Talk:Bayes' theorem/Archive 7

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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)

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/? cmɢʟee⎆τaʟκ 12:52, 6 June 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)

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)

This is really not a discussion of "what things are called" vs. "what things ought to be called". We all mostly agree that "Bayes's Theorem" is a very common name for this theorem – between "Bayes's/Bayes' theorem" (#1/#2) and "the Bayes theorem" (#3), the first version (#1/#2, with the two being spelling variants of the same) is likely more common. I encourage editors to debate "#1/#2 vs. #3" if there's a taste for this, but I could easily concede to #1/#2 being a good choice for the name of the article.

The real subject of this discussion (as it developed) is what the proper spelling is between two familiar versions: "Bayes's" vs. "Bayes'". This is not a matter of the debate about the article's name – it's a matter of debate about grammar/spelling rules of English language. As such, "Bayes's" is a more preferred and less ambiguous spelling variant than "Bayes'". I can elaborate further if anyone wants a more detailed argument as to why this is the case. As things stand now – and with #1/#2 (as opposed to #3) being a long-standing name of the article, my inclination is to correct the spelling under copyedit/typo-fixing mandate. Again, if anyone cares to hear more, I can elaborate why #1 is a more preferred and more correct version than #2: in short, although #2 is a form that is sometimes acceptable, #1 is acceptable universally. cherkash (talk) 07:05, 25 August 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)

Is this sentence correct?: "To see how this is done, let W represent the event that the conversation was held with a woman, and L denote the event that the conversation was held with a long-haired person."

Should not both occurrences of the word 'event' be occurrences of the word 'probability in the following sentence?

"To see how this is done, let W represent the event that the conversation was held with a woman, and L denote the event that the conversation was held with a long-haired person." — Preceding unsigned comment added by Acmjacmj (talk • contribs) 04:24, 5 October 2014 (UTC)

I don't think so. The events W and L are conjectures, which are resolved to either true or false. Since we cannot directly observe these facts, we wish to assess the likelihood that the conjecture is true (or false). The event and the probability of the event are not the same thing. I am not an expert, and I am sure this could be explained better. But I see your confusion, and for now, you're stuck with me. Haakondahl (talk) 19:21, 24 October 2014 (UTC)

Misleading introduction

I find the wording of the "Introductory example (epistemological interpretation)" to be extremely misleading. It states that "Bayes's theorem can be used to calculate the probability that the person was a woman" based only on the premise:

• the man had a nice conversation on a train
• it is equally likely that the man would converse with a man or a woman
• the other person had long hair

This is misleading because two paragraphs later it introduces two additional assumptions: that 75% of women have long hair and 15% of men have long hair. Are these assumptions in some way lesser than the 50% female assumption from the first paragraph? As it is, the introduction gives the impression that Bayes' theorem somehow distills objective probability from a vague premise. In reality, the accuracy of the result is completely dependent on the accuracy of the three quantitative assumptions:

• the probability of conversing with a woman
• the probability of a woman having long hair
• the probability of a man having long hair

What if the train is in the vicinity of the local Harley Davidson convention? That could invalidate the 15% assumption of men with the long hair and thus the entire calculation. I think the section should be reworded to clarify this dependence. Silverhammermba (talk) 17:20, 9 December 2014 (UTC)

Bayes' theorem is valid without Bayesian interpretation of probability

Some of this article assumed a Bayesian foundation for statistics; yet Bayes' theorem is wholly valid with a frequentist foundation. Although the article states that, it also sometimes assumes the Bayesian interpretation. In particular, Bayes' theorem does not require interpreting probabilities as beliefs. I have made some changes to the Introductions.
86.183.239.66 (talk) 22:59, 19 December 2014 (UTC)

Statement of theorem

The equation:

$P(A|B)={\frac {P(B|A)\,P(A)}{P(B)}},$

as mentioned in the introduction of the theorem, doesn't well reflect the idea of the theorem. Better to give the equation in the following form:

$P(A|B)={\frac {P(B|A)P(A)}{P(B|A)P(A)+P(B|A^{c})P(A^{c})}}.$

Madyno (talk) 21:47, 31 January 2016 (UTC)

Hello Madyno; this is covered later on in the "Forms" section. Often you don't need to split P(B) -- as in the cancer example -- and sometimes you do -- as in the next. I don't see how this form better reflects the idea of the formula. — Gamall Wednesday Ida (t · c) 13:56, 12 December 2016 (UTC)

Reconciliation with the form used in Nate Silver's book "The Signal and the Noise"

In chapter 8 of Nate Silver's book The Signal and the Noise, he presents Bayes's Theorem (in figure 8-3) as: xy / (xy + z(1-x)) How can this form of the theorem be reconciled with versions shown in this article? --Lbeaumont (talk) 00:13, 30 August 2016 (UTC)

Hello, Lbeaumont.

