Bayes' Theorem - Explained Like You're Five
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- Опубликовано: 11 сен 2024
- This video summarizes my (apparently helpful) answer to someone's question about Bayes' Theorem on Reddit's "Explain Like I'm Five" forum.
Bayes' Theorem allows you to look at an event that has already happened and make an educated guess about the chain of events that may have led up to that event.
You might have to pause the video in places since there is a lot of math squeezed into 9 minutes.
I'm happy to answer specific questions if you put them in the comments. If you need more help, I offer tutoring over Skype!
Can you do a video and explain it like I'm 3?
In the womb*
*male gamete
Lol
hahahahahahahahahahahahahahahahahahaha
I must be a very smart 5 year old to know about politics, taxes, elections etc lol
Thanks! I really really appreciate it. I read a whole book years based on Bayes' Theory, called The End of the World by John Leslie, one of my favorite books, but never felt confident about the math past. I'm so happy now. I feel like a gigantic weight has been lifted. I'm so happy. It was just the right speed. Thanks!!
Glad it helped!
Thank you so much for this! I'm a graduate student who has alway struggled with this kind of inference, and I finally get the fundamentals now. There are not enough thumbs up to express your awesomeness!
The video is not for five year-olds, but great presentation for a quick understanding for Bayes' Theorem.
I didn't anticipate actual five-year-olds watching it. I wrote the example for the ELI5 subreddit, but perhaps something like "A nontechnical explanation of Bayes' Theorem" would be a more appropriate title.
Dana Scheider agree with you..
Some slides left on screen for far too short a period - before they could be read in a few instances.
+Dana Scheider That it would.....
+Gilbert MacKay there is something called "pause/stop" button in youtube. Seems you are 4 :P
I wonder what people are complaining about here. This is the best explanation I have seen so far. Most textbooks I have seen don't even use numbers let alone explain. Although the "5 year old..." is kind of offline". Thanks Amelia.
..pffft!..Even for a 5 year old,your explanation is way too complicated:Can you explain it... like I'm a Fetus please?
I am for ever confused by Bayesianism and its subtleties. If this explanation is for five yo then I think I need one for a self replicating molecule............as in, please start real simple like for me.
lmfao 😂😂😂
Lol 😂😂
I don't know why everyone in the comments is complaining... I found this video very useful and very easy to understand! Thank you!
If a 5 year old gets that and I have no idea what she's talking about I must be dumb!
Chris Saunders
No, you re not. It s just that you don t have 5 years old, if you had you would have undertood that.
Wow, thank you so much! I'm studying for the GRE, and this video just shed more light on math for me than the many years of instruction. You should start a "Math like you're 5" channel, I'd watch! Thanks again, I like math a little better today.
Very easy and lucid explanation of Bayes Theorem. I had a lingering thought that there was something missing in my understanding but this video has changed the thought. Thank you!
it is a great example. Thank you for taking the time to share this with us. ignore the negative comments from others. most people who need to know this should understand the context of election, parties and tax cuts etc
This is the best explanation of any mathematical theory that I've ever heard. Really helpful for my reliability engineering exam. Thanks!
THANK YOU SO MUCH!!! I will literally be passing my first Probability exam because of this video!!! You disarmed this so well!!! Thank you!!
Btw ignore the "it's not for five year olds" comments; the magnitude of your explanation is equivalent!
You are AMAZING.
No one ever drew it out like this, everyone kept doing the Venn diagrams or writing out which part was needed but I think this helped me out a ton
Thank you so much, I have spent 9 hours struggling with someone else' explanation of Bayes theorem, I wish I'd watched yours first!!
lol "Explained like you're five", I was like 'yep, that's what I need'
the intro was the craziest whiplash ive ever had
Man this is intended for some seriously bright 5 year olds! But seriously, pretty great explanation. I only have a weak grasp of probabilities and statistics, but was able to follow pretty well. Cheers.
Wonderful video. I spent an incredibly long time searching youtube for an intuitive, concise answer. Much thanks.
