[pilowsky]

In fact, people use Bayes theorem all the time in their daily life.
Suppose you leave the coffee shop and want to cross the road (to get to the other side - of course).
The odds of being hit by a car if you don't look both ways are fairly high because the coffee shop is in the middle of town and there is a car driving past every 5-10 seconds.
A combination of the central limit theorem, and basic probability theory suggests to you that looking both ways and THEN crossing is a good idea.
Newtons three laws help you decide exactly when to cross.


Why go through all this? Because being hit by a car is a very serious problem.


What if you are on a deserted country road? Say in downtown St Pauls?
Would you still look both ways?
Yes, Bayes theorem in action.

[kenberg]

I am not claiming Baye's Theorem, in rough form or exact form, is unimportant. The issue was obscurity. There are a very large number of things I don't know and the same is true of everyone. For many, I think Baye's Theorem is on that list.

Here is something the paper might have said. It's along the line of your looking both ways, but it uses the false positive issue of the covid teast.


Suppose that there two towns, A and B and suppose, for convince, they have the same size. Suppose that far more people in A than in B have covid. We test everyone in both towns.
In A there are more cases of covid so there are more true positives. Also there are fewer people in A that do not have the virus, and the number of false positives is a set fraction of the number of non-infected, so there are fewer false negatives in A than in B.


Ok: A has more true positives than B, and A has fewer false positives than B, so the ratio of true positives to false positives is higher in A than it is in B.
So a person testing positive in A is more likely to have the virus than is a person who tests positive in B.
Hardly surprising, since more people in A have it.

To get exact numbers requires either having the formula or doing more work, but the point is clear: How to evaluate the likelihood of having covid based on a positive test result varies with the number of cases.

[pilowsky]

I agree with the statement, "Most people - including those that have heard of Bayes theorem - would be unable to explain it adequately."
Most people seem to have difficulty explaining anything to anybody.
I suspect that this is the major cause of bidding misunderstandings - and on a broader stage - relationship discord.


I am saying that to navigate our way through life safely, we unconsciously apply the thinking that is formulated in these laws and theorems.
Adolescent risk-taking is a good example of a failure to incorporate "Bayesian thinking" into daily life.


So is being a Trump supporter, not wearing a mask or being an anti-vaxxer.


The power of prayer will only get you so far, but it won't move the King to the other hand - except in BridgeMaster.

[kenberg]

 pilowsky, on 2021-April-28, 18:41, said:

I agree with the statement, "Most people - including those that have heard of Bayes theorem - would be unable to explain it adequately."
Most people seem to have difficulty explaining anything to anybody.
I suspect that this is the major cause of bidding misunderstandings - and on a broader stage - relationship discord.

I am saying that to navigate our way through life safely, we unconsciously apply the thinking that is formulated in these laws and theorems.
Adolescent risk-taking is a good example of a failure to incorporate "Bayesian thinking" into daily life.

So is being a Trump supporter, not wearing a mask or being an anti-vaxxer.

The power of prayer will only get you so far, but it won't move the King to the other hand - except in BridgeMaster.

I have taken some heat for bringing in personal experiences but I can absolutely assure you, with stake my life on it certainty, that no one on the block I grew up on had heard of Baye's Theorem. When I bought a used car when I was 15, Len, across the street, took ne aside to explain how to calculate miles per gallon. I still recall "You have to start with a full tank. A lot of people don't know that...." I have always been proud that at age 15 I had enough sense to listen respectfully and thank him Len was a very good guy, he watched out for me, but he did not know Baye's Theorem.

I am far from certain that any decent number of CEOs know Baye's Theorem. Or psychiatrists. Or novelists or poets. Or Joe Biden.

[thepossum]

 cherdano, on 2021-April-28, 12:19, said:

If you don't think Bayes theorem is obscure, you should get out of your bubble a bit more.

I know its a long time ago but I'm sure many people come across it at high school or even primary school

They may not remember it. I have very little recollection of when I first heard about all the obscure stuff I've forgotten

But I am a bit upset that you think its me living in a restricted bubble, or one of those ivory tower buildings etc

But seriously we are discussing a context of medical research and statistics - it frightens me that its obscure in those circles

Poor Rev Bayes indeed. Maybe he didn't care about it much either and his spirit has bigger concerns Maybe you don't have to worry about such worldly things anymore

Actually reading my source of all knowledge (Wikipedia) evidently he didn't realise how important it was either or he was just modest

