Bayes theorem, the geometry of changing beliefs

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Title	:	Bayes theorem, the geometry of changing beliefs
Lasting	:	15.11
Date of publication	:
Views	:	3,6 jt

When I read Kahneman and Taversky’s many years back, I found it very interesting, but I never thought it had much to do with probability (even though there are many probability examples), rather it’s about psychology and how people, or their presumed fast thinking brains, are very sensitive to the exact phrasing of the question, so much so that it doesn’t matter what the question actually is because they decide what the question ought to bebrbrIn the bank teller example, most people have decided that Linda is already known to be a bank teller, so the question is only whether she is also feminist or not
Comment from : @aroundandround

You say people are not expected to know this but you’d think given a context where it’s a natural question, people would guess that, after all, it makes sense that the thing we need more of has more people doing it
Comment from : @S8EdgyVA

I feel like its not necessarily even about the number of people, though thats an important point; farmers dont need to interact with people nearly so often, and do need to be tidy (planting in rows)
Comment from : @chrstfer2452

Came across this video on a whim and I gotta say, I studied computer science in college with multiple classes touching on this subject and this is by far the best explanation I’ve ever seen Fantastic teaching
Comment from : @FATMAN92769

People wouldn't consider the ratio of farmers to librarians when answering that question because it is irrelevant It was not stated, nor should be expected, that the person in question was plucked uniformly at random out of the US population They are simply given an example person, who in fact sounds like it was cherry-picked for the sake of the exercise Using the ratio of farmers to librarians in the population at large is flatly incorrect in this case
Comment from : @isodoubIet

you are gifted Grant! believe me! you changed my deep understanding of probability Thanks!
Comment from : @armankhalifehsoltani4223

With this, I will never forget Bayes Theorem! Thanks a lot man! Cheers
Comment from : @JM-ko8qz

Thank you so much!
Comment from : @fallingstones2396

well i think alltought 1 farmer can feed 1 million libartians i think steve is a hunter since their are allreadey enought libarians
Comment from : @ulyssesk7325

Man, you have the best Mathematics youtube channel in the world and evidently, you are the best mathematics tutor
Comment from : @user-jm2cp3oq4r

Given the description it is still more likely that Linda is both a bank teller and active in the feminist movement than that she is merely a bank teller, mainly due to the key phrase "social justice"
Comment from : @MotesTV

I'm so thrilled and grateful to have you as my math teacher Beautiful era to live in!
Comment from : @kingshukcs

ideal
Comment from : @forthefuture2273

LET'S GO!
Comment from : @pietromicelli11

i think the introductory example is disingenuous When people ask a question like that "here is a description of a person is he class A og B", it is not appropriate at all to assume this is person is randomly sampled from the population i think what is instead implied, the way most people hear such a question, is that the person is sampled from the archetypes of their respective classes Eg you take the x most libererian libererians and x most farmer farmers, and pick one why would you say its eigther a farmer or a liberarian if not Is a more valid answer that you think hes a teacher because those are more common?brbrnow i would say as an example to teach bayes theorem, this is not that bad However many people will use such thought experiments to try to convince people to use a more "logical" mindset The fact is in the real world when you are faced with a question like that, not asked by someone that designed it to trick you, cleansing your mindset from context, and trying to find a few variables and use math will be less accurate than using your intuition on the whole context of the question asked, why it was asked, who asked, etc
Comment from : @codelapiz

im not gonna lie this video pisses me off
Comment from : @38zech

I shall honour your channel in my inauguration Thank you
Comment from : @abexoxo

@3blue1brown could you also make a brief video on MAP and MLE Lot of love and respect for your work
Comment from : @Dutta1605

Watching this video again, I have to say, it's brilliant
Comment from : @e11e7en

whenever I saw classic probability problem of positive negative test result, I used to think bayes theorem is absurd as its telling the probability of having disease is lower even though the result is +ve But after watching this video, everything makes sense Much Thanks for this video :)
Comment from : @ashithen1833