I think had the title not mentioned a 5 year old this would have been far more to the point! Let’s face it - there’s no way one can try this on a 5 year old literally. But the spirit and the effort behind the video must be applauded. And it has garnered close to half a million views - working backwards in the spirit of Bayes p(video is good | it has garnered half million views) is clearly more “credible” than just p(video is good) 😊
I know I said this before but, this video is awesome and I thank God for you and this video. I had to do some much-needed review for an upcoming test and I was getting confused all over again. This is the only video so far which explains in layman's terms what the Bay-T is all about. Other videos are good at explaining the formula (and so is this one, btw) but I have yet to see anyone else explain the LOGIC behind the formula as succinctly as you do. Most of them explain the logic in pure Math Speak, even the ones who pride themselves on being easy for everybody. You explain the logic in plain English instead of MathSpeak and now I understand it. Don't ever take this down. You are a Godsend, mi reina XD
Very worthy thing to watch when you're procrastinating. Thanks Dana!
i have watched a few videos now without really understanding the theorem. After watching this, I now understand it.. i liked your example
I normally don't comment on you tube...but this helps tremendously
I think this is a fantastic presentation that most people can relate to. WAY TO GO
Math AND Politics?!?!?!?! Could she have made it anymore confusing?
Wow. Way to make people regret taking the trouble of explaining something to you, comment section.
Thank you, Dana. I am trying to wrap my head around a number of Theorems and statistical models and your explanation was very helpful.
That was exactly what I was searching for for a quick brush up on Bayes! Thank you!
This is the best explanation I've found of all the explanations I've seen. Thank you!!!
Wish you have used a better example for explanation..... after watching this the only thing i understood is how American politics work.
A really easy and one of the best ways to explain the Bayes theorem. Thanks Dana
Finally!!! A useful explanation.
Thank you!
Finally a clear description of Bayes theorem
I love this video and will go back to it again and again as a person learning this again after 30 plus year break. Please do more statistical videos for five year olds...
Statistical 'data' is often skewed, or simply includes that data which one would like reflected once it is collected, analyzed and finally presented as 'information'. Data (raw figures) > process > (usable) Information.
You cannot use a theory like this to determine outcome probability when you are basing the data on subjective information. It works as intended when the data is 'objective' and not 'subjective'; without bias.
Objective vs Subjective:
An objective perspective is one that is not influenced by emotions, opinions, or personal feelings - it is a perspective based in fact, in things quantifiable and measurable (in this case perhaps polls when concerned only with the numbers yielded by the polls and not the questions; still not reliable).
A subjective perspective is one open to greater interpretation based on personal feeling, emotion, aesthetics, in this case politics, etc., which are subject to volatile change by any number of factors (sickness, weather, personal perspective (aesthetics), monetary gain or loss, change in relationship).
this was EXACTLY what I needed to understand Bayes formula! TY :)
Why am I so dumb?????????????
+Aldora LaPlume Your'e already better than the majority of people as you are aware of your weakness :D
+Aldora LaPlume statistics is so confusing!
+Aldora LaPlume Because you are female.
+Jim Bob You are a bully. Stop being a bad person.
Erin Wolpert I'm not a bully. I am not a bad person. Your opinion does not count.
Dana, GREAT explanations!! I am taking a "Math for Data Sciences" class and have been flying through it until the final week and "Bayes Theorem". Achk...... It was poorly explained and very confusing. I was going to drop the class as I just couldn't get it. After watching your RUclips explanation I am excited about the possibilities and understand the way it works - cool stuff! Thank you for all you do!!!
PS I sing as a Tenor1 in a church choir. I'd love to hear you sing and check out your voice related vids. Thanks Again
Best Bayes' Theorem Introduction on RUclips.
Excellent explanation/clarification of a complex theorem!
