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Bayes' theorem explained with examples and implications for life.

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I didn't say it explicitly in the video, but in my view the Bayesian trap is interpreting events that happen repeatedly as events that happen inevitably. They may be inevitable OR they may simply be the outcome of a series of steps, which likely depend on our behaviour. Yet our expectation of a certain outcome often leads us to behave just as we always have which only ensures that outcome. To escape the Bayesian trap, we must be willing to experiment.

Special thanks to Patreon supporters:

Tony Fadell, Jeff Straathof, Donal Botkin, Zach Mueller, Ron Neal, Nathan Hansen, Saeed Alghamdi

Useful references:

The Signal and the Noise, Nate Silver

The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy, by Sharon Bertsch McGrayne

Bayes' theorem or rule (there are many different versions of the same concept) has fascinated me for a long time due to its uses both in mathematics and statistics, and to solve real world problems. Bayesian inference has been used to crack the Enigma Code and to filter spam email. Bayes has also been used to locate the wreckage from plane crashes deep beneath the sea.

Music from epidemicsound.com "Flourishing Views 3"

Holy ship! I never thought about this while studying Bayes theorem 😵😵

Were you talking about COVID ? :0! Nice Video!

5:55 What you said in the beginning is that the test identifies true as true in 99% of cases and identifies false as true in 1% of cases. That is not the reported accuracy of the test, sir, nor does it give us any insight into it, please do not confuse us. To tell us anything about the accuracy you need to convey in some form how the testing results measure up against the determined actuality of the situation. Unsolvable problems which is what you gave in the beginning ought to come with a warning... As for a conclusion (without getting into metaphysics, but sticking to the topic at hand) I feel a better one would be that, given how complex and multi-dimensional of a system life as a whole is, we frequently overestimate our ability to identify the determining factors of an outcome and thus become way too confident about it's overall probability while in reality we may only be aware of a very thin slice in the equation.

Hmm.. As you described it, it is a self-fulfilling prophesy, but it's quite often that the problem is that people don't see the flaw in what they were doing when they were testing, so they do new tests that they intend to make it more or less certain whether the first test gave the result they thought they get.. but the same flawed stipulation, or prejudice is used as a base for the second test too, so even if it looks from the problem in many ways differently, you haven't fixed the underlying problem. So.. What I would say is "Asking the Question".. Sometimes the answses depend only on the current knowledge and potential for new ideas.. it doesn't have to be that you are LOOKING for a specific answer, but currently available data, ideas, technology, etc, makes you blind for something.

I like that you did not provide an answer but set the stage for further consideration.

"she suggests..." There's your problem right there... you have a female doctor.

well I love veritasium and no disrespect while saying this. when he took p(H)=.001 he took in the factor of people who are not showing symptoms nor going for a test. I guess p(H)=probability of people that are truly diagnosed with this disease out of total tests done.(I know tests are 90% accurate but it is hard to determine exact number so we can start from this number ) what do you guys think about this? this will make the p(H|E) way closer to 90.

You predicted covid 19 man!!!!

Its that an UFO at 8:25 on the top corner? ? check it at speed 0.25

Derek is the best. He is so articulate, erudite and handsome.

Could this BE any more relevant in 2020?

Grats, very good explanation of Bayes.

re 2:10 "Incredibly"? Unbelievably? Perhaps he means unexpectedly, or even surprisingly. 1 in 11? I would not cross the street blindfolded with those odds! re 9:10 We should be grateful for 'black swans', even if they are Trumpian. (But not Nazi?) The nature of life is that new things happen spontaneously. How hard should we push for more change than 'nature intended'?

The disease example is actually a question in class 12 maths ....

Yes... probability chapter

I feel like ancient greeks used to talk about math like that, going on walks, and taking a stop to draw in the dirt with a stick

I'm proud i did not think that chances of getting disease is 99% ,

Great video. Thanks. Can you tell us the filming location in the video notes? What a beautiful spot!

Nah you gotta take into account your symptoms. You wouldn’t be testing 1000 people and only out of 1000 one will be infected. You’ll only be testing those with symptoms. More like 1 out of 50 who take the test will have the disease. If you test positive, then you likely have it.

Chances are 100% that you should get a different doctor - one that doesn't require theorems!

Bingo. You have no idea how important Bayesian theory is relative to Langer Epistemology Errors. When we encapsulate interpretive models Bayes techniques illuminate in an illustrative way. Where this all leads is nothing short of unification.

Привет Veritasium. Смотрел видео в переводе на русский. Оно меня очень вдохновило и заставило задуматься. Так сказать - взорвало мозг. Спасибо за годный контент)

you also have to factor in FALSE NEGATIVES (but that is if you test negative for the disease not if you test positive)

Seems like this is a good video to review, with all the Covid testing happening everywhere.

This feels so relevant to wants going on now.