I just took a look at that figure. In it, x, y, and z are numerical values for specific probabilities (with facetious flavour text). The expression you give is thus a specific instance of the following form of the formula,

$P(A\mid B)={\frac {P(B\mid A)\,P(A)}{P(B\mid A)P(A)+P(B\mid \neg A)P(\neg A)}}\cdot$,

where P(B) has been split along A. It is not intended as a general presentation of the theorem. — Gamall Wednesday Ida (t · c) 13:52, 12 December 2016 (UTC)

The visualization diagram has errors

In 'The "Visualization of Bayes' theorem by the superposition of two decision trees', P(not B | not A) instead of P(B | not A), and P(not A | not B) instead of P(A | not B). Mongoose700 (talk) 01:52, 19 November 2015 (UTC)

I concur, and would like to clarify the specific issues. In the WNW corner of the diagram, P(not B | not A) should be P(B | not A). In the ENE corner, P(not A | not B) should be P(A | not B). Since there are two P(not B | not A) and two P(not A | not B) in the diagram, I thought it should be made clear which need to be corrected. Kennkong (talk) 05:54, 27 November 2015 (UTC)

Known unknowns ©DonaldRumsfeld

I quote from the section

Cancer at age 65

"Suppose also that the probability of being 65 years old is 0.2%."

Any reason for choosing this insufficiently large figure, or was it just plucked out of the aether? According to one source, ("Global Health and Aging: Humanity's Aging" National Institute on Ageing. Retrieved 27 February 2017), fully 8% of the world's population is aged over 65. Does this figure of 0.2% bear any relationship whatever to any reliably reported incidences of cancer in over-65s? I speak as a sufferer of a rare form of a rare cancer, namely Hodgkin's disease.

"It may come as a surprise that even though being 65 years old increases the risk of having cancer..."

It certainly came as a surprise to me, especially since the main substance of this statement is unreferenced, according to 0.002% of active en:Wikipedians, ie >MinorProphet (talk) 23:08, 27 February 2017 (UTC)

MinorProphet: Plucked from the ether indeed. It is unfortunate to have a example with wrong figures and clear real-world implications, since they are not actually supposed to be the "main substance" of the statement, which is a purely numerical point about base rate neglect (the conclusion will probably still hold with real figures, since the base rate is low, but that's neither here nor there). The second example is probably better for that. Another example based on mammogram false negatives/positives, for which real figures should be readily accessible, might be better, if we must have a cancer-themed one. I am going to remove this one for now. — Gamall Wednesday Ida (t · c) 13:04, 28 February 2017 (UTC)

removed example; to be reworked at a later date — Gamall Wednesday Ida (t · c) 13:12, 28 February 2017 (UTC)

Cancer at age 65 Suppose that an individual’s probability of having cancer, assigned according to the general prevalence of cancer, is 1%. This is known as the “base rate” or prior (i.e. before being informed about the particular case at hand) probability of having cancer. Writing C for the event "having cancer", we have $P(C)=0.01$. Suppose also that the probability of being 65 years old is 0.2%. We write $P(65)=0.002$. Finally, let us suppose next that cancer and age are related in the following way: the probability that someone who has been diagnosed with cancer happens to be 65 years old is 0.5%. This is written $P(65\mid C)=0.005$. Knowing this, we can calculate the probability of having cancer as a 65-year-old $P(C\mid 65)$, by applying Bayes' formula: $P(C\mid 65)={\frac {P(65\mid C)\,P(C)}{P(65)}}={\frac {0.005\times 0.01}{0.002}}=2.5\%$. Possibly more intuitively, in a community of 100,000 people, 1,000 people will have cancer and 200 people will be 65 years old. Of the 1000 people with cancer, only 5 people will be 65 years old. Thus, of the 200 people who are 65 years old, only 5 can be expected to have cancer. It may come as a surprise that even though being 65 years old increases the risk of having cancer, that person’s probability of having cancer is still fairly low. This is because the base rate of cancer (regardless of age) is low. This illustrates both the importance of base rate, as well as that it is commonly neglected.< ref name="Kahneman2011">Daniel Kahneman (25 October 2011). Thinking, Fast and Slow. Macmillan. ISBN 978-1-4299-6935-2. Retrieved 8 April 2012.</ref> Base rate neglect leads to serious misinterpretation of statistics; therefore, special care should be taken to avoid such mistakes. Becoming familiar with Bayes’ theorem is one way to combat the natural tendency to neglect base rates.

Bayes' theorem, Bayes' rule and radical probabilism

I have just updated the Richard Jeffrey article and created the radical probabilism article. This article says that 'Bayes' rule' is the odds version of Bayes' theorem. Is that right? I never heard that. In any event, I am planning to start editing to include some the insights, and controversies. from radical probabilism. Comments would be welcome before I start.Cutler (talk) 16:02, 20 July 2017 (UTC)

Thanks for the article on radical probabilism. (I am quite pleased to learn that I am a "radical probabilist".). On "'Bayes' rule' is the odds version of Bayes' theorem", that's the kind of overprecise, unsustainable distinction that may hold at the scale of a classroom if you rap the knuckles of any transgressor, but in practice -- it seems to me -- the two are used interchangeably. — Gamall Wednesday Ida (t · c) 16:35, 20 July 2017 (UTC)

Alternative form vs example

@PabloStraub:. This is to notify you that I have removed the "alternative form" you added, and made the additional step explicit in the example -- which you cited as motivation -- instead. That seems the better way to me, given how trivially one goes from one form to the other. — Gamall Wednesday Ida (t · c) 13:08, 5 May 2017 (UTC)

Not sure what "alternative form" means, but it may refer to a problem I see in the Drug testing section. The first line matches the version of the theorem given in the Statement of theorem section. The second one does not. There is no clue, no way to figure out how P(+|User) P(User + P(+|Non-user) P(Non-user) is substituted for P(+).