Hello Sir, How are you? How is enjoying my RUclips channel? Thanks Sayed Hossain
SO HELPFUL! Thank you so much. This gave a much more helpful explanation that my professor and textbook! :)
I think its a very simple explanation for BT, but people watching this video should know what "probability trees" are before hand, otherwise they are going to be very confused with numbers and terminology used on this Video, let me try to help a little bit:
The formula:
P(A|B)=[P(B|A)*P(A)]/P(B)
The "|" in the formula can be read as "given that", i.e. P(A|B) can be read as "the probability of A being true, given that B is true". P(A) is read as Probability of event A.
The question:
We want to know which candidate from either Parties was elected, given that the taxes were cut for business.
In other words, we want to know P(D|a) and P(R|a), and compare them to know which candidate was more likely to win.
Elected President:
This part refers to the probability that either party's candidate was elected
P(R)= 0.5
This can also be interpreted as "P of D not being elected" or P(ND)
P(D)=0.5
This can also be interpreted as "P of R not being elected" or P(NR)
This two P's should be the ramifications of the first node.
Taxes for business were cut:
Then we have the probabilities of "cutting taxes to business" by either candidates, in the video "a" represents the probability of cutting taxes, and a' represents the probability of not cutting taxes, this can also be represented by a YC and NC respectively, if it makes it easier for you, just remember that YC is the same as P(a|D or R). This probabilities should be ramifications of the previous ones, being "the second nodes".
So we can put them in order
YC given that D: =.25
NC given that D= 0.75
YC given that R =0.5
NC given that R= 0.15
The "tree":
I can't draw a tree here, But I will simplify it with a list.
N1.1: P(D)=0.5
N2.1: YC=0.25 (represented as P(a|D))
N2.2: NC=0.75 (Represented as P(a'|D))
N1.2: P(R)=0.5
N2.1: YC=0.85 (represented as P(a|R))
N2.2: NC=0.15 (Represented as P(a'|R))
The "paths":
This can be useful to visualize the elements of the bayes equation, the paths are multiplications of first nodes with the second nodes, as follows:
Path 1= P(D)*P(a|D); (N1.1*N2.1); "P1=P(D)=0.5 *"YC=0.25 {P(a|D)}"; P1=0.5 *0.25; P1=0.125
Path 2= P(D)*P(a'|D); (N1.1*N2.2); "P2=P(D)=0.5 * NC=0.75 {P(a'|D)}"; P2=0.5 X 0.75; P2= 0.375
Path 3= P(R)*P(a|R); (N1.2*N2.1); "P3=P(R)=0.5* YC=0.85 {P(a|R)}"; P3=0.5*0.85; P3=0.425
Path 4= P(R)*P(a'|R); (N1.2*N2.2); "P4=P(R)=0.5*NC=0.15{P(a'|R)}"; P3=0.5*0.15; P4=0.075
Solving the problem:
We make our formulae
P(R|a)=[P(a|R)*P(R)]/P(a)
P(D|a)=[P(a|D)*P(D)]/P(a)
Search for the elements of the formulae:
We already know P(R) and P(a|R) from the tree, but we dont know P(a). To know P(a) we can check the paths that end up with "cutting taxes" and add them. In other words we check for the paths that have the elements P(a|R) and P(a|D), namely the results of Path 1 and Path 3.
P(a)=P1+P3; P(a)=0.125+0.425; P(a)=0.55
We are now ready to replace values in the formulae:
P(R|a)=(0.85*0.5)/0.55
P(R|a)=0.772 or 77.2%
P(D|a)=(0.5*0.25)/0.55
P(D|a)=0.22 or 22%
Conclusion:
We can see that it is more likely that the president is republican, given that the taxes were cut for business.