I'm at about 1:00 and decided to figure it out myself. Let's see if I got it right. So we have 3 different percents 1. 0.1% of people have it 2. The test correctly identifies 99% of positive cases 3. The test incorrectly identifies 1% of negative cases With such, since 0.1% of people have it, that means 0.099% of people both have it and actually get a positive result. Then, we have the 99.9% of people who don't have it. If the test incorrectly identifies them as positive 1% of the time, that means 0.999% of people get a false positive. Since we know the character in this has a positive result, we only need to focus on the positive result cases. 0.099% of the population gets a true positive and 0.999% of the population gets a false positive. This means a total of 1.098% of the population gets a positive result. If we then divide the true positives by total positives and multiply by 100 (since the result is a drcimal) we see that only roughly 9% of positive results actually have it. Final answer before watching: You have about a 9% chance of having the disease. Now let's see where I messed up lol. Will edit this comment after watching Edit: just a minute later I find out I got it right what. I guess you're just going to have to trust me that I actually did this before he did, but wow that was pretty cool to find out i did my math right

don't you think it is inaccurate to take p(H) = 0.1% it should be more of number of positives out of number of tested...hence the p(H|E) will turn out to be much higher

As for your last thoughts here... applies to addiction recovery thoughts too... that's something I've been thinking about this applies to... "trying the same thing over again while expecting different results".

Where is this hike? I wanna go hike there

Heh, I watched the very same topic a few years back here, in french. Also Mr Phi gives this disease a name, the smurfitis. Don’t play with you smurf! :) That was a memorable moment! svfrom.info/history/video/Y6mIpo-xqrFxe7o

awesome making education good!

This aged well

True for P and E Not equal to 0 as would make it undefined.. And

great video.. wished someone had explained like this in my probability class

would recommend watching this video together svfrom.info/history/video/eL2Ad6e6rJiSrq4

Who's here after Elon Musk's tweet? For those who don't know, he said that after having symptoms he took the same test 4 times, in the same day, with the same machine and the same nurse; 2 results came back positive and 2 came back negative.

Can we know the time of the day by the image with your shadow?

Damn bro thanks so much

6:46 *me thinking about shadow.* 🙄😅😁 Imagine a light traveling and send it's wave which travel some distance to wall it strike. *suddenly after a complete traveling of a light wave I put my hand.* (whatever opaque thing) in between light source and the wall. *Will my shadow will not illuse for very very short time?* As remaining light wave behind hand when a light wave travel still there with speed c but takes time by our perspective _(acc to light's perspective there is no distance so speed and no time) so very very very small time no shadow or????_ plz tell

Hi

Veritasium guy at 0:18: "tested positive for..." Literally everyone in 2020: "Cuhronuhvaaarus?!"

So today Elon Musk said on Twitter that he had 4 PCR antibodies tests and he got 2 positive and 2 negative results. 2 weeks after FDA's warning about false positives in these tests.

thanks your videos are amazing

great video greaaatt video with great ending. Perfect veritasium ending

I feel compelled to mention Cromwell's Rule: "I beseech you in the bowels of Christ to think it possible that you may be mistaken". Never set priors to zero or unity in any field that you actually plan to think about.

I'm in a highly competitive field and deal with quite a bit of impostor syndrome, and I really needed to see this today, thank you!

So Derek, would you consider doing this calculation for the pcr data for Covid19? :) or would that be too hot a topic to touch?

In the top five best SVfrom videos I’ve ever seen. Pure poetry. Science with social impact. Really great 🙏🏻

Particularly relevant now with the false positives of SARS-CoV2.

Thank you

For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.

You are a good person.

😁

Oh yes! Thank you for that!

The equation looks like PewDiePie thingy

99% of those who have the diesase and 1% of those who haven't. Wait a minute! ;)

The explanation starting from 2:20 to 2:56 is very good and intuitive, but there is a wrong calculation at 2:51. If you do the math, the correct chance is 0.090163934. However, at 2:51, the calculation of 1/11 is equal to 0.09090909. This is because, even though there are a total of 11 people, "the chance of being a true positive case (as a person of the 1/11 people)" ~ is different from ~ "the chance of being a false positive case (as a person of the 10/11 people)". So you cannot simply say your chance is 1/11. You need to weigh each chance for the correct calculation.

I’d like to change always working in low paid jobs

Does anyone else see the UFO starting at 6:42??

Thanks for an excellent explanation of this subject. Too often in statistics classes do instructors forgo introducing this and when brought up, don’t really understand the process and what it means for research. For most students it’s beyond intuitive understanding, even though they do use it sub consciously for making the same decisions in life because they don’t change the approach.

i guess the testing is true for Corona

Superb PoV!

There is no rational basis for the assignment of probabilities to novel events about which you have no prior information. There are however and unlimited number of irrational bases for assigning such probabilities. This is the classic zero-frequency problem that appears in, for example, data compression algorithms and, apparently, spam filters.

can you use a different cameramode/selfi mode next time, I got "seasick/motion sickness" watching this stablisation/warp thing effect. :)

what is the probability of having positive results for covid-19 if you haven't got it ?

In the UK, the government doesn't even provide this information. How can you begin to trust any data?

Baye seemed to have a strong philosophical influence on his work.

just be uncertain about your priors :)

This has huge implications in the political thinking of humans, that's why those above are so busy trying to get us to think some things are just good or bad without any reasoning

To be fair, Laplace might not get a theorem, but he does have a transform and an equation named after him.

this video would be a great teaching example for all teachers around the world

Error matrix be like:

2:55 There is one imposter among us.

The example doesn´t count for the normal case when we are being tested due to symtoms or genetical disposition. Where there is a pre-selection of the persons being tested. For those people - a vast majority in a normal situation - the probability of having the disease, pre-testing, is a lot higher than 0,1 %, right? Hence the accuracy is a lot higher. But i surely cast a shadow of the idea of broad testing, if it´s not for to get a general, pandemic picture. For the individual it´s not very useful.

I don't know what it is, but something about seeing you walk along that overwhelmingly beautiful landscape with the moon's great presence in the sky floating over everything. I can't describe it. This looks like something from thousands of years in the future... but it wouldn't be planet earth that you're standing on- instead a new world we've inhabited

It's why philosophy is an essential study.

I love statistics just as much as I love boolean algebra.

Hi, I like your video. Could you let me post it to my aiqiyi.com account in China?

Blows my mind, ever time. I've watched this video 40, maybe 50 times by now and it always sends me into a self-reflective spiral. Thank you Veritasium, thank you.

Using Bayes Theorem, what's the probability of receiving a single positive COVID-19 result meaning you have COVID-19?

I just realized... Veritasium 420 XD

The problem with Bayes, which I've studied extensively and use every day, is that it can't be applied equally well to all types of data. Essentially, Bayes is an average of an average. The thinking is that the average of the average will weed out all the outliers, but that doesn't work if the datasets that the original average were derived from were faulty. Bayes might work relatively well with diseases that have clear cut outcomes like terminal diseases, but the best example of Bayes NOT working is the 2016 Election. All of the polls that showed Hillary Clinton winning were wrong because their datasets were fundamentally flawed, thus taking an average of them yielded an incorrect result. Want to know one of the major flaws of COVID policy? Double counting. We were told that we were short tens of thousands of hospital beds and ventilators because we were going to have the regular flu season patients PLUS COVID patients. Do you see the double counting error? COVID patients are often the old frail patients who would have needed that bed or ventilator anyway because they are the ones more likely to get the flu. We were never short ventilators or hospital beds. COVID and flu patients, which are often one and the same, were double counted. Using Bayes for COVID potential morbidity is actually ridiculous because there is no clear cut outcome. Asymptomatic people never get tested because they don't even know they have a disease. People who die WITH COVID are often tabulated as dying FROM COVID. (millions of people die WITH warts every year, but they don't die FROM the warts). Again, averaging averages with Bayes is useless if the datasets are faulty to begin with. But... there are a lot of people making a lot of money pushing Bayes and other statistical snake oil on government officials and corporate executives who don't want to admit they have no clue about statistics.

This was great, thank you!!!

Welp, he has correctly predicted COVID, uh yeah that's kinda creepy

Tell this one to all the Corona panicers.

7:30 hit home. I always thought bayesian models was more or less HOW people thought; tbf I learned about it for the first time in a language developement course. But your notion of it as problematic to someone's development or self appraisal is very insightful V.

A lot of comments are talking about flaws in the approach as it is explained. Here is another one: the test can make a mistake in two ways: false positive and false negatve. The beginning of the video talks only about false negatvies, then in the Bayes formula 99% (1%) was used in two different contexts, so it is assumed that this error rate is the same for both cases.

Doing the same thing over and over again, and expecting different results means you take Bayes Theorem into account, and are probably right!

Bayes' Theorem = universe-sized game of You Sank My Battleship!

6:53 Look up at the top left of the screen. It looks like a UFO. Now what’s the probability of this hypothesis being true given that it’s a sunny day?

not me watching this right after my statistics midterm

Interesting. I have no math knowledge but I got the right answer, because it just seemed like common sense, that it'd be about 9% chance.

*Meteor lands on a person, killing him. Bayes' Theorem: "There is only a 9% chance that he was actually hit by a meteor." Cold Hard Facts: "Hold my beer..."

Maybe it would be a good idea to make an experiment in reading the Book of Mormon. It has a promise that if you read it with sincere intent, then God will show the truth of it to you. If you have 100% certainty that there is no God, then never mind.

no result repetitives : datting apps

Corollary to Mandela's theory: No one's a murderer until their first murder.

i guess this also applies to covid tests

When I was watching this, I felt like I understood the bayesian trap, but now after video ended, I feel like a fool because I can't quite articulate the same. I'm starting to questioning my memory retaining abilities or is it natural because I'm not familiar with topic itself.

Air pollution looks crazy far away in the background. That city's having a nice bath in a proper dark grey cloud.

"Thought to himself"? As opposed to... that he got telepathy (thinking to someone else) down pretty well?

What? 1 in 1000 is not 1%. The whole premise of the explanation is wrong.

8:55 It's Vaas's definition of insanity. Doing the same thing and expecting a different result.

Zachary Wiebe10 timmar sedan