What seems to bother/confuse me is that bayse theorem just looks like a static equation about joint probability It seems to just describe a static reality But the interpretation is a dynamical/iterative scheme to update subjective belief brbrThe libertarian-farmer example has a hypothesis that has a well defined prior probability (the fraction of librarian is a objective reality) In other context, the probability about belief is fundamentally ill defined For instance, the likelihood of string theory is correct (over all current theory) has a definite binary answer while our assignment of prior probability is totally ill defined and subjective This example is more about updating subjective belief while the librarian-farmer example is more about describing well defined static reality One example requires some kind of iterative convergence to give rigorous result while the other give rigorous result without the need for iteration
Comment from : @bohanxu6125

If 3b1b was everyones math teacher,humanity would be hundreds of year ahead in terms of techonology
Comment from : @necastavasbriga5989

bruhh I dont get it
Comment from : @dweeder1453

Very well explained, congratulations!!! I would like to ask if on the minute 4:20 there should be 40 instead of 4?
Comment from : @AIEasySolutions

as a statistics major this is so beautifully done, the intuitive understanding of probability takes years to achieve, yet you managed to beautifully present it in a video, congrats ❤️
Comment from : @michacuylits7254

🎯 Key Takeaways for quick navigation:brbr00:00 🧠 bEntendiendo el objetivo del Teorema de Bayes/bbr- El objetivo del Teorema de Bayes es comprender cómo la nueva evidencia debe actualizar creencias previasbr- Se plantea el caso de Steve y cómo nuestras percepciones iniciales pueden no considerar la información relevantebr- Bayes ofrece una fórmula para actualizar creencias basadas en evidencia, no para determinarlas completamentebr04:52 📊 bComprendiendo Bayes’ Theorem: Fórmula y aplicabilidad/bbr- Bayes’ Theorem calcula la probabilidad de una hipótesis después de observar evidenciabr- La fórmula de Bayes implica la probabilidad previa, la verosimilitud y la probabilidad de la evidenciabr- Aplicaciones de Bayes en ciencia, inteligencia artificial y en cómo modelamos nuestras propias creenciasbr08:54 🤔 bAmpliando la intuición sobre la probabilidad más allá del Teorema de Bayes/bbr- La importancia de representar mentalmente muestras representativas para comprender mejor la probabilidadbr- Ejemplo de Kahneman y Tversky sobre cómo la presentación de la información afecta nuestras percepcionesbr- Probabilidad vista como proporciones y la utilidad de la geometría en la comprensión de Bayes' TheorembrbrMade with HARPA AI
Comment from : @Cuansf

It is the best video I have ever watched about Bayes theorem! I am also looking forward to tutorials about making the video I really like this style!
Comment from : @yijingwang7308

Bayes theorem is good - in my mind it is a way of quantifying being 'holistically thorough' or 'sherlocking' it I think there may be value in finding a more widely applicable opening example
Comment from : @autumnthriller

I think I know too many librarians for the example to work on me the way it was supposed to, in particular the "shy and withdrawn with very little interest in people" part made it not feel particularly more suited to being a librarian, which is a job that in fact requires a LOT of public interaction
Comment from : @HunterJE

I think of it as "probability of a true positive divided by the sum of the probability of a true positive and a false positive"
Comment from : @KCObamacan

Proportion is the word! Thinking about probability in terms of proportions just makes it so comprehensible and easy
Comment from : @avimandavia6154

The best way to approach any problem is to break it down into simpler problems , look for patters and possible manipulationsbrbrBut how to do that?😂brI am able to break it down , I am able to identify patterns (sometimes not) but the part of doing serious and out of the box manipulation, I am not able to do it Teach me😊
Comment from : @theinterpreter3705

Thanks!
Comment from : @realdealbasile

thank you so much i finally got the point thank you thank you thank you
Comment from : @xxxx3732

I just want to say, thank you for this point of view
Comment from : @mirovskii

Can't Thank you enough for the illustrations that make everything clear and easy to recall Also, the fact that it is not just about teaching the formula but the concept and the notion of it is what we all need Thanks a million
Comment from : @alaaseada4659

I need to repeat watching this 100 times
Comment from : @macaion897

THANK YOU this video is very very very didactic and easy to understand Your channel is amazing!!!
Comment from : @GabriellaVLara