Let's try another one. How many people have heard of Heisenberg's Uncertainty principle. I imagine almost all of them wouldn't have a clue what it really is but many people talk about it all over the place - and that's at a rather higher level of maths than Bayes' Theorem - although before I cause any offence the maths that comes from Bayes' gets fairly advanced at times

[pilowsky]

 kenberg, on 2021-April-28, 19:34, said:

I have taken some heat for bringing in personal experiences but I can absolutely assure you, with stake my life on it certainty, that no one on the block I grew up on had heard of Baye's Theorem. When I bought a used car when I was 15, Len, across the street, took ne aside to explain how to calculate miles per gallon. I still recall "You have to start with a full tank. A lot of people don't know that...." I have always been proud that at age 15 I had enough sense to listen respectfully and thank him Len was a very good guy, he watched out for me, but he did not know Baye's Theorem.

I am far from certain that any decent number of CEOs know Baye's Theorem. Or psychiatrists. Or novelists or poets. Or Joe Biden.

I still agree with you!
I also think that personal experience can illuminate general principles.
So I enjoy reading your comments in the context of the way you experience your life.
As I tried to say above, although most people may not be able to formulate Bayes theorem, they still manage to behave in a way that reflects the operation of Bayes theorem.
Why else would they look both ways when crossing the road in a ghost town like Adelaide.


People with no comprehension of how to formulate Newtons laws still understand that (most of the time) when an apple falls from a tree, it ends up on earth.
Where they have difficulty is when I ask them, "If the earth is rotating, and you jump into the air, why do you land in the same place?"


An American physicist called Julius Sumner Miller used to have a TV show about physics in life when I was a child.
Here's a sample.


Miller was a great one for explaining the effects of heat - or lack thereof.

[helene_t]

I don't think it's a big deal whether people know it's called Bayes's theorem (I never remember how to make the genitive of a proper noun that ends with an S, btw), or if they can read the notation usually used to write it up.

It's not a big deal either if they know how to use the words "conditional probability", "marginal probability", "prior probability" and "posterior probability" correctly.

What is a bit of a problem, though, is that a lot of people just don't understand proportions and probabilities at a very basic level, and maybe fail to appreciate their lack of understanding. Things like the prosecutor's fallacy. You can get an expert witness to tell the jury that "if the guy was a random person unrelated to the crime, there would be only 0.0001% chance of a DNA match". And then they think it means that there's a 0.0001% chance that the guy is innocent.

Or you can write on social media that "20% are false negatives" and who knows what the denominator is (and by what gold standard a false negative is distinguished from a true negative etc), but somehow people will think the number means something even without any further clarification.

Or you can say that "20% disapprove of the policy" and people respond differently to it than if you had said that "80% don't disapprove".

Statistics is difficult to communicate. Maybe not more difficult than so many other things. Biochemistry and physics are probably more difficult. But the problem with statistics is that it would be good if politicians and journalists understood a bit of it. Just the most basic things. Not anything involving formulas more complicated than calculating percentages.

[thepossum]

 helene_t, on 2021-April-28, 20:24, said:

I don't think it's a big deal whether people know it's called Bayes's theorem (I never remember how to make the genitive of a proper noun that ends with an S, btw), or if they can read the notation usually used to write it up.

It's not a big deal either if they know how to use the words "conditional probability", "marginal probability", "prior probability" and "posterior probability" correctly.

What is a bit of a problem, though, is that a lot of people just don't understand proportions and probabilities at a very basic level, and maybe fail to appreciate their lack of understanding. Things like the prosecutor's fallacy. You can get an expert witness to tell the jury that "if the guy was a random person unrelated to the crime, there would be only 0.0001% chance of a DNA match". And then they think it means that there's a 0.0001% chance that the guy is innocent.

Or you can write on social media that "20% are false negatives" and who knows what the denominator is (and by what gold standard a false negative is distinguished from a true negative etc), but somehow people will think the number means something even without any further clarification.

Or you can say that "20% disapprove of the policy" and people respond differently to it than if you had said that "80% don't disapprove".

Statistics is difficult to communicate. Maybe not more difficult than so many other things. Biochemistry and physics are probably more difficult. But the problem with statistics is that it would be good if politicians and journalists understood a bit of it. Just the most basic things. Not anything involving formulas more complicated than calculating percentages.

