# Talk:Bayes' theorem

## 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)

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 ${\displaystyle P(C)=0.01}$. Suppose also that the probability of being 65 years old is 0.2%. We write ${\displaystyle P(65)=0.002}$. 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 ${\displaystyle P(65\mid C)=0.005}$.

Knowing this, we can calculate the probability of having cancer as a 65-year-old ${\displaystyle P(C\mid 65)}$, by applying Bayes' formula:

${\displaystyle P(C\mid 65)={\frac {P(65\mid C)\,P(C)}{P(65)}}={\frac {0.005\times 0.01}{0.002}}=2.5\%}$.

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.

## Alternative form vs example

. 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)

## 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)

## 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)