Hii, I am steve
Comment from : @dhruvilpatel4218

The statement evidence should not determine belief but only update your prior beliefs also cannot be taken as an absolute It is contingent on the evidence and the nature of the belief under consideration, isn't it?
Comment from : @surajv1986

amazing video thank you so much!!!!
Comment from : @antonisstellas741

I found that the parts “has a need for order and structure” and “passion for detail” to be the traits more becoming a librarian
Comment from : @NightnessDev

What would be a number value to "It's easier to get somebody to believe a lie than to get them to believe that they have been fooled by a lie"? Is there a friction coefficient?
Comment from : @GeoScorpion

I really enjoy watching your videos Thank you for expanding knowledge in such a beautiful way ❤
Comment from : @armandavari5556

"Rationality is not about knowing facts, it's about recognizing which facts are relevant" brbrThat sounds like a quote, is it? If so, what's the source, I'd like to quote it"
Comment from : @stevenowens4511

Man I love you!
Comment from : @user-mp2ct6qy2w

The question does not give any indication, not even a vague one, of Steve being a random pick from a population Hence to make that assumption would be illogical, and have a low probability of being true
Comment from : @simont6439

This is the worst explanation i have ever seen Time to see some indian guy explain this as straight forward as can be
Comment from : @mahedihassanrafin7493

Just for the sake of trying to understand the problem with Linda, I think it might be useful to consider 2 things: 1 Saying either she is a bank teller or a bank teller and an active feminist, I think, makes people conclude the "bank teller" answer means "she is bonly/b a bank teller" as in, she is specifically bnot/b participating in feminism in any way (some might even extra erroneously think the question is asking whether or not she is for or against feminism), which her bio seems to contradict 2, I mean her description is so close to saying "I am a passionate feminist" that ignoring that when answering the question seems almost insanebrbrI guess what I'm saying is I would argue the bstudy/b is inherently flawed, and not the conclusions people are coming to when answering that The first issue, farmer vs librarian, on the other hand, does not have this problem So those results are probably much closer to the truth
Comment from : @kittenbouquet

Also funny because that description is almost as applicable to farmers as to librarians
Comment from : @danielmagee8637

Great for understanding Bayes' theorem, but that paper's questions are obviously useless - the Linda question is an XOR,
Comment from : @ChristopherBradfield

Dude, you are a magician your videos have opened up this new world for me, which was so unapproachable to earlier, so beautiful Thank you so much for these videos
Comment from : @pratikpatil87

Finally a clear explanation of Bayes Theorem that's easy to understand, thank you!
Comment from : @AndrewCatanach

Genius!! Thank you so much
Comment from : @marianavillabona2022

The PIs are very cute
Comment from : @Fjodorz

Comment from : @oofsper

Genius
Comment from : @alamey4442

Thanks!
Comment from : @shiluo4728

Amazing video! The illustrations are really useful!
Comment from : @flaviopibetagama

Love it!!!
Comment from : @Carol-ppp3189

I was so confused in this topic U really explained this so easily Thank you!!!
Comment from : @studlee

I am very thankful to you for this explanation
Comment from : @wickedclamor4882

Nobody explained me bayes theorem in the way you did Won't forget it for life Thanks Grant
Comment from : @ayanangshudasmajumder112

i think the appropriate answer to the farmer/librarian conundrum would be 'not enough information'brbrwith a little thought it's clear both a farmer and a librarian could possess the listed characteristics a more telling quality would be (eg) does he prefer to work outdoors in all kinds of weather or does he prefer to work inside a climate controlled environmentbrbrmy first thought would not be to wonder about the ratio of farmers to librarians in the general population tbh
Comment from : @cinidude

Thanks!
Comment from : @nintendan

Freddy cono e madre viva maduro
Comment from : @eliastsoukatos2

Steve is an NPC
Comment from : @AlvaroMartinGrande

More vaccinated than the non-vaccinated in the hospital in a society where 90 of the people is vaccinated!! What a weird and suspicious phenomenon??? How can it be?? It's not an accident for sure!
Comment from : @karoltrzeszczkowski9567

So basically we’re saying “out of the people that *are actually shy like Steve*, what is the proportion of them that are shy librarians already?” Because to claim Steve will be likely to a librarian due to his shyness, we need to have seen evidence that librarians tend to be shy in the first place
Comment from : @randywa

