title of section in Stoyanov’s book is literally: «About a role of probability in independence of events.» Only he results this example of three Bernoulli’s trials and makes a conclusion that only probability defines independence of events. Unfortunately I have Stoyanov’s book in Russian only:) Of course the Stoyanov’s example only is not OR. - Helgus 00:10, 30 May 2006 (UTC)[reply]
Delete per Helgus, also after Ryan Reich's rewrite. --Lambiam ^Talk 11:12, 29 May 2006 (UTC)[reply]
Delete - this is an opinionated essay by the author. The first part is already in Statistical independence; the rest is pointless as it fails to give context or purpose of the article. (Note that the author's Eventology article is also up for AfD - see above). B.Wind 17:44, 29 May 2006 (UTC)[reply]
Comment I'd vote weak keep except that the article is fairly weak as it stands. I agree with the move to "common misconceptions' instead of "delusions", since the latter word connotes psychosis. Potentially this is a worthy topic, but the article needs a lot of work, to say the least. Michael Hardy 00:53, 30 May 2006 (UTC)[reply]
Delete There may be something there to merge into Statistical independence, but the title is also bad. — Arthur Rubin | (talk) 21:21, 30 May 2006 (UTC)[reply]

Comment. I think, that Ryan Reich could write very necessary paper under the name "Causality and stochastic dependence?" (see offer of CSTAR) in which this Stoyanov's example for an illustration is used:) - Helgus 04:09, 31 May 2006 (UTC)[reply]
Comment. I agree with Lambiam that the "misconception" debunked by the example is in fact the converse of what is described in the article. Apart from that, I tend towards merging. JPD (talk) 13:55, 31 May 2006 (UTC)[reply]
Keep, good article and good mathematics. Stifle (talk) 22:13, 1 June 2006 (UTC)[reply]
Delete. Parts worth keeping are already in statistical independence. Gandalf61 09:39, 2 June 2006 (UTC)[reply]
Comment I added the notion of self-independence to both this article and the statistical independence article, since this notion more briefly illustrates the difference between statistical independence and vernacular notions of independence. Calbaer 19:52, 2 June 2006 (UTC)[reply]
Isn't it misleading to write, just like that, "an event is independent of itself"? Here is a less dry everyday (literally) example. The event of the sun rising today has no bearing on the probability of it rising tomorrow (assuming that probability to be 1), so these events are statistically independent, even though having a common underlying mechanism. I hope this example is illuminating (pun intended). --Lambiam ^Talk 21:01, 3 June 2006 (UTC)[reply]
That example is not as paradoxical in my opinion, since it does not address actual events of probability zero nor does it address the odder notion that something can be statistically independent of itself. I think the notion that an event can be independent of itself is powerful due to the seeming paradox; it gets to the heart of what the original author was saying, that independence is only statistical not philosophical or absolute. I have the example of picking 0.5 out of the unit interval in the statistical independence entry (to which I could add the Durrett reference if needed). Unfortunately, nontrivial real-world examples are hard to come by, since possible but zero measure events imply infinite divisibility or infinite time, either of which is arguably not a given in the current universe. Even the sun rise example need not be an almost sure event (e.g., what if the earth is destroyed by a comet, etc.). (Perhaps a physicist could come up with a simple-to-understand real-world example where zero measure does come into play, one that both expert and layman can understand and agree upon, but I'm no physicist.) Calbaer 03:52, 4 June 2006 (UTC)[reply]
I'd support any of the merges listed above. Obviously an ill-chosen title, but the information here would almost uniformly be considered notable and verifiable in another context. Note the references; I don't know if they have been there teh whole time. savidan^{(talk) (e@)} 23:30, 3 June 2006 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.