I'm just upset at the use of the words obscure and anomaly in the article - especially one about medical/health research

[pilowsky]

 thepossum, on 2021-April-28, 20:04, said:

I know its a long time ago but I'm sure many people come across it at high school or even primary school

They may not remember it. I have very little recollection of when I first about all the obscure stuff I've forgotten

But I am a bit upset that you think its me living in a restricted bubble, or one of those ivory tower buildings etc

But seriously we are discussing a context of medical research and statistics - it frightens me that its obscure in those circles

Poor Rev Bayes indeed. Maybe he didn't care about it much either and his spirit has bigger concerns Maybe you don't have to worry about such worldly things anymore

Actually reading my source of all knowledge (Wikipedia) evidently he didn't realise how important it was either or he was just modest

It's a bubble that includes all the kids that did advanced maths in high school.
In Australia, this means about 12% of males and 8% of girls. http://bit.ly/MathsInAustralia


People sometimes tell me that they just don't have the maths gene.


Lucky for them they weren't born in China since they also don't speak Chinese.

[thepossum]

 pilowsky, on 2021-April-28, 20:31, said:

It's a bubble that includes all the kids that did advanced maths in high school.
In Australia, this means about 12% of males and 8% of girls. http://bit.ly/MathsInAustralia


People sometimes tell me that they just don't have the maths gene.


Lucky for them they weren't born in China since they also don't speak Chinese.

I reject the suggestion that Bayes' Theorem (especially the simpler formulation) is regarded as advanced maths. Its very basic. And the suggestion its advanced is part of the problem we all face in the world. Are we talking about a group of people who think any maths past 1+1=2 is advanced. Having said that though having sat through the advanced proof of 1+1=2 its not as simple as most toddlers would think

EDIT I think people are frightened off stuff (or were) simply by making things seem obscure and scary - or maybe just uninteresting when they can actually be fun or relevant. Sadly The Guardian is in the lets keep things scary and obscure camp

EDIT 2 But something I always found curious was why maths is always so mystified and off on its own but various other disciplines seem easily understandable by everyone, so much so they are all experts on those disciplines

EDIT 3 But as always we are debating at cross purposes. I was upset about the use of the words in an article communicating something to people and everyone thinks I expect people to know what the theorem. Its what irritates me most about many forms of science/maths communication

EDIT 4 Also, as has happened before everything seemed fine until a couple of people went ad hom. Its always unnecessary. And at the risk of splaining ad hom is when people try to undermine another person rather than just discussing the issue. Its just upsetting. You make a light hearted comment along with a load of other people. Then come back a day later and find someone has had a go at you. Then when you try to defend someone else piles in and so it goes.

[Gilithin]

 sfi, on 2021-April-28, 15:41, said:

The Pythagorean theorem is the only one that comes to mind.

Mass-energy equivalence, E = mc², would be top of my list of widely known formulae.

[pilowsky]

 thepossum, on 2021-April-28, 20:37, said:

I reject the suggestion that Bayes' Theorem (especially the simpler formulation) is regarded as advanced maths. Its very basic. And the suggestion its advanced is part of the problem we all face in the world. Are we talking about a group of people who think any maths past 1+1=2 is advanced. Having said that though having sat through the advanced proof of 1+1=2 its not as simple as most toddlers would think

EDIT I think people are frightened off stuff (or were) simply by making things seem obscure and scary - or maybe just uninteresting when they can actually be fun or relevant. Sadly The Guardian is in the lets keep things scary and obscure camp

EDIT 2 But something I always found curious was why maths is always so mystified and off on its own but various other disciplines seem easily understandable by everyone, so much so they are all experts on those disciplines

EDIT 3 But as always we are debating at cross purposes. I was upset about the use of the words in an article communicating something to people and everyone thinks I expect people to know what the theorem. Its what irritates me most about many forms of science/maths communication

EDIT 4 Also, as has happened before everything seemed fine until a couple of people went ad hom. Its always unnecessary. And at the risk of splaining ad hom is when people try to undermine another person rather than just discussing the issue. Its just upsetting. You make a light hearted comment along with a load of other people. Then come back a day later and find someone has had a go at you. Then when you try to defend someone else piles in and so it goes.

Don't think anyone is "having a go at you" - just the opposite.
I don't think something learned at High School can be terribly advanced - although I just looked at the curriculum and it looked a bit scary.
Glad I don't have to do it again.

[Gilithin]

 thepossum, on 2021-April-28, 20:37, said:

Having said that though having sat through the advanced proof of 1+1=2 its not as simple as most toddlers would think

That rather depends on which proof. Alfred North Whitehead and Bertrand Russell famously took over a thousand pages for their proof, albeit in the particularly repetitive set notation of 1910. I can barely imagine sitting through that. The normal proof in Analysis 101 is by comparison child's play.

[hrothgar]

I don't recall ever seeing Bayes theorem discussed prior to going to university. (I don't consider this too surprising, because when I went through high school, statistics wasn't part of the core curriculum in New York state)

My nephew graduated HS in New Jersey a year back and is much more precocious in math than I.
I sent him a text and asked him whether this is covered in school these days.

[kenberg]

I'm from the dark ages but I'm with Richard here. I was, by the standards of my community, a seriously weird adolescent. I read Scientific American, I drove over to the University on Saturdays for free math lectures, I sat in on a college physics course in the summer before my senior high school year,. Still, I don't think I learned Baye's Theorem before I got to college.
And how about in college? I took a humanities course from John Berryman. I found his depth of knowledge and his intelligence to be stunning. Did he know Baye's Theorem? Ok, I never asked him. But I would not bet on it, Dante was more his thing. And the guys I drank coffee with at The Ten O'Clock Scholar? I doubt it.

Just about anytime someone says "Everybody knows that" I think the speaker needs to get out more and look around.

[hrothgar]

 kenberg, on 2021-April-29, 06:55, said:

I'm from the dark ages but I'm with Richard here. I was, by the standards of my community, a seriously weird adolescent. I read Scientific American, I drove over to the University on Saturdays for free math lectures, I sat in on a college physics course in the summer before my senior high school year,. Still, I don't think I learned Baye's Theorem before I got to college.
And how about in college? I took a humanities course from John Berryman. I found his depth of knowledge and his intelligence to be stunning. Did he know Baye's Theorem? Ok, I never asked him. But I would not bet on it, Dante was more his thing. And the guys I drank coffee with at The Ten O'Clock Scholar? I doubt it.

Just about anytime someone says "Everybody knows that" I think the speaker needs to get out more and look around.

I also wonder whether this might be a generational thing.

A lot more interest has been given to Bayesian methods over the past 30 years or so. (I think in part because the methods are much more practical with a whole bunch of processing power and good high level stats languages). And, in turn, this has lead to attempts to popularize the methods.

[Cyberyeti]

I did Bayes theorem at school, but only did any proper Bayesian statistics (priors etc) when I did my degree many years later

[pilowsky]

There is also the possibility that the breadth of the curriculum varies between countries.
Obviously, the "cream always floats to the top" - except in politics and in some areas of management where the other stuff has a much higher buoyancy (see Mr Wikipedia for excellent explanation with fun equations).
The United States ranks 25/40 in Science (no masterpoints for them), 28 in reading and 24 in Science.
Here is an interactive heat map I just made in google sheets for Maths. http://bit.ly/WorldMathsRank
The Brighter the red colour (or color for post-Suess readers), the higher the rank.
It's a bit out of date - not sure about the current state.
Hong Kong, Finland and South Korea are =1st.
Tunisia, Indonesia and Brazil are =38th.
White countries did not participate.
(Data Source: Organization for Economic Cooperation and Development, OECD PISA (Program for Student Assessment) 2003 database).

[Cyberyeti]

 pilowsky, on 2021-April-29, 18:30, said:

There is also the possibility that the breadth of the curriculum varies between countries.

There's also a change over time.

I was at the end of my school career in 1983 where I did double maths A level (and study beyond that to do the Cambridge entrance exam), I graduated nearly 30 years later in what was effectively applied maths/stats. The second year of my degree was less tough and rigorous than my final year at school (and I was able to verify this as it appears I forgot to return one of the school textbooks, the third year of the degree was a big step up from the second). When you try to answer a question in some 3rd year coursework using the wrong technique and get the solution out, to get a comment from the tutor to the effect that you'd done a truly epic feat of integration well beyond the scope of this degree by doing something that was entirely routine at A level ...

I used to attend a study weekend where you got to chat informally with some of the tutors, and they pretty much all said that they could no longer set questions they set even 10 years before as they'd be much too hard for current students.

[barmar]

 thepossum, on 2021-April-28, 20:04, said:

I know its a long time ago but I'm sure many people come across it at high school or even primary school

It's been 4 decades, but unless things have changed significantly I doubt it. I probably learned it in the Probability and Statistics class I took at MIT, but I don't remember it specifically.

I've encountered it a number of times later in life because I happen to read things like Scientific American. I'd be very surprised if people who don't deal with technical or mathematical information on a regular basis know of it by name.

Yes, our brains use the principle it describes on a regular basis, although intuitive probability and statistics is often incorrect. The field of behavioral economics, as discussed in books like "Thinking Fast and Slow" and "Predictably Irrational", explains the systematic errors we almost all make.

And even knowing Bayes Theorem doesn't make it easy to apply in daily life. It takes extreme rigor to overcome the tendency to use normal intuition.