How this substitution can be made may be obvious to Bayes experts, but this page should be readable by the non-expert, like me. It could be that the page needs a new section on Alternative form. Thanks. Jack Harich (talk) 22:12, 4 September 2018 (UTC)

Later I noticed there's an Alternative form section further on down in the page. Thus the problem is a forward reference. The article assumes the reader has read something that occurs later on the page. This could be corrected with something like "The second equation is explained below." Thanks. Jack Harich (talk) 18:02, 5 September 2018 (UTC)

Use of apostrophes

Most style guides I consulted agree that the possessive of a singular noun is formed by adding 's, even if the noun already ends in s. So shouldn't we call it "Bayes's theorem"? 75.166.124.172 (talk) 20:04, 26 September 2016 (UTC)

Some interesting discussion about it, here --> http://english.stackexchange.com/a/92269 Top5a (talk) 01:05, 23 January 2017 (UTC)

See the discussion at Talk:Stokes'_theorem#Requested_move_4_December_2018. Note that the consensus was to keep it as "Stokes' theorem" as per WP:COMMONNAME. Danstronger (talk) 02:29, 16 January 2019 (UTC)

unclear intro

For example, if the probability that someone has cancer is related to their age, using Bayes’ theorem the age can be used to more accurately assess the probability of cancer than can be done without knowledge of the age.

Is this what is meant?

For example, if the probability that someone has cancer is related to their age, Bayes’ theorem enables using the age of a person to more accurately assess the probability of that person getting cancer than can be done without knowledge of the age.

--Espoo (talk) 09:43, 13 April 2020 (UTC)

Yes, I think your understanding is correct; the current wording is unclear and rather clunky. But it should be possible to improve this even further and give some idea of what this is all about even to readers who don't have much mathematical knowledge, and who won't read beyond the first paragraph. We should open with the simpler term 'risk' rather than 'probability'. Also, we don't need to mention a specific disease right at the top. I've boldly changed the wording to the following, but improvements are welcome:

"For example, if the risk of developing health problems is known to increase with age, Bayes’ theorem allows the risk to an individual of a known age to be assessed more accurately than simply assuming that the individual is typical of the population as a whole."

MichaelMaggs (talk) 12:11, 13 April 2020 (UTC)

Removal: Visualization of Bayes'theorem

The diagram has been removed by an IP, on grounds that it is "just confusing unless accompanied with an explanation". I'd tend to agree. Keeping a link here, and pinging author and uploaders User:Qniemiec, Mgunyho and Zorakoid for comments and in case improvements are possible.

Visualization of Bayes'theorem.

— Gamall Wednesday Ida (t · c) 20:59, 28 July 2017 (UTC)

Hi there, I've just undone the removal of the picture which works fine since I've uploaded it two years ago, not only within Wikipedia community, but also in teaching Bayes' theorem in school and/or university. The more that simply to claim that something is "just confusing" fails to be a profound reason for such a removal in my sight: if the anonymous remover (not even a registered Wikipedia user) had invested at least some time and/or effort in analyzing what the picture shows, he or she had found that it depicts the relation between, or superposition of two event tree diagrams, the second of them often called the "inverse event tree". Since it's the essence of Bayes' theorem and formula, that any event "A AND B" can be reached in two ways (as the equation on the bottom of the picture shows): either first letting "A" happen, and then "B, provided that A has happened", or vice versa. And as far as I know, this is commonly teached knowledge in stochastics, so I don't understand why the anonymous remover claims this to be "just confusing", or what him or her actually confuses, if he or she understands all the remaining, often far more complex content of the article. Ok, but if this should be necessary to make the picture less "confusing", I'll add the superposition issue to the picture's legend. --Qniemiec (talk) 10:08, 29 July 2017 (UTC)

I'm a postdoctorate researcher in statistics and I don't know what on earth you are trying to show with that graph. Which are the two superimposed event trees? How does this relate to Bayes' theorem? (Looking at it a lot it's flooded with extraneous or confusing details. As far as I can see only a quarter of it is relevant? The colours, the little pie charts on the nodes, the arrows, all of that is actually irrelevant?) Maybe as part of an university course this can work, in a structured curriculum where you are introduced event trees and you construct that diagram piece by piece with a lecturer explaining each step. Throw it in there and imagine everyone knows what you mean, and well, good luck. Go look at event tree and see it it equips the reader to understand that graph. I'm not gonna edit war this with you, if you think this chart should be included at a minimum you need to rewrite your comment and include it in the article, and probably expand the event tree article a whole lot as well. -143.234.1.111 (talk) 15:51, 31 July 2017 (UTC)

