most people in the general public don’t know Bayes’ theorem
Really? What probability do you assign to that statement being true? :D
I assign about 80% probability to less than 25% of adults knowing Bayes theorem and how to use it. I took physics and calculus and other such advanced courses in high school, and graduated never having heard of Bayes’ Theorem. I didn’t learn about it in university, either–granted, I was in ‘Statistics for Nursing’, it’s possible that the ‘Statistics for Engineering’ syllabus included it.
Even bumping the 30% up to the 56% who have “some college” and using the 44% for a estimate of the true ratio of possible-Bayes’-knowledge, that’s only just 25% of the US adult population.
(I’ve no idea how this extends to the rest of the world, the US data was easiest to find.)
You did your research and earned your confidence level. I didn’t look anything up, just based an estimate on anecdotal evidence (the fact that I didn’t learn it in school despite taking lots of sciences). Knowing what you just told me, I would update my confidence level a little–I’m probably 90% sure that less than 25% of adults know Bayes Theorem. (I should clarify that=adults living in the US, Canada, Britain, and other countries with similar school systems. The percentage for the whole world is likely significantly lower.)
I have heard that the US system is particularly bad for an advanced country.
In terms of outcomes, the US does pretty terribly when considered 1 country, but when split into several countries it appears at the top of each class. Really, the EU is cheating by considering itself multiple countries.
Actually it is quite good (even for an “advanced country”) if you compare the test scores of, say, Swedes and Swedish-Americans rather than Swedes and Americans as a whole.
If you choose maths as one of your A-levels, there’s a good chance you will cover stats 1 which includes the formula for Bayes’ Theorem and how to apply it to calculate medical test false positives/false negatives (and equivalent problems). However it isn’t named and the significance to science/rationality is not explained, so it’s just seen as “one more formula to learn”.
Offhand, 1⁄2 young people do A levels, 1⁄4 of those do maths, and 2⁄3 of those do stats, giving us 1⁄12 of young people. I don’t think any of these numbers are off by enough to push the fraction over 25%
As far as I know, it’s been formally demonstrated to be the absolutely mathematically-optimal method of achieving maximal hypothesis accuracy in an environment with obscured, limited or unreliable information.
That’s basically saying: “There is no possible way to do better than this using mathematics, and as far as we know there doesn’t yet exist anything more powerful than mathematics.”
What more could you want? A theorem proving that any optimal decision theory must necessarily use Bayesian updating? ETA: It has been pointed out that there already exists such a theorem. I could’ve found that out by looking it up. Oops.
What more could you want? A theorem proving that any optimal decision theory must necessarily use Bayesian updating?
There already is such a theorem. From Wikipedia:
A decision-theoretic justification of the use of Bayesian inference was given by Abraham Wald, who proved that every Bayesian procedure is admissible. Conversely, every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.
As far as I can tell from wikipedia’s description of admissibility, it makes the same assumptions as CDT: That the outcome depends only on your action and the state of the environment, and not on any other properties of your algorithm. This assumption fails in multi-player games.
So your quote actually means: If you’re going to use CDT then Bayes is the optimal way to derive your probabilities.
And the list of notable problems that have been solved using Bayes is...? Bayes doesn’t tell you how to make your informaton more copious or accuate, although there are plenty of techniques for doing that. Bayes also doesn’t tell you how to formulate novel hypotheses. It also doens’t tell you how to deal with conceptual problems that are not yet suitable for nnumber crucnhing. It looks to me like Bayes is actually a rather small part of the picture.
And the list of notable problems that have been solved using Bayes is...?
Half of statistics these days is Bayesian. Do you want to defend the claim that statistics solves no notable problems?
PS: -T-w-o- Three downvotes, and not a shred of counteargument. Typical.
As usual, I add my downvote to whining about downvotes. Since you think it’s ‘typical’ and this vindicates your claims, I’m sure you’ll be pleased that I’m helping prove you right.
Great. Then the UK education sytem is exactly right in teaching Bayes as part of statitistics, but not as a general-prupose solution to everything. ETA: But surely the LW take on Bayes is that it is much more than something useful in statistics.
Do you want to defend the claim that statistics solves no notable problems?
No, I want to defend the claims that Bayes is not as a general-prupose solution to everything, is not a substitute for other congnitive disciplines, is of no benefit to many people and is of no use in many contexts.
As usual, I add my downvote to whining about downvotes
Please inform me of the correct way to indicate that the karma system is being misused.