Solving from Paths:
We know that P(a) is the result of the sum of P1 and P3 [P(D)*P(a|D) + P(R)*P(a|R)], we also know that P1= P(D)*P(a|D), so we can replace this elements in the formulae:
P(R|a)=[P(a|R)*P(R)]/P(a) is the same as P(R|a)=P3/(P1+P3)
0.425/(0.125+0.425)= 0.772 or 77.2%
P(D|a)=[P(a|D)*P(D)]/P(a) is the same as P(D|a)= P1/(P1+P3)
0.125/(0.125+0.425)= 0.22 or 22%
I'm not sure if it's because I have a cognitive disability, but I had a relatively good concept of Bayes Thereom and now I'm just stressed out and confused. This isn't 'explain to me like I'm five', this is 'explain to me like I'm relatively accustomed to maths above the 9th grade level, understand politics in any capacity, can keep track of a sudden, massive influx of extraneous information that is poorly elaborated in one medium or another (either the slideshow or your description), and do not experience any cognitive issue that would make attempting to both read a slideshow and listen to someone who is speaking in a manner that is completely disregarding the slide being presented a problem'.
I had to stop watching because I thought I was going to cry. I don't normally have trouble digesting complex concepts very quickly, so it's definitely how it was laid out. Mostly it just made me feel like I'm five, and I didn't really learn anything except how much I don't like myself.
I don't get whiny bitches like ***** on RUclips. If you didn't like the video, move on to the next one, or downvote it. Why do you have to whine?So you have a cognitive disability, does that mean every video on here has to cater to your specific disability? Stop being such a runt!
@@poloandscotch shut up dude
Well put, and easy to understand. Thumbs up for such a helpful video!
I am not sure that I can do the math right this minute, but I do have a better explanation of the reason for doing these problems based on your example. Thank you for posting this.
I'm five and a half years old. I still don't get it.
That's odd. At least you spell better than a lot of college graduates.
Im Fore years old and I am undtestand
Thank you Dana. Your teaching skills are top notch.
@sirKr0n0 Thanks for watching! I'm so glad it was helpful!
@Dana Scheider : Thanks a lot Dana, Bayes theorem was becoming slightly clumsy but you explained it in such lucid fashion and in such a step by step fashion that it is "Crystal Clear" now. Appreciate your effort and heartfelt thanks
omg thank you so much!!! such a cool theorem and i wouldnt have discovered how interesting it is if it werent for your clear explanation
I dont think a 5 year old knows what a democrat and republican are, just saying. Great video though, helped me understand it
I think this is the first time someone explained to me with "The outcome is already known." Oh....that makes more sense.
Thank you, this was very helpful! I'm glad I found this video because I have an AP Stats test tomorrow over probability :S and this really clarified Bayes' Rule
How would a five year old know the political system?
+amphibianvoice "Explained Like You're Five" is the name of the subreddit; it does not imply that Bayes' Theorem, which is explained in a simple format here, could in-fact be understood by five year olds.
very easily explained. i spent the entire day on bayes theorm and at the end I found this and yaaaaay! i get the sense of this theorem :)..
Incredibly thorough and helpful. Only wish I would have seen it BEFORE my quiz haha cheers.
This explains everything BUT the Bayes' Theorem... Everyone explains the theorem like you do: Here is the formula, sub in the stuff. It will be great to re-do the video, explaining the intuition behind the reason why you need to multiply P(a|D) [in order to find out P(D|a) for example], by P(D) and divide by P(a)? I think that's the hard part for most people. Not substituting numbers.
Thank you! This is exactly my problem and I have yet to find someone who can do this for me -_-
Awe Awe
I agree very much. I also feel that making P(R) = P(D) = 0.5 simplifies the situation to an extent that the finer point of Bayes' Theorem is missed. Under those conditions, having 0.85 and 0.25 as the chances for either president doing a suffices to calculate the chance of having P(D|a) and P(R|a).
Agreed! The problem is: we want to understand the reasoning behind the Bayes formula.
do you got any good explanation? Thanks in advance
She did an excellent job. Now people use your brain along with her example and a venn diagram.
After all this is all about conditional probability where you have the intersection of two events.
Eccentric but creative example. You could have flipped the tree, but well laid out overall. Thanks. I may use this in my classes.
That was a great example and it was also explained very clearly. Thanks for your time and trouble in doing that, as it helped me a lot.
Thanks! