The Bayesian Trap

Bayes' theorem explained with examples and implications for life.
Check out Audible: ve42.co/audible
Support Veritasium on Patreon: ve42.co/patreon
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"

[@eiccio7770]

the guy that found the formula in Bayes’s papers after death and still gave credit to Bayes without trying yo appropriate it for himself is truly a man of science

[@khoavo5758]

I’d categorize that behavior under “not a scumbag”, but sure.

[@jesusbermudez6775]

yep, there are few like him

[@KufLMAO]

@@khoavo5758I see no contradiction

[@saats2502]

or maybe he is the one who discovered the theorem but he wanted to give credit to Bayes 👁️👄👁️

[@jesusbermudez6775]

Don't tell me there are such altruistic people in a world where it is me, me, me, me, and only me@@saats2502

[@pamphlet3786]

"So what do you do for a living?" "Oh the usual, drive to an open field, walk a mile, and talk to myself for a bit."

[@sitearm]

don't forget, also: "fly photodrones, build up biceps by holding cameras at arms length, record & edit multiple video and audio segments, research & think about stuff, write & memorize scripts..." ; p

[@jf8138]

poop.

[@sizzlinsj8135]

Yeah and this requires a heck of a time :P

[@industrialdonut7681]

+sitearm LOL I'm so glad I'm not the only one who thinks that's got to be killer holding the camera out like that!

[@chris_1337]

A better answer: "Show people cool stuff while also inspiring them"

[@mobius8561]

came for the mathematical insight, stayed for the existential crisis

[@RioboCabotD]

ikr

[@Flylikea]

😂😂😂😂😂

[@lemonettreeee]

​@@RioboCabotD1:05

[@JeffreyEdwardsD]

You nailed that one on the head. Surprise lovely ending.

[@HiVizCamo]

Maybe do some self-reflection on your priors. That is, are they valid, have they been formed by propaganda? Do they need to be updated, modified, or even overturned?

[@BC-yv8ew]

One of the best pieces of advice I’ve gotten is to always leave yourself room to be wrong. It infuses a certain amount of humility into things. Feels like this is the mathematical proof that advice.

[@luckymandragoran8471]

Absolutely this ^ I was taught it as "dont paint yourself into a corner" although I spent most of time wondering why someone might paint the floor. If God and the 7 deadly sins exist then arrogance is the 8th

[@vandutch4220]

I’ve worked in IT close to 30 years and this single concept of troubleshooting based on what I could have broken has most consistently produced favorable results. Often in the process of ruling out issues that I could have somehow caused, I find the correct answer, even in cases where it turns out it wasn’t actually my fault.

[@BengtSviu]

especially in love and war?

[@fury_blade9303]

@@luckymandragoran8471 well pride is already one of the 7…

[@richardndungu2815]

Obviously nothing is absolute

[@indylockheart3082]

"Well this can't be good." The first caveman to witness a sunset probably

[@frosty3693]

Followed by the people who learned to measure time, and the length of a day, and noticed that the days were getting shorter.( they started timing after June) Though there was no internet at the time for huge panics, there were probably more sacrifices, human and otherwise, until a positive change was noted and verified, followed by a big party. About December 25??? (not being anti Christian here as there were many fertility and other celebrations about that date and Christianity may have just co-oped one.)

[@enomiellanidrac9137]

more likely to have been: "MY EYES! THE PAIN! MAKE IT STOP!"

[@krantinebhwani6125]

@@enomiellanidrac9137 *re-opening eyes completely wide to challenge the sun* "BEGONE DEMON I SHALL NOT WITHER AT YOUR INFINITE BUR- MY EEYEEEEEEES"

[@a..d5518]

@@frosty3693 but 12/25 wasn’t even close to “his” so called birth day

[@JannPoo]

I don't know if that ever happened for sunsets, since people were probably accustomed to those before they even developed the ability of coherent thoughts, but it certainly did happen when they witnessed solar eclipses.

[@caio.tavares11]

This 10 minute video was better at teaching Bayes Theorem than my whole Stochastic Processes class in the university.

[@gamingSlasher]

Yes, people that understand statistics cant explain it to people that dont.

[@carlosbelo9304]

because once you get the logic behind it, everything is obvious and you can't really go back :)

[@eideticex]

Certainly. Always struggled with the concept despite "knowing" it. Didn't even realize I had intuited it with a similar line of thinking as Veritasium. I've always had that intuitive understanding that if you were told something over and over again. Regardless of how much to the contrary you may feel or believe. You will come to believe what you have been told. It's with this thought that I always try to treat people like they are much better than they may be at current. I don't think it's a coincidence that it usually works to get people to understand things they never thought they could. However I know it may just be correlation with cause laying in inspiring confidence, since we all know how important confidence is to learning and understanding something.

[@RaghavanNS]

The part about professors not teaching properly is not accurate , my prof really did a good job with teaching Bayes and other methods .. there's still a probability of good profs 😊

[@ionaf9]

It's funny I can't remember exactly but something ridiculous like around 90% of uni profs thought that they were above average at their job. Just an interesting thought.

[@chloemccarthy2297]

I needed this video. I needed to know that a famous mathematician had doubts their research was worth publishing.

[@dickurkel6910]

Why?

[@globesurfer122]

It was more that he thought it was so obvious that he didnt need to publish it. Not that he had doubts about it.

[@chloemccarthy2297]

@@globesurfer122 Those are the exact doubts I have, what you just described.

[@ameennazeer12]

Did you go forward with publishing ?

[@alhsihtisharfnao7816]

@@globesurfer122 um you did not read the comment correctly, the comment says they needed to know that a famous mathematician had doubts their research was worth publishing, not that they had doubts about their research, but that they had doubts about their research being worth worth publishing/not publishing- ig you did not read it completely/correctly?

[@anandanarayanan_n_2191]

This is the kinda content I want, I don't want a long commentary on advancing tech or difficult problems, i want simple explanation of fundamental and simple principles and their meaning in our everyday lives Great work veritasium

[@tochoXK3]

"I don't want a long commentary on advancing tech or difficult problems" I wonder if you have LessWrong and their talk about "Baysianism" in mind

[@gotaro69]

​@@tochoXK3not OP, but lol u nailed it

[@RichardBuckerCodes]

I really like the bit about 0% or 100% certainty.... it explains a lot of things.

[@les6230]

Love that Veratasium comes back and interacts with these comments from older videos. Says alot about what he does this for.

[@Hacker4748]

Wasn't that told in a wrong way, though? To be 100% sure about some thing is bad but to be 0% sure is good, it means to be ready to be convinced by evidence. Perhaps the example was supposed to be "being 100% sure about a thing being true or not true is bad".

[@douglaspovedaescucha1693]

Being 0% sure of something means that you are 100% sure of the contrary, the issue here is ‘certainty’, and skeptics will always be between 0 and 100 but never 0 or 100

[@Hacker4748]

@@douglaspovedaescucha1693 "Being 0% sure of something means that you are 100% sure of the contrary" Uh, no, absolutely not, that's the point. Being 0% sure means one has zero idea about what is true and what is not. If I told someone "bazee is doing some blaking" he'd have no idea what a bazee is and what blaking means, so he'd be 0% sure about if it was true or not. Maybe it was, maybe it wasn't, he'd have no way to tell, so he'd be 0% sure. Being 0% sure of something means the probability of it happening (or being true) is 0.5.

[@Hacker4748]

@@AaronLebahn The exact quote was: "It's possible for some people to hold that certain things are true with a 100% certainty, and other people to hold those same things are true with 0% certainty." That is not about Bayes' theorem. So, while you're right, you're talking about something else. Being 0% sure of something means the probability of it happening (or being true) is 0.5.

[@declination2327]

“Keep the company of those who seek the truth- run from those who have found it.” ― Vaclav Havel

[@arendwittmar4007]

That doesn't make any sense

[@letsfindsomepeace9207]

Yo explain what you mean by this. I swear people love leaving random quotes under KZbin videos. Some of them make so sense.

[@estefanolivares9199]

@@arendwittmar4007 think religious people who erroneously cling to their truth despite giant holes in their system Those who seek Truth will change their thinking as they pursue the flaws

[@klmnopq]

I found the truth

[@DannyGruesome]

@Parker Sullins that is exactly the meaning of the quote sir

[@jkenzo87]

I really like the part where you reflect on Bayes' theorem and essentially describe bias and how doubt is a necessity to approach the truth. Thanks!

[@macmac1022]

Just look at what science and philosophy does, falsifies things. My favorite philosopher did a lot of to find out what something is, understand what it is not. I always liked what voltaire said doubt is not a pleasant condition but certainty is absurd.

[@checkerface5710]

@@macmac1022 if certainty is absurd what can you do to prove something?

[@datswingfromnaruto5810]

Indeed, priors are the most challenging part of the equation. Considering the OP's example of the rare disease, I must say that a real life clinical scenario is much different. People don't just randomly get tested for a horrible disease. The testing comes after the doctor notices particular symptoms. So in a real scenario the prior would be "The Frequency of Disease In People Who Show Certain Symptoms" which would be much higher than "The frequency of the illness in general population."

[@anantjha4624]

I guess that "doctor's clinic" Analogy was given as just an example to understand bayes theorum

[@Amor_fati.Memento_Mori]

@@anantjha4624 I think the op was just attempting to point out where the example fell short by saying, "in the real world", and understood that it was indeed just an example.

[@EdgeMasterPro]

True for many diseases but also explains issues with population screening. Mammograms come to mind.

[@jrodartec]

You are certainly correct. Nonetheless, your posterior would still be updated by the accuracy of the test, and not identical to it. In covid, given false positives were 10% likely, people often thought that when receiving a positive test they would be 90% likely to having it. While sometimes it should be much lower (if symptoms and disease frequency are low), given that these symptoms also show up for a number of different, more frequent diseases.

[@fisch723]

I’ve been binging House MD, and this comment rings true. 😀

[@shawnnoyes2776]

Yes, this video inspired me to go back to school, and finish my degree. Class started today. Thanks! -Shawn

[@danihrndzld]

How's it going?

[@jacoboribilik3253]

Since he dropped out once, the most sensible thibg to conjecture is that he dropped out once again.

[@zucc4764]

@@jacoboribilik3253 it's impossible for him to graduate too, since the prior probability of him graduating is 0%. It's therefore impossible for any non-graduate to graduate. Bayesian trap.

[@jacoboribilik3253]

@@zucc4764 yes, that is also true. I am switching to a frequentist approach for this question.

[@DennisZIyanChen]

@@zucc4764 you have completely misunderstood how this works. But I hope you are joking even though it's not at all a funny joke, more self-revealing if nothing else.

[@ffttossenz]

Normal probability KZbin tutorial: some dude in front of a white board Veritasium: walking in nature talking about men in caves

[@narayanraikhere1]

true af........ man

[@RedStallion2000]

Here's another presenter you might like :) interestingengineering.com/video/this-youtuber-explains-logarithms-bob-ross-style

[@klausstock8020]

Even the classical form of lecture can be entertaining, if done right: kzbin.info/www/bejne/nofMnomwnNl3bNk

[@irfankarim6463]

I watched this video again after 6 years. A lot of things have changed for me, you made science interesting and then there was no looking back for me. I love you, Dr. Derek Muller. Cheers to the day you decided to leave your full-time job as a professor and started to make these videos that can reach so many more people.

[@TorQueMoD]

I heard the phrase years ago "If you do what you've always done, you'll get what you've always got". It's interesting to see the etymology of that concept. Thanks for sharing!

[@sjoerdstougie]

came for a mathematical fun fact, stayed for a life lesson :)

[@voorhalven]

Now you can count on yourself?

[@filipmanov8951]

@@voorhalven i still cant ,i can see this only when i am high

[@njb444]

I grew up in southern california and have hiked the trail in this video several times, although I moved away while there was still a drought. Seeing how green everything is now is quite a shock!

[@donovanmorgan7944]

njb444 where is it

[@austin9845]

If I'm not mistaken, this overlooks semi valley, it's the Upper Las Virgenes Canyon Open Space Reserve/Chatsworth peak/Santa Susan nuclear research lab meltdown area. I don't know exactly which park it is since they are all connected

[@ColinCren]

I was pretty sure it must be the Santa Monica Mountains. I think that's Albertson Road at the north end of Chesboro Park. I've MTB'd that a few times, it'd be pretty cool to run into Derek on a hike.

[@Animenite97]

I'm pretty sure there still is a drought.

[@ColinCren]

There is because ground water and reserves aren't back to normal, but all the rain has made for a very green spring.

[@lakshannavarathna7689]

I absolutely love this video. The first time I learnt Bayers theorem, like you said it really felt counter intuitive. But the you see the Bayesian nature of real life decisions. You can never make a calculated guess about the final outcome without the knowledge of its prior. The only case that you’d know for certain is when your prior is either 0 or 1. It’s an amazing piece of mathematics.

[@cosalidra759]

I hope Derek Muller sees this message. This line "recently my concern has been opposite , that maybe we are too good at internalising the thinking behind Bayes' theorem". I watched this video again today after 5 years and it has taken new meaning and this line gave me goosebumps. That's because I was recently acquainted with the free energy principle and the theory that we have Bayesian brains. Our brains predict our reality ALL THE TIME and it constantly collects evidence for it's own existence ( self-evidencing ) through sensory data. This is how our brains work and this could be an understanding of consciousness by first principles. These are the theories of one of the top neuroscientist in the world right now, and all time, Karl Friston ( who is the most cited neuroscientist ever ) .

[@thoyo]

In school I would often resign myself to the "fact" that I'm just not good at math. Now I'm learning to program and teaching myself math and discovering a world that I once barred myself from exploring.

[@lquinn7212]

Same with me. Basically I was gas lighting myself.

[@mkj1887]

Do yourself a favor and learn the derivation of the quadratic formula. Doing so is a milestone in anyone’s mathematics education.

[@thoyo]

Will do. Thanks!

[@jimwerther]

Lots of people had lousy math teachers, thus reaching a similarly faulty conclusion.

[@selvamthiagarajan8152]

Power to you.

[@mediawolf1]

I'm enjoying successively updating my understanding of Bayes' theorem by watching different people's takes on it. I also like that the moon is in this video.

[@megadeathx]

That was bothering me. Is the moon at an orbit super far or is Venus super bright in the video pickup for whatever reason? Glad to have some added certainty to my assumed expectation. I am now 91% confident it's the moon.

[@deepanshhh]

I watched 3blue1brown's video before this one and I loved that video but I have to say that this video was a much better prior.

[@Norsilca]

@@megadeathx The moon isn't actually very big in the sky. It's just our perception that makes it seem big. Try taking a photo of it with your phone and see how big it appears there.

[@sahilsagwekar]

im going through it too; just a year later than you

[@lordbuss]

Meta-Bayesianism!

[@TheSebastienmoreau]

I have been having similar conversation for months. I am a firefighter/paramedic in San Francisco and this conversation is essential. Thank you I realized that I have been having a 3 part response to my friends/colleagues. Understanding, debate, solution…

[@Akerfeldtfan]

The definition of your prior is SO important. In your case, I think there's a bit of a weak assumption with that .1% prior. Namely, it's .1% in, apparently, a random sample. But you, the sick person, are NOT a random person. You're a person with symptoms. So it would be more accurate to take into account not just the incidence in the overall population, but also the % of people with this set of symptoms that then get diagnosed with that particular disease. Much harder to estimate, of course, but also far more accurate imo.

[@nunocordeirodossantos5741]

IMHO I also believe that’s a fair assumption. However for pure mathematical explanation this example was ok.

[@ruukinen]

I assume if using this more "accurate" priori would only increase the chance after the first test by a percentage or lower it then there is no point in doing the more accurate priori. Just one iteration blows the accuracy in the assumptions out of the water.

[@shubhamsoni2058]

Veritasium should delete this

[@AmberPollard]

Thank you so much for saying this!!! I stopped the video after this analogy to try to figure out why the concluding percentage made sense, and I thought about it several times a day for 3 days because I couldn't understand how the .1% prior was the same as the person who showed symptoms.

[@LmaoOldAccount]

You would be right, except that in this hypothetical, the symptoms shown by you *are not specific to the disease*. They are general symptoms which could be caused by any number of diseases/conditions, or it might not even be a condition at all! So that's why it makes sense to still use the .1% prior. But I agree, people should definitely consider this in a real life situation. Figuring out those initial estimates is the hard part, and people should always be open to the possibility that they didn't consider something. I believe people can get better at this with experience.

[@jonwatte4293]

The 91% is only true if the second test is statistically independent. In practice, causes for false positives may be correlated, eg genetics or other factors triggering the indicator in the test, being tied to the person.

[@cartermcclung]

This is what I was thinking as well. A good simplification, but potentially troublesome under the wrong circumstances.

[@drewmandan]

This why it makes more sense for the verifying test to be of some other indicator. If you think about it, this is what differential diagnosis is! Don't just decide based on one symptom or test, but after running many different types of tests and ruling things out.

[@VSHEGDE1947]

Yea that's because he used the disease as an analogy for the theorem

[@zacedx]

same thoughts I had

[@feridbelgaid1946]

@@VSHEGDE1947 This is actually called Naive Bayes because it always assume independence between events

[@pcsecuritychannel]

Great video. This is the kind of content I love to see. I don't care about the editing or production quality, as about the depth of content, the concept, and how well it is explained. Keep it up, Derek.

[@tomservo75]

I thought the production quality was pretty good though :)

[@pierrecurie]

So much shaking, so much motion sickness. @___@

[@-Omega]

keep up the great videos leo!

[@slinkytreekreeper]

I'd rather see a go pro on a handheld gimbal than wobbly video and constant hand switching because it's too heavy. Great video content, lacking production for such a huge subscriber/Patreon base

[@dsshakespeare]

Please! Come on you shades, stop with the 'positive criticisms.' Great video; and, even greater delivery! In context there's outliers of course. Outcomes and conditional probabilities may very well depend on our behaviors; yes, but there's an aspects of culture, luck, and the lack of free will as well. Thanks...

[@RajParekh07]

I cannot believe how good Derek is. Putting perspective to so many things, I never thought it that way before. Kudos.

[@pukid]

It has recently occurred to me that the highest paid people in an organization tend to be those who attempt to ask and answer "what" and "when" questions (decisions), while all of the "how" and "who" questions (discovery) are delegated to subordinates, who are paid less. I've dedicated my career to being the most valuable team member by constantly proving that I can solve for "how", and I'm starting to wonder if I need to change course slightly. I've caught myself in a loop where I'm given positive feedback for being an excellent person to delegate to instead of showing that I can be a reliable decision maker, which is a path to a better financial position.

[@bashrath1]

my favourite genre of trap

[@HaydenLau.]

God of Shitposting It's only gay if you keep your eyes open :)

[@Razzileful]

it's only gay if their mother's maiden name begins with a c

[@ozi8226]

It's not gay if you say "no homo".

[@CosmicErrata]

Bae's theorem.

[@WobblyBits_X]

It's not gay unless you spread the truffle butter on your toast for breakfast.

[@LuciaFiero]

While I was recovering from cancer treatment my best friend died of cancer, while I was recovering from losing her, my mother died suddenly of cancer. Since my girlfriend's cancer came back 3 times before it killed her, I am haunted by the fear of recurrence, which has me stuck in a rut. My continuing weakness after treatment isn't helping. When I started watching you this month, your enthusiasm penetrated my gloom, but just barely. The more videos I watched the more of your "expect the best" pep talks I've found, this being the latest. I've made some plans this week for this coming winter and am resisting the thought that things will continue to go badly for me. I found myself Friday looking forward to something for the first time in a very long time. Today I invited friends to join me in my plans and they agreed. The nagging voice saying "it will all go wrong," is still there, but I've decided to just be happy that I felt a modicum of enthusiasm for the future for the first time in a very long time. I will keep you posted if you are interested in my anecdotal evidence.

[@nitinchaudhary8914]

How are you now? Hope you doing good.

[@morgothpt5737]

Please tell us, 2 years after, you're OK and happy... 🙂

[@saumyaranjan9256]

Waiting for an update.

[@LuciaFiero]

I wish I had better news to report. I have been in bed for the past few days feeling run down with a recurrent rash. Going to get a blood test to see if it's leukemia or something less serious. I rarely get out of the house anymore. And of course now because of COVID I am afraid to mix with crowds, because of my poor health. Which leads to feeling isolated, which leads to depression. Downward spiral since the COVID crisis started.

[@nitinchaudhary8914]

@@LuciaFiero my english isn't good, hope i am able to convey what i want to say. Don't overthink about your report now because doing that wont change report or anything and just dont worry about it your report will come fine only. And about loneliness and depression I really don't know what's the solution for it but I can tell one way to overcome depression, Atleast a little bit. See, Why we feel soemtimes more depressed than normally because we take a hell lot of stress on just too small things in life which are bad and just temporary like evrything else and if we try to do opposite that is try to enjoy those small things with a more happy heart and have more feeling of gratitude about every good thing which happens to us, wether big or small, i think that way we our mind will stay more cheered up. I hope this helps and also above these my prayers are with u, hope u will be totally happy and healthy soon.

[@krzysztofkosydar4545]

Absolutely great insights into the Bayesian theory. I really loved also your personal thoughts about how we may get used to the results and how we can change something. Really amazing.

[@lunickiwrites7256]

I come back to this video pretty much yearly at this point, and it's always a great reminder of updating my priors.

[@perniciouskitten]

just like Ronnie Coleman said “If you always do what you’ve always done..you’ll always get what you always got”

[@gvc76]

good one, but my inner nerd says that there is an element of randomness in everything, so in some cases you won't get what you always got :)

[@juansigales5645]

Like the great philosopher Jagger once said “You can’t always get what you want”

[@AgnideepSarkar90]

@@gvc76 yr inner nerd is linear

[@peterjansen7929]

That's what the man said before increasing his overdraft again …

[@tjdoss]

"Our actions play a role in determining outcomes and in determining how true things actually are" - well put.

[@timothytraveller9044]

Mind officially blown. The theorem is one thing, the explanation exceptional. Thanks for such a great way of putting it.

[@jaysharma5822]

That is a really cool video! Bayes theorem feels more intuitive now, and I'll try to apply it more often in day-to-day scenarios. Thank you so much dude!

[@tomservo75]

Nicely done, I use this example with my Statistics students often. You bring up a good point about the difficulty of assessing the prior probability. If our approach is that 0.1% of the population has the disease, and that's of the general population. But the general population is not being tested. We assume, don't we, that people are randomly tested whether they show symptoms or not, but in reality if you are tested then there's an increased likelihood that you have it, so the 0.1% might not apply to patients actually being tested.

[@assasin1992m]

Explain me this: We already knew at the first bayesian, that the patient had tested positive, the result was a 9% probability of the patient having the given illness. When the bayesian was updated with this "new" information, the probability jumped to 91% in favor of havingn the illness. But we already had the information, of being positive to begin with, how then can it show different probabilities (not to mention such a large difference)? What happens if we make the same test an infinite number of times, and update the bayesian an infinite number of times? There is seemingly never any new information present!!

[@distico]

The test is made by a different lab each time, so there is new information. Even it's done by the same lab, a new test always bears new information, since it's done at different times and because of random errors in testing.

[@KryzMasta]

weallbfree Remember: it's a thought experiment. The idea is to set the stage as clean as possible, without all sorts of extra information to contaminate the result. This is why he says "no particular symptoms". Also, this particular thought experiment is mostly used to explain to medical students what statistical reliability of tests really means, if you don't know anything else about the patient. This says something about the test, and particularly the statistics of it. But you do address an important problem with this thought experiment: some people actually use this kind of reasoning to doubt doctors. And then they've entirely missed the point.

[@ctwardy]

MP: I think you're asking why there is "motion" here at all. Start with the cleanest setup, where we imagine the patient is selected at random, and we imagine the tests happen in stages over time. Before taking the test, we ask the chance he has the disease. That would be the background rate, which is given as 0.1%, or 10 in 10,000. Then our patient tests positive on a 99% accurate test, and we ask again. Of an imagined 10,000 people tested, we'd expect to identify the 10 with the disease, and falsely tag 100 others. That's 110 positive results, of which only 10 have the disease: about 9%. At this point his chances are about 9%. We then get an *independent* test, also 99% accurate. Of the imagined 110 tested again, it tags all 10 with the disease, and 1 of the other 100. Now his chances are 10/11, or 91%. // // The math is the same if the tests happen simultaneously. What's important is the number of tests, their accuracy, and their independence. If 3 witnesses report an event, I'd take that as more credible than if only 2 or 1. But, not if all 3 are just repeating what they read in the newspaper: that's not 3 reports, it's 3 copies of 1 report. I'm now really sure what the paper said, but only as sure of the event as the paper is accurate.

[@bobbobby548]

Each test adds information with 99% certainty. Probabalistically, this is the definition of "adding new information"...

[@lauramarin7522]

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!

[@royalzarka241]

This is my favourite Veritasium video (my favourite video so far). I especially like the philosophical aspect discussed. The notion that just because something hasn't happened, it doesn't mean it won't or the idea that you must continue to re-evaluate your suppositions, especially related to matter of opinion. It's perfectly ok to allow prior results to dictate your insight into future results for things that are objective, but for matters of opinion, it is necessary to be aware that it is always possible that you do not have enough information to come to a conclusion. There is always the possibility that you may be wrong or at least not entirely correct.

[@nicholasbrunning]

Now imagine Bayesian thinking upon seeing several UFOS at once. 😂 That's a dragon of all priors.

[@shailendumohapatra4275]

Sir, the sheer amount of thought that you have put into this video tells me how deeply to have understood the theorem and how deeply you know yourself. Thank you sir.

[@777ElCazador]

Does anyone know where this was filmed? The location looks beautiful ANSWER: Turns out it's the Santa Monica Mountains near Los Angeles. Big thanks to Veritasium for answering!

[@derbistheeternal2947]

777ElCazador people are saying that it was filmed in southern California.

[@777ElCazador]

Thanks for the reply. I live in So Cal but it doesn't look familiar. If anyone knows of a more specific location it would be appreciated; I'd love to go hike there.

[@milanpatel5593]

Albertson Fire Road and Palo Comado Fire Road. Seems to be what most agree with

[@frankschneider6156]

Earth, solar system, milky way, local group, Laniakea supercluster No need to thank me.

[@danchisholm1]

777ElCazador I agree. We have had lots of rain which would make it green but the topology doesn't quite look right.

[@TheSaxRunner05]

Covid-19 is everywhere, youtube recommends me a video about math from 2017 ... but also about being testing positive for a disease.

[@michaelerhardt2549]

this is how it should be

[@domesticterrorist483]

Makes you wonder how many false positives for the CCP flu are occurring? I am still trying to get info on how accurate the test for the virus is. Anyone know? It certainly isn't better then 99 % especially if the test is made in China.

[@Eddison33]

@@domesticterrorist483 Cannot tell about everyone, but here, in Ukraine, any test samples (regardless of whether positive or negative) are transported by plane to a lab in London for verification. The statistics are updated from the data of that British lab. So, basically, there's a delay because of the means to make the test more reliable. I may guess it's a common practice and the developed countries do it much faster.

[@wolflordy3193]

@@domesticterrorist483 There are a lot of false positives. The exact amount is unknown. The reason being is that many tests are being done by swabs, which detect the presence of the virus. Whether that virus is alive enough to be active cannot be determined. And whether that virus actually infected you, versus just being on some mucus membrane and failed to permeate also cannot be determined. Combine that with how common the symptoms are, there are a ton of false positives. Luckily some areas are doing antibody tests, which also have not been reliably measured in terms of false positive rate, is expected to be fairly accurate. Even so... That doesn't mean our death count is anywhere near accurate. But that's a different story

[@ddrome15]

@@wolflordy3193 With the same logic, there have been a large amount of false negatives since the percentage of infected is still low.

[@angeloperezceo8101]

Your a blessing to this universe. The world won't not have been the same without you. I appreciate everything and anything you create.

[@Eric-cj7qn]

Came here to study Bayesian Updating for my university's Finance exam and I just love the reflection on the theorem and how you link it to a broader context!

[@johnshaff]

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

[@carrielynn808]

The application of Bayes Theorem to argumentation and philosophy is so intuitively perfect. I love the connection you made with your analogy and the idea that expecting the same results will, in fact, affect your experiment / measurement / argument.

[@stevencooke6451]

I feel it links to that human tendency to use confirmation bias to "prove" that many things cannot change.

[@souravsarkar7605]

Just an excellent piece of work !! These 10 minutes video may have taken 10 years of internalisation of the theorem!!

[@NZL50505]

Very good. One of the best explanations of how Bayes can be applied to both hard statistical analysis and day-to-day discussion.

[@myself915]

Literally learning this in high school right now, except they just tell me the formula and how to use it, but not anything about where it comes from or why it makes sense. I think this video really improved my understanding of this, so thanks for that!

[@canesvenatici9588]

Dislikes from 9% of people who actually got the disease after being diagnosed positive on the test.

[@AgnideepSarkar90]

only 1.3k pple now., one yr later cant judge the probability of having covid just by seeing dislikes , ha

[@irinejpapuga]

Thank you for this video 🙏, it is to the point. No college professor ever explained it to me in such straightforward and clear way. You' the best!

[@bhaskary2362]

This is the best video ever made on Bayes' theorem. I keep coming back to it every time i forget the intuition behind it :")

[@eeriksp]

Wonderful! Really nice how you connect the world of logic with the wider philosophy and make it actually useful in life outside the abstract math realm.

[@christiancamilootero8944]

I love the way he turned a beautiful mathematical expression into a great motivational video

[@mithrandirthegrey7644]

I remember taking a Bayesian Stats class in college my senior year and it just blew my mind. Loved that class. Though I never ended up using what I learned it has always been in the back of my mind when reading any statistic.

[@cola-z9219]

Your optimism is contagious

[@jiteshjangid369]

Man i think you should start a podcast.You talk really well. Thank you.

[@nybcp]

100%

[@dukeofworcestershire7042]

@@nybcp Better not debate with you

[@LiamInviteMelonTee]

Come on @veritasium , you just said experimentation is essential

[@sanjj_1]

@@dukeofworcestershire7042 i dont get it

[@dukeofworcestershire7042]

@@sanjj_1 Looking back on my comment, I don't either.

[@pratishthar1202]

This wasn't just interesting, with a lot that has happened with me, I needed to think about this. Thank you so much for being this amazing person who gives out information and insight so wonderfully.

[@TIGNOBB]

Your perspective of life honestly is amusing to me and it actually enhances my senses...brings me back to focus.

[@Ryan-gx4ce]

This is my favorite veritasium video. Come back to this all the time.

[@himanshubhoria1832]

This question came in my exam yesterday. I had watched this video and I'm really thankful to you Derek

[@Brunoenribeiro]

begins with a math question ends with life advice i love this channel

[@eddieb8615]

Thank you so much for your videos.. Really connected to this one on some personal levels. Just been feeling so discouraged lately, but I can see how my internal Bayesian calculator could be contributing to my hopeless feelings. Trying new things right now!

[@Paroxysm80]

Just randomly came across this, and I can't applaud you enough for this vid! It made learning about and comprehending Bayes' Theorem so interesting :)

[@UnwantedCommentary]

Here I was thinking this would go into the Machine Learning uses, but instead you brought up some insightful philosophy. You rock!

[@CharlesCarlsonC3]

This is turned out to be really important show in retrospect! Thanks!

[@vantablack7512]

Been not wanting to upgrade or update anything that I own because it costs money. I don't want to become someone that's afraid to try things. I needed to hear this. Thank you.

[@dodikynawollen5599]

I love how you explain things! Makes it easy to understand.

[@guillaumelafleche9477]

Thank goodness for thinkers, the world needs more of them.

[@CombraStudios]

We know thinkers are useless when those who should listen don't

[@mickeymac132]

That helped me in a weirdly spiritual way. Good info, thanks for explaining that so cleanly for us

[@VdonnyV]

Amazing material as always. You have no idea how much time you are sparing me with all your great explanation made out of perfect analogie! Simply Bravo, Derek 👏 👏 👏

[@magicalmusic882]

I love this video as an example of how maths is a tool and can assist with understanding the world, but this adaptation of how Bayes theorem can be applied is truly inspirational! You really can change the world if you change your perception of it and your potential capabilities that you have never dreamed of tapping into! Unthought known...

[@percheronphenom]

So that was basically an understandable scientist doing a subtle life coaching on all of us who watched, while strolling up & down some nice landscape I think we need more of that :) !!!

[@nixp]

I had heard about "Bayesian probability" and felt like learning more about it, as I know nothing about it. The conclusion you draw at the end is about getting accustomed to results like rejection, which is something I have often dealt with and felt bad about. It gave me a new perspective on things. I think you are an amazing speaker and have a great way of getting worthwhile ideas across. All the best.

[@CAT15407]

This is very helpful for my upcoming business analytics midterm for my MBA program next week. Keep up the good work.

[@JLP4444]

The most interesting part of this is how obvious and intuitive it becomes once the terms are clearly defined and a representative sample is used rather than an abstract formula.

[@alonsos3382]

I had never seen such a good explanation! I wish my professor was like this

[@manasisnehal1572]

Felt very nice when you asked at the end "is there anything like that you're thinking about? " :)

[@JohnByrneAus]

Thank you for this video. This was a gift and a reminder for me that things don't always have to be as I experience them to be right now. Thank you!

[@lukasklupfel2927]

Your videos should be part of school curriculum all over the world. This sparks so much joy of thinking inside of me. Your channel is truly refreshing and imo the best all around science channel on KZbin. Entertaining, informative, (thought) provocative and extremely well researched, and I always leave with an enlightened feeling. Thank you guys for your work and passion, it shows in your content and has truly changed my perspective on the world. Greetings from Germany :) PS: Would you do something on the LHC Cern?

[@dddmemaybe]

I like the thought "Set a Precedence" for this video. A precedence for existences, to break illogical 100%'s and give way to constructiveness. Let go of one hundred and find twenty-five fifties.

[@SantiagoAbud]

Yo', 7 years later, I am learning about Bayes Theorem in college. And this hits so hard.

[@pedrol.mammini4940]

I love how this just fits perfectly after studying Hume, I researched for a bit and discovered this paper was written a little bit after Hume's Induction Problem. Very nice!

[@mibeseev]

Pease keep doing your fantastic job. I know: You only explain what others found. But you do it in such a great way that this deserves credit from all of us.

[@tdcsguy]

1:49 It usually doesn't get emphasized enough how hard it is to get a good prior. For instance, Derek's prior of just taking the incidence in the general population is probably already invalid. Why? Well, you show the symptoms of the disease, that means you are already far more likely to have the disease than joe everyman next to you. Why is this an issue? Well, Bayes' theorem is really good at showing you the highly counterintuitive odds of something being true, you just need to know the priors. And that is a huge wild card, everything stands and falls with the prior. You can use highly biased priors to "prove" your point, you just need to convince your audience that these priors are valid (and to some extent, Derek already did this by convincingly endorsing a likely inaccurate prior). You could argue, for instance, that human made climate change is a myth even though we have strong evidence to suggest so. You could just say, well what are the odds that us tiny puny humans can have an impact on the global scale evironment? It's infinitesimal! Just look at the size of our planet! It's HUGE! So let's just input prior p=10^-13 or something (weight of all humans / weight of the earth). I know, it's ludicrous, but try arguing against that in front of a crowd that doesn't understand the intricate details of Bayes' theorem. That notwithstanding, Bayes is great, and it is superior to standard frequentist statistics when used correctly. However, I feel the potential to "cheat with statistics" is also far more severe with Bayes. It doesn't solve all our problems. tldr: Always check if the prior is valid! Edit: spelling

[@danmcann94]

That was an excellent and insightful comment. Thank you dear! I definitely learned something.

[@cleanseroftheworld]

Marc Züst My problem is that you had no particular symptoms. If it was a bad cough or runny nose, that would be palpable evidence of a sickness, but since the only symptoms are the person being "under the weather," this is much harder to theorize as feeling bad could simply be due to stress or something else not involving a disease at all. It is possible for joe everyman to be a part of this test because the "symptom" is so vague and common that the only way to have any sort of certainty whether or not the average man has it is by testing everybody with the symptom, unless they have an allotted disease, which still requires testing. tl;dr the vagueness of the illness allows a general population prior to be plausible.

[@austindrapen8959]

just commenting because I want to insure this stays up if Derek won't pin it.

[@LowPriceEdition]

I'm not sure but I think this describes the problem I've had with describing to some friend, many of wich are graduates in highly scientific fields, the error of using general statistics around the controversial DAPL. I've had a lot of statistics for failure of pipelines in general thrown at me as proof of DAPL being unsafe but it doesn't take into account the vast array of knowns that would dramatically alter the specific probability of failure once you've selected DAPL specifically. For instance basic things like failure rates and modes for above ground vs below ground etc...

[@wobblysauce]

+

[@charlesbukenya2054]

Just beautifully said. You've earned a sub.

[@catet_al_quadrat]

Possibly the best video on the internet 👏. Mathematically interesting but beautiful and creative at the same time 💚

[@nicholasparliament4648]

as a med student this is one of the best explanations of Bayes theorem ive heard and is so central to how we should think about testing in medicine.

[@moonspear]

By the way Derek, with respect to your medical test analogy, the application of Baye's theorem to the second test is not without complications. Most of the time in the medical field, a false positive is not completely based on chance, but rather, the presence or absence of physiologic variations that trigger a positive test result in the absence of the disease in question. So regardless of whether or not a patient has a disease, a second test measuring the same biologic marker, phenomena, etc. will more likely than not yield the same result, as the thing being measured likely does not fluctuate much (for if it did fluctuate a lot, it would not be used by the medical field as a test for anything, as it would be too unreliable). The only time you could apply Baye's theorem to a second test in a medical context would be if you used a different test for the disease that measured a completely different pathway or in a totally different manner from the first test.

[@danielearwicker]

Moonspear true. This is similar to the mistake of thinking that the second time a couple has twins it must be extremely unlikely, whereas in fact some couples have a greater propensity of having twins and so the first set is an indicator that they are more likely to have another set. They are not independent probabilities.

[@nb8947]

Great point. I always bring this up when people say the ban on homosexual men donating blood is prejudice. What people think is a great screen can give bad blood the all clear multiple times. The only way to make a real dent in contamination is removing high risk people from the pool.

[@andymcl92]

This is a good point. He does mention the test being run by a different lab, but I guess going in to that aspect of probabilities would have taken a bit too long to explain properly, and may have just taken away from the point that your positive test for a rare disease may not be quite as bad as you think.

[@muhamadhamdy6576]

Such examples are common in any probability course, and are only examples. They usually go along the lines, "a medical test is used to measure a certain disease, if there is x% random factor in the measurement then determine....", but the random factor part is cut to make it simpler for beginners. So yeah, the measurement is of course not completely random but involves a random factor.

[@ProfessorPolitics]

Moonspear This was fascinating to read, thank you for your insight!

[@Sypower94]

Great video. Nice scenery, interesting ideas, well-spoken individual. Thanks Derek :)

[@nakulraj5642]

Thank you. Bayes theorem is a life changing theorem and you explained it very good. Thank you once again.

[@bjornlindrooth9886]

I wish the world were run by people like you instead of politicians. Always enjoyable and enlightening to watch your videos. Keep up the good work.

[@ayushkastruggle3572]

Conclusion: Get tests done twice

[@ChilloutLibrary]

This man predicted covid 😷

[@snippletrap]

How many Covid "cases" are based on a single positive test?

[@robertjarman3703]

@@snippletrap Not many. COVID-19 tests aren't as much about knowing who needs treatment like who needs to go to the hospital right now. It's about the epidemiological spread of the disease, especially by people who don't know they have the virus, both asymptomatic people, people who are not sick yet but will but don't have symptoms, and those who will never have symptoms and never have had symptoms but can also spread the disease, and also those who have minor symptoms that could also easily be thought to be something much less spreadable like just a typical runny nose for a few days. A COVID-19 test of course also helps doctors with those actually sick, they know more specifically what they face and what to give the patient, but it's not as relevant as the other three categories for the spread of the disease. Given the costs are low in most cases, especially in countries with good benefit programs to help protect people in this situation like great sick leave, staying home for 14 days, probably taking a second test to confirm results and staying home the rest of the time, is fairly simple, although annoying.

[@jojor1312]

@@robertjarman3703 if the testing has a 70% sensitivity and 95% specificity (which is about avg for such tests, iirc) and assuming that 5% of the general population are asymptomatic carriers, applying the concepts in this vid would suggest that a person testing positive has a 58% chance of actually being ok (ie uninfected). Imagine the consequences of wide-spread testing of asymptomatic persons in relation to quarantining, contact-tracing, stress for the individual, etc given that there is a greater likelihood that they would not have covid when testing positive....

[@robertjarman3703]

@@jojor1312 We don't know much about the virus to begin with and our tests aren't designed to match it that well compared to a disease we've known for decades. We can't make many assumptions about what it can and can't do. Ergo: we do still need to test a lot. A second test will do better. In fact: we could do two tests administered by two different people and assessed by different labs at the same time.

[@Actanonverba01]

This is one of the most straightforward explanations of Bayes Theorem I've seen. 'No mucking about just got to the point.

[@upsteer1]

When I see a Jeremy Clarkson inspired comment, I hit like.

[@luismatos684]

Great explanation. Helps me see life from a different perspective. We reason and conclude with probabilities as our certainty. CHANGE is the only certainty.

[@A_ghost_afraid_of_itself]

This is kinda the therapy my brain needs and it made me cry. It gives me hope. Thank you!

[@akashdtx]

There Derek does it again, first in the 'learned helplessness' video and now here. The quote is - “It always seems impossible until it's done.” - Nelson Mandela. // Just Messing around.... another cheerful video that made my day. Thanks.

[@kalebbruwer]

Akash Sahoo // Did you comment that out?

[@mjtsquared]

he forgot a ;

[@TheSam1902]

The turkey found that, on his first morning at the turkey farm, he was fed at 9 a.m. Being a good inductivist turkey he did not jump to conclusions. He waited until he collected a large number of observations that he was fed at 9 a.m. and made these observations under a wide range of circumstances, on Wednesdays, on Thursdays, on cold days, on warm days. Each day he added another observation statement to his list. Finally he was satisfied that he had collected a number of observation statements to inductively infer that “I am always fed at 9 a.m.”. However on the morning of Christmas eve he was not fed but instead had his throat cut. It doesn’t matter how many cases we list during our inductivist reasoning, nothing guarantees that the next case will lay in this inference we deducted from our observations, as the possible experiments and observations are infinite by number and type. That's Russell's Inductivist Turkey

[@laurynaslubys5845]

You forgot probability of turkey being eaten.

[@mikeharrington5593]

Samuel Prevost Probability overridden by infinite timeless variability?

[@slinkytreekreeper]

Impressive Turkey that can tell the time

[@grahamlyons8522]

Hume's theory.

[@grahamlyons8522]

LL Why else would the turkey have her throat cut?

[@randymartin9040]

Your videos regularly blow my mind. Thank you for your channel, thanks so much!

[@michaelraemisch1605]

Great 10 min! Absolutely love the life interpretation from about min 7 on! Keep your beliefs flexible!