Great. Then the UK education sytem is exactly right in teaching Bayes as part of statitistics, but not as a general-prupose solution to everything. ETA: But surely the LW take on Bayes is that it is much more than something useful in statistics.
Now you’re just backing off your claim. What happened to your list?
Then the UK education sytem is exactly right in teaching Bayes as part of statitistics, but not as a general-prupose solution to everything.
First point: if Bayesian statistics is half of statistics, the description of the UK course is of it as being way way less than half the course. Therefore the UK system is very far from being ‘exactly right’.
Second point: The optimistic meta-induction is that Bayesian statistics has gone from being used by a literal handful of statisticians to being widespread and possibly a majority now or in the near future; therefore, it will continue spreading and eating more of statistics in general, and the course will get wronger and wronger, and your claims less and less right.
No, I want to defend the claims that Bayes is not as a general-prupose solution to everything, is not a substitute for other congnitive disciplines, is of no benefit to many people and is of no use in many contexts.
So you’re just splashing around a lot of bullshit and distractions when you demand lists and talk about the UK course being exactly right, since those aren’t what you are actually trying to claim. Good to know!
Please inform me of the correct way to indicate that the karma system is being misused.
What’s the point of indicating when it’s not being misused?
What’s the point of indicating when it’s not being misused?
You have your opinion, on that, I have mine. You can state your opinion, I can’t state mine. I can’t discuss the censorship, because discussions of censorship are censored.
It’s in a downvoted thread.So it isn’t visible.If negative karma doesn’t do anything regarding the visibility of comments, why have the button? Sheesh.
And so begins another goal-shifting, like the list or like the claim of ‘censorship’, this time to defining karma systems. Pardon me if I don’t care to continue this game.
I took physics and calculus and other such advanced courses in high school, and graduated never having heard of Bayes’ Theorem.
Must be a problem of the American school system, I suppose.
I didn’t learn about it in university, either–granted, I was in ‘Statistics for Nursing’, it’s possible that the ‘Statistics for Engineering’ syllabus included it.
Did they teach you about conditional probability? Usually Bayes’ theorem is introduced right after the definition of conditional probability.
I assign about 80% probability to less than 25% of adults knowing Bayes theorem and how to use it. I took physics and calculus and other such advanced courses in high school, and graduated never having heard of Bayes’ Theorem. I didn’t learn about it in university, either–granted, I was in ‘Statistics for Nursing’, it’s possible that the ‘Statistics for Engineering’ syllabus included it.
Only 80%?
In the USA, about 30% of adults have a bachelor’s degree or higher, and about 44% of those have done a degree where I can slightly conceive that they might possibly meet Bayes’ theorem (those in the science & engineering and science- & engineering-related categories (includes economics), p. 3), i.e. as a very loose bound 13% of US adults may have met Bayes’ theorem.
Even bumping the 30% up to the 56% who have “some college” and using the 44% for a estimate of the true ratio of possible-Bayes’-knowledge, that’s only just 25% of the US adult population.
(I’ve no idea how this extends to the rest of the world, the US data was easiest to find.)
You did your research and earned your confidence level. I didn’t look anything up, just based an estimate on anecdotal evidence (the fact that I didn’t learn it in school despite taking lots of sciences). Knowing what you just told me, I would update my confidence level a little–I’m probably 90% sure that less than 25% of adults know Bayes Theorem. (I should clarify that=adults living in the US, Canada, Britain, and other countries with similar school systems. The percentage for the whole world is likely significantly lower.)
I hear Britain’s school system is much better than the US’s.
Once you control for demographics, the US public school system actually performs relatively well.
Good point.
It’s not great by international standards, but I have heard that the US system is particularly bad for an advanced country.
In terms of outcomes, the US does pretty terribly when considered 1 country, but when split into several countries it appears at the top of each class. Really, the EU is cheating by considering itself multiple countries.
The EU arguably is more heterogeneous than the US. But then, India is even more so.
How’s it being split?
I actually thought someone would dig up and provide the relevant link by now. I’ll have to find it.
You mean comparing poorer states to poorer countries?
Actually it is quite good (even for an “advanced country”) if you compare the test scores of, say, Swedes and Swedish-Americans rather than Swedes and Americans as a whole.
I wonder what that’s controlling for? Cultural tendencies to have different levels of work ethic?
Hmmm. So it’s “good” but people with the wrong genes are spoiling the average somehow.
The UK high school system does not cover Bayes Theorem.
If you choose maths as one of your A-levels, there’s a good chance you will cover stats 1 which includes the formula for Bayes’ Theorem and how to apply it to calculate medical test false positives/false negatives (and equivalent problems). However it isn’t named and the significance to science/rationality is not explained, so it’s just seen as “one more formula to learn”.
Offhand, 1⁄2 young people do A levels, 1⁄4 of those do maths, and 2⁄3 of those do stats, giving us 1⁄12 of young people. I don’t think any of these numbers are off by enough to push the fraction over 25%
Maybe you guys could solve that problem by publishing some results demonstrating its exteme significance
As far as I know, it’s been formally demonstrated to be the absolutely mathematically-optimal method of achieving maximal hypothesis accuracy in an environment with obscured, limited or unreliable information.
That’s basically saying: “There is no possible way to do better than this using mathematics, and as far as we know there doesn’t yet exist anything more powerful than mathematics.”
What more could you want? A theorem proving that any optimal decision theory must necessarily use Bayesian updating? ETA: It has been pointed out that there already exists such a theorem. I could’ve found that out by looking it up. Oops.
There already is such a theorem. From Wikipedia:
As far as I can tell from wikipedia’s description of admissibility, it makes the same assumptions as CDT: That the outcome depends only on your action and the state of the environment, and not on any other properties of your algorithm. This assumption fails in multi-player games.
So your quote actually means: If you’re going to use CDT then Bayes is the optimal way to derive your probabilities.
And the list of notable problems that have been solved using Bayes is...? Bayes doesn’t tell you how to make your informaton more copious or accuate, although there are plenty of techniques for doing that. Bayes also doesn’t tell you how to formulate novel hypotheses. It also doens’t tell you how to deal with conceptual problems that are not yet suitable for nnumber crucnhing. It looks to me like Bayes is actually a rather small part of the picture.
ETA;
A similar point is cogently argiued by RichardKennaway here
PS: -T-w-o- Three downvotes, and not a shred of counteargument. Typical.
Half of statistics these days is Bayesian. Do you want to defend the claim that statistics solves no notable problems?
As usual, I add my downvote to whining about downvotes. Since you think it’s ‘typical’ and this vindicates your claims, I’m sure you’ll be pleased that I’m helping prove you right.
Great. Then the UK education sytem is exactly right in teaching Bayes as part of statitistics, but not as a general-prupose solution to everything. ETA: But surely the LW take on Bayes is that it is much more than something useful in statistics.
No, I want to defend the claims that Bayes is not as a general-prupose solution to everything, is not a substitute for other congnitive disciplines, is of no benefit to many people and is of no use in many contexts.
Please inform me of the correct way to indicate that the karma system is being misused.
Now you’re just backing off your claim. What happened to your list?
First point: if Bayesian statistics is half of statistics, the description of the UK course is of it as being way way less than half the course. Therefore the UK system is very far from being ‘exactly right’.
Second point: The optimistic meta-induction is that Bayesian statistics has gone from being used by a literal handful of statisticians to being widespread and possibly a majority now or in the near future; therefore, it will continue spreading and eating more of statistics in general, and the course will get wronger and wronger, and your claims less and less right.
So you’re just splashing around a lot of bullshit and distractions when you demand lists and talk about the UK course being exactly right, since those aren’t what you are actually trying to claim. Good to know!
What’s the point of indicating when it’s not being misused?
I am not going to give a full response, because your comments are obstreporous, but See RichardKennaway’s discussion for LW’s oeverarching hopes for Bayes, and its limitations
You have your opinion, on that, I have mine. You can state your opinion, I can’t state mine. I can’t discuss the censorship, because discussions of censorship are censored.
You’re stating it right now. Oh the ironing.
It’s in a downvoted thread.So it isn’t visible.If negative karma doesn’t do anything regarding the visibility of comments, why have the button? Sheesh.
And so begins the equivocation on ‘people have to click a button to see it’ with ‘censorship’.
And so I ask you a second time: what is the button for?
And so begins another goal-shifting, like the list or like the claim of ‘censorship’, this time to defining karma systems. Pardon me if I don’t care to continue this game.
OK. You cannot give an answer that will not embarass yourself. Got that.
Must be a problem of the American school system, I suppose.
Did they teach you about conditional probability? Usually Bayes’ theorem is introduced right after the definition of conditional probability.