Sorry that my graph confuses you, and I wonder that this concept of two superposed event trees appears new resp. strange to you, as it's the basement on which Bayes' formula is introduced at my place already in high school, i.e. that for each event tree an "inverse event tree" exists, with the opposite order of decisions resp. probabilities, e.g. the first tree beginning with A or Not-A, and then each branch branching again, now into B and Not-B, while the "inverse tree" first branches into B and Not-B, and not earlier but then again, now into A and Not-A, and at the very end both trees end in the same 4 events: (A AND B), (A AND NOT-B), (NOT-A AND NOT-B) and (NOT-A AND B). Hence each of these 4 final states can be reached in two different ways, either by first, or second tree, and this is what the formula at the very bottom says, from which it's only one last step to Bayes' formula. Sounds comprehensive, doesn't it? Didn't they teach it this way to you in school?
And as far as it concerns the colors, my initial PNG picture also took them into consideration, chosing complementary colors for each branch, so A was in cyan and NOT-A (as not-cyan) in red, while B was in blue, and NOT-B (as not-blue) in yellow, and inverting the graph on the display, this relation between opposite decisions and colors always remained, but the guy who transferred it to SVG didn't realize this aspect, and messed it up unfortunately. And what should I rewrite as a comment, if all what's on the graph is already commented by formulas and text at its very left side? --Qniemiec (talk) 23:04, 5 August 2017 (UTC)

I have worked in statistics and probability for 50 years. Never ever before seen the notion of super-imposed event trees. It may be a nice way to teach Bayes to some audiences, but it is not a usual way to do it, so I am not sure it belongs in wikipedia! Richard Gill (talk) 07:46, 8 January 2020 (UTC)

I've also had over 30 years of experience, and the diagram just looks intimidating and confusing, making Bayes' Theorem more complicated than it actually is. The detail and color are bugs, not features--- they add to the confusion. It is more a neat deeper insight than a simple introduction. Also, it it would need to be explained in the text---diagrams shouldn't be free floating. I'm going to delete it, since a few years have passed by.

--editor3 20:53, 18 April 2020 (UTC)

Drug Testing example

In the first example, "Suppose that a test for using a particular drug is 99% sensitive and 99% specific." It would be better to make it "Suppose that a test for using a particular drug is 99% sensitive and 98% specific." Then the reader would be able to interpret the numbers in the formula better, rather than having to think which 99% is the one that applies in each place. I would have changed it, but the diagram would need to be changed too, so it would be better if whoever drew the diagram did it.

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editeur24 (talk) 20:59, 18 April 2020 (UTC)

Drug Test Example

I'd like to address this very common example application of bayes' theorem. The formulation is critical here, because it can be very misleading as far as I see it: If a person is tested and the test is positive, then the likelihood of the person actually being a drug user is 99% according to the specificty of the test, because if the person was not a drug user the chance of the test yielding a positive result is 1%. Same goes for the opposite case in this example.

The probability calculated in the example is the chance that a person is actually positive when drawn from the set of all persons with a positive result. And it is not surprising that this chance actually is not that high, because the number of nondrug users is so much larger in this example. — Preceding unsigned comment added by 77.6.167.3 (talk) 22:03, 4 October 2019 (UTC)

Well, that's the point of the example, isn't it? Richard Gill (talk) 07:47, 8 January 2020 (UTC)

Mr. Gill is right. Everything's unsurprising once we understand it, but examples like this are pretty stunning when first encountered.

---editeur24 (talk) 21:31, 18 April 2020 (UTC)

Should a section be added on the psychology of Bayes' Rule?

This article is pretty long already, but maybe a section on the psychology of Bayes' Rule would be appropriate, since it is a big subject in psychology. The article Base rate fallacy already covers a lot of that ground, but perhaps not in quite the way a section here would. --editeur24 (talk) 21:49, 18 April 2020 (UTC)--editeur24 (talk) 21:49, 18 April 2020 (UTC)

Bayes' Theorem, Rule, or Law-- all are correct

There was an edit and undo on this today, neither by me, but I thought I'd comment. It can be Bayes' Theorem, Bayes' Rule, or Bayes' Law. THey're all pretty much the same. In economics, my field, we say "Bayes' Rule" most often. If you say Theorem, you probably should state it as a theorem rather than as a guide to calculations. Personally, I think it should be Bayes's rather than Bayes', Jesus's rather than Jesus', and so forth, because it avoids confusions with plural possessive's as well as being more logical and sounding better and being perfectly possible to say out loud, but I think maybe Wikipedia has chosen to go with the inferior style of Bayes', and if that's true, we should go with house style.

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editeur24 (talk) 18:26, 25 April 2020 (UTC)

I was just looking through the Wikipedia Manual of Style at https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style#Dashes and I see that actually Wikipedia house styles *is* to say Bayes's Rule, as I argued for above, not Bayes' Rule:

"For the possessive of singular nouns, including proper names and words ending with an s, add 's (my daughter's achievement, my niece's wedding, Cortez's men, the boss's office, Glass's books, Illinois's largest employer, Descartes's philosophy, Verreaux's eagle). Exception: abstract nouns ending with an /s/ sound, when followed by sake (for goodness' sake, for his conscience' sake). If a name already ends in s or z and would be difficult to pronounce if 's were added to the end, consider rearranging the phrase to avoid the difficulty: Jesus's teachings or the teachings of Jesus."

Thus, I'm going to change the start of the article to make that the standard version, though I'll include the "Bayes' Theorem" as an alternative. Really, the article title ought to be changed to fit house style, but I'm too much of a novice to know how to do that.

-- editeur24 (talk) 16:15, 30 April 2020 (UTC)

Drug Testing-- should Figure 1 be dropped?

What do people think about Figure 1 in the drug testing example? It's a fine diagram, but it seems to me that the text does a better example of making the same point using its 1,000 test numerical example and the figure is just something extra for the reader to have to process. But I am a newcomer and wonder what other readers think. Also, the diagram's placement doesn't work right with the text at the moment. I don't know enough about Wikipedia editing to know how to fix the word wrapping to make it look prettier. --editeur24 (talk) 21:29, 18 April 2020 (UTC)

I like visuals, and I think the figure should stay. But I am also having difficulty with the arrangement of that section. There are three sets of data, without corresponding explanations. Comfr (talk) 17:08, 7 August 2020 (UTC)

Blue Neon image

The image is surely nice but it's irrelevant the way you write the theorem or the physical support. I mean, captioning images of texts like "A Comics Sans text of Bayes Theorem" or "A wall writing with Bayes theorem" is quite distracting. — Preceding unsigned comment added by 79.37.198.178 (talk) 16:38, 6 October 2020 (UTC)

Redundant section in Generalization , maybe???

I am not a specialist in Bayesian theory but it seem that sections 7.1 and 7.2 are, except notational differences, the same.

If there are not the same, maybe someone who is an expert can add a clarifying note in the article. Otherwise maye someone who is more knowledgable in can consolidate this section? — Preceding unsigned comment added by 2601:280:4B80:A490:C3F:408C:C0B2:D8C6 (talk) 22:43, 29 October 2020 (UTC)

Requested move 12 October 2020

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: No consensus to move. While MOS:POSS appears to stipulate the move, it has been reasonably disputed, and there is a strong point that most reliable sources simply do not spell this as Bayes's, so we do not want to invent spellings. No such user (talk) 07:42, 20 November 2020 (UTC)

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Bayes' theorem → Bayes's theorem – Bayes's is the style preferred by Wikipedia for non-plurals ending in s. This move has been attempted before but there is a redirect page called Bayes's theorem and apparently a problem arose with multiple redirects. I think the current position should be reversed - there should be a redirect page called Bayes' theorem which redirects to this page, which should be renamed Bayes's theorem Moletrouser (talk) 08:42, 12 October 2020 (UTC)

@Moletrouser: I'm afraid you made some technical mistake trying to create a requested move. I think you forgot the double right curly braces. But do take a look in the archives for previous discussions. The existence of a redirect at "Bayes's theorem" is not a serious obstacle; I think people probably generally disagree with you on the merits. --Trovatore (talk) 19:25, 10 October 2020 (UTC)

@Trovatore: It was just as you said - clumsy me. I have corrected my error; let us see what happens now. Moletrouser (talk) 08:42, 12 October 2020 (UTC)

• Support. When I learned English, I was told that the genitive marker of a word ending in an "s" is a plain apostrophe only if that "s" comes from a plural form. If it's actually part of the word then the ending is "'s". This theorem was named after a guy whose name is "Bayes", it's not a case of one baye vs. multiple bayes. JIP | Talk 19:21, 12 October 2020 (UTC)

@JIP: One big exception to that general rule in English (which you may not be aware of, since English isn't your first language) is historical figures whose names end in S. Jesus and Moses are commonly given as examples, where their possessive forms would be rendered as Jesus' and Moses' in English. See Archimedes' screw and Jesus' interactions with women as examples of this construction. Bayes would come under this exception as a historical figure himself. Rreagan007 (talk) 02:00, 13 October 2020 (UTC)

No, I didn't know that. The rule that the genitive ending being "'" instead of "'s" in words ending in "s" only happens in plural words is logical and makes sense, but I didn't know names of historical figures are an exception. That is completely illogical in my mind. It's not as if there ever were a single baye, jesu or mose. JIP | Talk 22:12, 14 October 2020 (UTC)

Of course we don't have to decide here whether it's logical, so this is a digression, but for what it's worth I think it's a phonetic thing. If you write Jesus's you should pronounce it /ˈdʒiːzʌz.ɨz/ or something like that, and it sounds awkward; the last two /z/s want to slur together. --Trovatore (talk) 22:27, 14 October 2020 (UTC)

• Meh. I'm pretty sure Bayes' theorem is more common in the wild in high-quality sources. This whole thing strikes me as a bit of overreach by the MOS contingent. But in the end the move won't really matter much, so I suppose I don't mind if we just get it over with and don't have to talk about it again. --Trovatore (talk) 20:14, 12 October 2020 (UTC)
• Oppose per WP:COMMONNAME. The current title is clearly the common name based on the Google Ngrams. We aren't creating a possessive from scratch here. The possessive has already been created by reliable sources for this particular topic, and those are what we should follow. Also, as I point out above, historical figures such as Jesus and Archimedes have a possessive form commonly rendered as Jesus' or Archimedes' in English. (see Archimedes' screw and Jesus' interactions with women) I think Bayes qualifies as a historical figure, so his possessive form should be rendered as Bayes' under standard English grammar rules. Rreagan007 (talk) 21:38, 12 October 2020 (UTC)
• Question: Where is the indication that "Bayes's is the style preferred by Wikipedia for non-plurals ending in s"? —BarrelProof (talk) 04:31, 13 October 2020 (UTC)
• Oppose per Rreagan007. The reliable sources call it Bayes' theorem. Wikipedia shouldn't use a name that's different from what the sources use. MartinPoulter (talk) 10:41, 13 October 2020 (UTC)
• Comment: Does this make a difference on the pronunciation? Is the name pronounced "bayes theorem" or "bayesees theorem"? JIP | Talk 22:14, 14 October 2020 (UTC)
  • This is somewhat disputed; there are people who might write Bayes's but pronounce it /beɪz/. For me, though, the answer is yes -- I would pronounce Bayes's as /ˈbeɪz.ɨz/ and Bayes' as /beɪz/. --Trovatore (talk) 22:31, 14 October 2020 (UTC)
    • Yeah when I'm reading it, I'm definitely inclined to pronounce "Bayes's" as /ˈbeɪz.ɨz/ . Though my high school English teacher would say that the pronunciation should not change and should be /beɪz/ . Rreagan007 (talk) 23:54, 14 October 2020 (UTC)
• Oppose per Rreagan. WP:COMMONNAME is still policy here. -- Calidum 01:17, 19 October 2020 (UTC)
• Support per all modern style guides and our own (MOS:POSS). Commonname is about name, not styling of the name. Dicklyon (talk) 02:04, 19 October 2020 (UTC)
• Yeah, support per Dicklyon. Tony (talk) 03:42, 19 October 2020 (UTC)
• Support. We have a guideline on this for a reason, based on the majority of off-site style guides on this point, which are actually reliable sources on English orthography. WP:COMMONNAME is is not a style policy and has nothing to do with punctuation questions like this. It's the policy that tells us to prefer some spelling of Bayes's theorem" versus (any spelling of) the less common "Bayes's law" or "Bayes's rule", substantively different names, not just style variants. The style questions are MoS matters. MoS is applied at RM every single day. People who think COMMONNAME is a style policy are confused.  — SMcCandlish ☏ ¢ 😼  08:26, 19 October 2020 (UTC)
  • Comment. This is not a punctuation question nor a styling question. This is a spelling question. The difference is an actual letter, s, not a punctuation mark. --Trovatore (talk) 16:56, 19 October 2020 (UTC)
  • Comment. It's a style guide issue when you are creating a possessive from scratch, not when the title of the topic itself uses a possessive based on reliable sources. This topic could also just be "Bayes Theorem" without a possessive, but reliable sources have chosen to use a possessive form for this topic. Rreagan007 (talk) 19:00, 20 October 2020 (UTC)
• Support per Dicklyon and SMcCandlish. Possessive forms are indeed a matter of style, and are covered in detail in style guides, including ours. We should be consistent in our use of them. CThomas³ (talk) 17:01, 20 October 2020 (UTC)

The style guide is used to determine how you create possessives from scratch, not how you title an article whose topic includes a possessive. That is governed by article titling policy, specifically WP:COMMONNAME. For example, if we were to strictly follow the style guide, then Pythagorean theorem should be moved to "Pythagoras's theorem". But of course we won't do that, because most reliable sources use "Pythagorean theorem" instead. Rreagan007 (talk) 19:02, 20 October 2020 (UTC)

That's interesting. I'm personally not aware of any section within our style guide that says "Pythagorean theorem" is unacceptable. Where are you seeing this? CThomas³ (talk) 02:04, 21 October 2020 (UTC)

It's just another way of constructing a possessive with an adjective form rather than an apostrophe and S. We could call this article "Bayesian Theorem". Rreagan007 (talk) 02:32, 21 October 2020 (UTC)

Certainly that's one interpretation, though mine would be that "Pythagorean" is a more general form than a true possessive: "of, pertaining to, and/or related to Pythagoras", whereas "Pythagoras's" is more properly "belonging to Pythagoras". While similar, I don't believe they would be considered true synonyms of each other. As an example, anyone can attempt a Herculean task, but it's unambiguous who performed Hercules's labors. CThomas³ (talk) 07:02, 21 October 2020 (UTC)

Seeing as our article on Pythagorean Theorem gives "Pythagoras's theorem" as an alternative name, I'd say in this context they are indeed synonyms of each other. Rreagan007 (talk) 03:14, 22 October 2020 (UTC)