As a child of a library household growing up in the middle of a rural agicultural bubble, that "meek and tidy" bit was a lot to process! (In my time I have observed both farmers and librarians displaying a very wide range of behaviours!)
Comment from : @greentape7817

I will get a tattoo of this formula on my arm
Comment from : @sonnguyenhoang5024

LOL
Comment from : @hdd_1230

Thank you my man
Comment from : @hamedazimi2726

May anyone could tell me by which software can make this kind of video?
Comment from : @planepaper4347

It is an excellent explanation, but as a few others have already indicated, you've made an error by equating verbal misunderstanding with cognitive fallacy Implicit to the listener in the first question is that the questioner is talking about a population of two people (one librarian and one farmer) rather than the population as a whole Kahneman is much more careful to define conditions in his version of the question (Tom W), but ultimately, makes the same mistake by not accepting that questions in human language depend a great deal on context and unspoken assumptions I am not saying that such cognitive fallacies are unreal; just that language is a slippery animal that can be hard to pin down
Comment from : @squillomeister

You explain Bayes theorem in under 7 minutes My lecturer could not do that in 90 minutes Btw I’m in a QS top 20 university
Comment from : @lym3718

condition is a more appropriate term here than evidence meek is a criterion or condition, not evidence there are a total of 24 people who fit this condition!
Comment from : @fa7234

aha its quite simple, Steve likely to be a farmer because he is a male bbig brain intensifies/b bhalf read thinking fast and slow falls out the bag/b
Comment from : @leonhardeuler4292

"Rationality is not about knowing facts, it's about recognizing which facts are relevant" - I'm borrowing this line Fucking gold!
Comment from : @krishnakumarsubramanian3292

0:35 "Multiple different levels of understanding" Bayes Theorem This means we need bayes theorem to understand Bayes Theorem??!!
Comment from : @madhukrishnavallabhajosyul6996

That stereotype is created by Hollywood 😅
Comment from : @VinayakPattanashetti

The whole problem arises from semantics of unspecified conditions in a questionbrDefault cultural standard is to compare average librarian with average farmer, so the answer is that it’s more likely that average librarian is shybrMeanwhile what you refer to as new evidence is data needed to resolve the question with added specified condition: accounting for population statistics, thus not avarage, but any given librarian or farmer insteadbrYou can not retrospectively state that the first (default) answer is false, because you would have to update the question as wellbrIncompleteness of original request does not invalidate the given answerbrIt’s like asking: what is the chance that one of twelve crayons has a lucky color?brProblem is ill defined, because lucky color is a subjective definition of condition, which can be interpreted in many ways: my lucky color, color which is considered lucky in my culture, our culture, any culture, etc
Comment from : @tayablackrose29

Talk about a lightbulb moment! This is genius Of COURSE it's about proportions and therefore, geometry Thank you!
Comment from : @johnhibble7637

I shared an analysis of Bayes Theorem and the Monte Hall problem with Steve Strogatz about 12 years ago, based on Byrne ;)
Comment from : @rjbriggs547

I frequently share this video with LabLeak deniers to get them started on understanding that it's the only explanation worth considering at this point
Comment from : @skenzyme81

My teacher who has an experience of 20 years recommended your channel bro great work dude
Comment from : @vamsikrishna3315

That second question about Linda was used in a training seminar I went to for my job, and many people not only chose option 2, but continued to argue for it after it was explained
Comment from : @Preserbius

Reminds me of partial derivatives and chain rule, fascinating
Comment from : @milespiano

John grew up very interested in science He has a high IQ and is very adventurous brbrDoes John work at Amazon or is he an astronaut?brbrDid you say Amazon because it is statistically more likely? Cool That means details of a person’s life aren’t even relevant to such a question brbrThe question you should have asked is “what job is a person more likely to attain, astronaut or Amazon?”
Comment from : @jordonlongley6576

god those two examples where so fucking bad and his response to people's "wrong" answers was even worse this is why statistics is only as useful as the person using it
Comment from : @Atomic-Monkey

thanks a ton @3blue1brown, you are changing the P(H/E) of good teaching/better worldbryou are one of those very few people who are changing the world for goodbrone concept and one video at a timebrcheers!!
Comment from : @sas-ko1ve