# Talk:Bayes' theorem

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## An excellent figure

On the topic of making the article more accessible, I suggest using figure 2 of the article by Spiegelhater et al. 2011. The only problem is that it is probably copyright protected, but something similar should be easy to come up with (using your beetles example, for instance).

Spiegelhater, D., M. Pearson and I. Short. 2011. Visualizing Uncertainty about the Future. Science, vol. 333, pp. 1393-1400.

Do you mean Fig. 2 in http://www.sci.utah.edu/~kpotter/Library/Papers/spiegelhalter:2011:VUAB/? cmɢʟeeτaʟκ 12:52, 6 June 2014 (UTC)

## "... sufficient to deduce all 24 values" ??

I can't really identify 24 distinct probabilities in the picture that illustrates tree diagrams (frequentist interpretation with tree diagrams); in the matter of fact I see only 16. — Preceding unsigned comment added by 85.110.18.176 (talk) 22:40, 18 February 2014 (UTC)

## Probability wrong.

>Bayes' theorem can be used to calculate the probability that the person was a woman.

I'm sorry, but my statistics professor at the University of Michigan, Eugene Rothman, who must know what he is talking about as he has a PhD in statistics and is a professor at the University of Michigan, says that probability applies only to events that have not happened yet, not for events which have already happened, like the conversation.

If it applied to events in the past, the probability would be one of two discrete values, 1 (100%), or 0 (0%). — Preceding unsigned comment added by 63.84.231.3 (talk) 12:28, 25 March 2014 (UTC)

Your professor is correct in the sense that the man was talking to either a man or a woman, and whatever gender of that person was is 100% certain to him, but the probability in this case is describing the effect of having observed an event. It's a subtle difference; note that at the beginning of that section there is the statement, "Not knowing anything about the conversation." We haven't observed the gender of the person, so the best that we are able to do is calculate the probability that he had been talking to a woman. It doesn't change the facts, it just applies a probability which best describes the likelihood of that person's gender based upon all the information we have.

As a different example which more explicitely shows how we still need to apply probability to "events in the past," imagine a game of poker. There is one card left to appear and you need an Ace to win. The deck was pre-shuffled and therefore the outcome of this final card is something that's already been decided. You can't say that an Ace will appear 100% of the time or 0% of the time, can you? JaeDyWolf ~ Baka-San (talk) 15:19, 25 March 2014 (UTC)

For this specific instance, yes. — Preceding unsigned comment added by 63.84.231.3 (talk) 19:28, 25 March 2014 (UTC)

In a sense, yes you can, but what good is that? Technically, the event has already occurred but we have yet to observe it, so the best we can do is apply the information we do have, including our degrees of uncertainty. The probability isn't incorrect; you're simply taking a different interpretation of the facts which, while technically accurate, is less "useful" from a probabilistic standpoint. I'd actually be curious to hear your professor's comments on this conversation! JaeDyWolf ~ Baka-San (talk) 17:14, 28 March 2014 (UTC)

Yes, this is exactly classic contention between Bayesian statistics - where "probabilities" have interpretations as strength of beliefs, and frequentist statistics - where probabilities are interpreted as something more like "how often the outcome will turn out this way if we do this experiment many times". FWIW, since this a surprisingly touchy point for many people, I think it would be better for the article not to presume either definition; the same theorem applies in both schools of thought, and there is no sense making it narrower than necessary. Would be good to tidy up, or at least explicitly state which definition is being used throughout the article --Livingthingdan (talk) 15:31, 4 August 2014 (UTC)

Having read the article over, I submit that the ambiguity is in a few places: Firstly, the Introduction and Introductory Example, both use a Bayesian interpretation without saying so; We could tidy that section up... but that will lead to the article becoming quite repetitive when the distinction is made again in the very next section. Secondly, the "Examples" section, labels one example as "frequentist" when in fact all three examples are frequentist. --Livingthingdan (talk) 15:40, 4 August 2014 (UTC)

Hi Livingthingdan, I hear you on the interpretation thing. Actually I need to make a correction on the Introduction and Introductory example. "Posterior probabilities" should be "Conditional probabilities". I tried to be as basic as possible since yes there are at least 2 different ways to interpret Bayes. Anyways, I think it is a good idea to keep the 2 forms of the theorem near the top since both are quite commonly encountered and try to smothen out the wording so that it can be applicable to both schools of thought you mentioned. People will be familiar more with these than other forms of Bayes like the "Odds" form. The reason why I put 2 common forms of Bayes in an Introduction section is because the introductory example was not clear and it did use a strength of belief interpretation. I hoped that at least the Introduction could lead the reader to the introductory example and provide some understanding. The article is a bit messy and needs some editing for sure. Please feel free to edit what you see fit. --Mayan1990 (talk) 01:11, 5 August 2014 (UTC)

## Equal number of men and women on train... unnecessary assumption

I had to stop reading immediately when I got to the phrase "assuming there are an equal number of men and women on the train." There is no reason to assume this, and no reason to do so. Having no information about about the number of men and women yields the same result. I'm a little afraid to keep reading at this point, but I'll soldier on.

It actually says, 'the probability that he was speaking to a woman is 50% (assuming the speaker was as likely to strike up a conversation with a man as with a woman)', but I am not sure what your actual complaint is. Could you clarify please. Martin Hogbin (talk) 16:26, 16 May 2014 (UTC)

## name of the article

I want to re-open several dated discussions, all of them dealing with the spelling of the theorem's name. To add a twist on two common alternatives, it's not just a question of Bayes' vs. Bayes's (as a proper form of possessive – and indeed the subject of majority of previous discussions), but also of "the Bayes theorem" vs. "Bayes'/Bayes's theorem" (as an attributive use vs. possessive/genitive use). None of the earlier discussions ended with a clear conclusion or consensus.

So three alternatives of the article's name that were discussed before are:

1. "Bayes's theorem"
2. "Bayes' theorem"
3. "the Bayes theorem"

(Note: the #1 vs. #2 distinction is purely orthographical (and is distinguished mostly in writing, as although the pronunciations vary they tend to be similar for many people); whereas #1/2 vs. #3 distinction is grammatical, and is based on use of different grammatical constructions, and as such is more easily distinguishable both in speech and in writing. So the preference of #1/2 (vs. #3) seems to be fairly well established, with preference between #1 and #2 being of more ambiguous nature – and hence the point of majority of discussions.)

I summarize below all substantive arguments for each case, taking them from the previous discussions for ease of reference (1, 2, 3, 4)

1.

• Proper, more classical use of a singular possessive: Bayes's, even simply from the way it's spelled, is unambiguously a possessive of a singular noun "Bayes". It can't be confused with a possessive of plural noun Bayes (which would stand to be a plural of Baye).
• This use is supported by many manuals of styles and grammar books (both classical and modern).
• Even if some of modern English usage is more permissive in terms of misspellings and/or spelling rule simplifications (partially aided by amounts of online content not having been properly copy-edited), not a single source that permits Bayes'/Jones' would go as far as claiming that Bayes's/Jones's is wrong. (Examples of reverse are abundant.)
• Hence this variant should satisfy both grammar purists and those who don't care one way or the other.

2.

• Definitely not a correct usage according to more classical sources of English grammar, which permit very rare exceptions to the rule of adding 's to a singular noun already ending in "s" (proper usage always being Jones's for a singular name Jones, etc. – with one of the few rare exceptions being Jesus').
• Modern usage (especially in press and online) and present-day manuals of style (again, many of them are based on periodicals and press, and are indeed published or affiliated with them) are more permissive of "Jones' " for singular nouns ending in "s". Again, it must be noted that none of them are restrictive of the "Jones's".
• Another argument was online usage: comparing google stats on both terms revealed prevalence of this variant in online sources. This by itself is barely an argument, since sometimes common (and widespread) mistakes are easily propagated and copied over.
• This also reflects a common misconception about usage of 's or ' after singular nouns ending in "s". Almost invariably in discussions when someone claimed the latter is right, he/she seemed to be unaware of differences between formation of possessives of singular and plural nouns ending in "s" (making up one common rule for both) – that is, until someone more knowledgeable pointed out the distinction. So this is probably an example of the rule that may be often taught incorrectly in primary education, since it can be argued that even grammar teachers could at times be prone to similar simplifications. Hence, a common misconception about how to spell singular possessives of the nouns ending in "s".
• (maybe dubious) "Bayes' " was customary at the time when the theorem was published, and has thus become ingrained.

3.

• This one is, grammatically speaking, the attributive use of a singular noun Bayes. Examples given were "the Smale theorem" vs. "Smale's theorem" (with both being grammatically correct and indeed used – and hence the preference not being well established), as well as "the Gauss lemma" and "Zorn's axiom" – with only the mentioned alternatives being used predominantly.
• So the tie-breaker here would probably be common usage, which seems to favor the possessive use vs. the attributive use.

So the summary is:

1. Proper, classical, non-contradictory usage – if only less often used online. In encyclopedia, we should probably side with proper and unambiguous usage rather than with inherently ambiguous usage and/or misspellings (however commonly encountered).
2. Permitted by some modern manuals of style, also is more commonly encountered (note: this statement is true only about online sources – since the frequency of use in printed sources is hard to establish). But, is also confusing due to inherent ambiguity (as in "theorem of multiple people named Baye" vs. "theorem of a single person named Bayes").
3. A less common grammatical usage (that is, less common with respect to this particular subject), although technically and grammatically correct.

As a side benefit of using #1, we may start seeing shift towards more common online usage of #1 outside Wikipedia. Wiki is a widely replicated and consulted resource, so for better or for worse, the choices between commonly used spellings tends to be affected by the choices in Wikipedia – especially in fairly confusing cases like this one. cherkash (talk) 05:11, 14 June 2014 (UTC)

You obviously care a lot about something which most others care less about. One thing you should bear in mind is that Wikipdia is not intended to set trends but to reflect them. We should use the term that is most commonly used in reliable sources. Martin Hogbin (talk) 09:00, 14 June 2014 (UTC)
There is a difference between "commonly used" (as in a "commonly used misspelling") and "grammatically correct". We would most likely agree that "the Bayes theorem" is not a very commonly used term, whereas "Bayes's/Bayes' theorem" is probably more common. As for the choice of two possible spellings of "Bayes'/Bayes's", we should probably choose the one that is grammatically more correct and the one meaning of which is not ambiguous (i.e. "of one person named Bayes", rather than confusing it with "of many people each named Baye"). cherkash (talk) 05:31, 24 June 2014 (UTC)
I agree that "Bayes's Theorem" would be a more appropriate title for the article. It's what people call it, and it's grammatically correct. I actually typed in "Bayes's Theorem" when searching for this article, because that's what I expected the name of the article was -- I was surprised to find otherwise. Chris Mounce (talk) 18:09, 18 July 2014 (UTC)
There is indeed a difference between "commonly used" and "grammatically correct" and WP policy is that we should use the former. We must call things what they are called not what they ought to be called. Google show 48K hits for "Bayes's theorem", and 730k hits for "Bayes's theorem". My dictionary (Collins) gives only Bayes'. Whatever you might think the theorem ought to be called it is called Bayes' theorem. Martin Hogbin (talk) 18:40, 18 July 2014 (UTC)
Point of fact, the only difference between "commonly used" and "grammatically correct" is a certain amount of lag time. Sometimes generations, sometimes epochs, but in the end, what is commonly used becomes grammatically correct. Although this does not settle your question vis a vis the name of the article, it might help you sleep better at night. 66.175.162.174 (talk) 21:24, 29 July 2014 (UTC)