Gravitational radius is given as an alternate name for Schwarzschild radius, but that does not mean "gravitational" is a synonym of "Schwarzschild". Likewise, "Pythagorean" and "Pythagoras's" are also two fundamentally different words that happen to be used in this context to refer to the same theorem. In contrast, "Bayes'" and "Bayes's" are not two different words: they are two different constructions of the exact same word, differing only in style. Therefore, while COMMONNAME would dictate the use of both "Pythagorean theorem" versus "Pythagoras's theorem" and "Scharzschild radius" versus "gravitational radius", we don't apply it for "Bayes'" versus "Bayes's". That's a matter for our style guide. CThomas³ (talk) 05:13, 22 October 2020 (UTC)

Well, no, they are certainly not the exact same word. For one thing, they're pronounced differently. It is not a pure styling issue. --Trovatore (talk) 06:13, 22 October 2020 (UTC)

• Comment. This exact same issue has come up before in a requested move for Stokes' theorem, and the consensus there was to not move the article. Rreagan007 (talk) 19:11, 20 October 2020 (UTC)
• Oppose per WP:COMMONNAME and per Rreagan007. We can't just invent a new name for a term of art. It wouldn't matter if it was irregular grammar, an unusual spelling, whatever. This is a name, not running text, so style concerns are irrelevant here; both math texts and general-public accessible sources (e.g. "The Theory That Would Not Die") use "Bayes'" in general (although that book usually calls it "Bayes' rule" to be sure, based off a quick reminder Google - I've read it, though). SnowFire (talk) 19:19, 28 October 2020 (UTC)

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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.

Empirical proof

Is there empirical proof for Bayes' theorem? That is, does it correctly predict empirical facts? Or is it just an aproximation in the absence of an understanding of the true nature of reality? — Preceding unsigned comment added by 2003:DF:9736:858:FD3E:36C5:9C9:FEF3 (talk) 17:17, 24 November 2020 (UTC)

References to the recent use of 'Bayes-Price theorem'

More and more mathematicians and historians are using: Bayes-Price rule / theorem.

• 'Bayes-Price theorem' used throughout. Liberty's Apostle; Paul Frame (University Press Wales; 2015). Probably the most comprehensive book on Richard Price.
• By modern standards, we should refer to the 'Bayes-Price Rule'. Price discovered Bayes' work, recognised its importance, corrected it, contributed to the article, and found a use for it. The modern convention of employing Bayes’ name alone is unfair but so entrenched that anything else makes little sense. - Sharon Bertsch McGrayne, The Theory That Would Not Die; New Haven; 2011; p. 11. Also here online.
• Bayes & Price, 1763 (Neuroscience & Biobehavioral Reviews, 2015) cited in Science Direct here.
• It would be more accurate to refer to the theorem as the Bayes-Price rule, as Price's contribution was significant.. By Anne Marie Helmenstine, Ph.D. Updated August 12, 2019; Thought Co here.
• ..referred to as Bayes' law or Bayes' rule (Bayes and Price, 1763); Henrik Singmann; R Documentation here.

... please add.

Citations without page numbers are useless (see WP:INTEGRITY). --Omnipaedista (talk) 10:06, 28 February 2021 (UTC)

@Omnipaedista: Page numbers are only placed on books. Only one of the above is a book, and as you can see, I've added the fact that the term 'Bayes-Price theorem' is used thoughout the book. However, as you insist on page numbers, some of these include: pp. 44, 45, 46 and 67. Cell Danwydd (talk) 08:13, 21 March 2021 (UTC)

Covid-19 testing application

This 2021 article covers Covid-19 testing in relation to Bayes' theorem. It could perhaps be usefully worked in? But I'll leave it statisticians to make that judgement. RobbieIanMorrison (talk) 08:41, 18 April 2021 (UTC)

References

Point of grammar

This is not a maths point (or math point, if you're using US English), but a grammatical point. The attribution here calls for a possessive, and the subject is singular, so it's "Bayes's Theorem". Writing it "Bayes' Theorem" multiple times doesn't make it correct.

By all means call it Bayes Theorem, or Bayes-Theorem, but "Bayes' Theorem" is grammatically incorrect.

I agree with you, but we are stuck with what appears in reliable sources which overall appear to favor Bayes' Theorem. Constant314 (talk) 01:09, 5 February 2022 (UTC)

It's not a grammatical error; some style guides still say to do it that way; see Apostrophe#Singular_nouns_ending_with_an_"s"_or_"z"_sound. Wikipedia style guide MOS:POSS says to do "Bayes's", but "Bayes' theorem" is the common name / official name of the theorem, so I think it's right that we say "Bayes' theorem" but "Bayes's" for every other case. Danstronger (talk) 18:53, 5 February 2022 (UTC)

Use and abuse of Bayes' theorem: should we mention Swinburne?

Dear all,

My mention of the book The Existence of God (book) (TEOG), on See also in the article Bayes' theorem (BT), was removed, while i noticed that it was a controversial and speculative use. I think one should NOT use BT with fuzzy input: then you can get the quotient of two unknowns, good luck to all! However, TEOG REALLY IS an elaborate and formally correct application of BT, so we can mention it.

(Another misuse of BT - i think - is the cold case analysis in Rosemary Sullivan: The Betrayal of Anne Frank, 2022. BT is used there to calculate a probability of 0.85 that AF was betrayed to the nazis by an Amsterdam Jewish notary, who wanted to save his own daughters. The book has been severely criticised in the Netherlands. Again, i think that BT should not be used for speculative use, but i don't have a proof... I tentatively surmise that misuse of BT is quite common.)

As TEOG is mentioned on Wikipedia, we should notice this in the main article on BT. Swinburne is a famous author at Oxford University, who has edited a book of experts on BT called Bayes's Theorem, Proceedings of the British Academy, Oxford University Press 2012, reviewed on jstor https://www.jstor.org/stable/3489183 .

• Should we mention The Existence of God (book) as (speculative) use of BT under See also?

(Adding a section on correct use of BT is an option?)

Thanks, Hansmuller (talk) 22:43, 20 February 2022 (UTC)

One of the things that help make a good encyclopedia article is discretion. Not every peripherally related topic should be part of the article. It is obvious to me that The Existence of God is an example of the misuse of probability theory. I haven't read the book, but I would expect to see good math with unsupported assumptions about the underlying probability space. It is really more of an example of garbage-in, garbage-out.

Everything we add to the article should be beneficial to the reader. I do not want to blindly lead the reader to an example of misuse and leave him to figure it out for himself. I do not mind leading the reader to such a topic, if the fallacies are clearly discussed within the target article, which is not the case in The Existence of God (book). If that topic is added to the article, then the reader should get notice that it is not an example of good use. If you had added EoG as an example of bad use, i probably would not have given it a second look, but it might get challenged by someone who perceives an anti-theist bias. They might then demand a reliable source that says EoG is an example of bad use. Anytime you touch on the subject of God or religion, you have the chance to set off an idiological battle, that we just don't need on this article.

Simply labeling the book as controversial isn't likely to be challenged, but I do not think it gives the reader enough guidance. The problem is that EoG is not a bad example because it misuses the machinery of BT. Rather it is a bad example because it missuses the concept of probability. With regard to BT, the book is just noise.

The bottom line is that I do not see any benefit to the reader of adding The Existence of God (book) to Bayes' theorem. Constant314 (talk) 23:13, 20 February 2022 (UTC)

I agree with User:Constant314. I see no real benefit of citing "The Existence of God" on this page. Just because someone uses it, it does not mean that it belongs in this article. This article is about an introduction to Bayes Theorem, it uses, and applications, so it should stay on track than deviate into WP:COATRACK. However, Richard Swineburne's book that actually deals with Bayes Theorem (Bayes's Theorem, Proceedings of the British Academy, Oxford University Press) is generic enough that it may be worth mentioning since it looks at the limits of Bayes Theorem itself.Ramos1990 (talk) 00:45, 21 February 2022 (UTC)

Measure theoretic formulation?

Should there be a section on the measure theoretic formulation (the most general) of Baye's theorem? 2604:3D09:797D:3500:C5E3:E884:A679:6419 (talk) 04:30, 24 May 2022 (UTC)

Hey stop protecting the among us edit

One user has been protecting a single image that has been placed there by a redditor as a meme. Remove this image, NOW! 2607:FEA8:A75F:C00:3C65:D60A:1BEB:FE0E (talk) 12:04, 28 September 2022 (UTC)

See discussion above. Also, there's no need to shout. Edderiofer (talk) 12:12, 28 September 2022 (UTC)

Semi-protected edit request on 1 October 2022

Source number 4 features a mispelling of the word "probability". The source is found in "statement of theorem" near the bottom. 81.96.180.55 (talk) 01:25, 1 October 2022 (UTC)

 Done Cannolis (talk) 03:50, 1 October 2022 (UTC)

Request change in article protection to partial protection.

All the edit warring has been by IP editors. It is sufficient to block those. Constant314 (talk) 20:06, 2 October 2022 (UTC)

It's always the others. [1] [2] [3] [4]

So full protection, while perhaps a rare choice in response to this kind of edit warring in practice, is clearly justified. Justifying semi-protection is more difficult; I usually point towards the "IP hopping" part of WP:SEMI when doing so. The main disruption in such edit wars does usually come from one single IP hopping editor who can't be properly reached through their IPv6 talk page and who refuses to discuss until it becomes a technical necessity. ~ ToBeFree (talk) 00:02, 3 October 2022 (UTC)

Thanks for the quick response. Constant314 (talk) 04:28, 3 October 2022 (UTC)

6.1 Propositional logic

The explanation of the relation of Bayes Theorem to propositional logic is not clear to me, although I know propositional logic. In particular, the text does not explain what is denoted by the lowercase $a$ in the formula ${\frac {P(B\mid A)a(A)}{P(B\mid A)a(A)+P(B\mid \lnot A)a(\lnot A)}}$

Not sure when this concern was first brought up, but the article currently states just before this formula that a(A) is "the prior probability/base rate" of A. I think this resolves the matter. Edderiofer (talk) 11:41, 3 October 2022 (UTC)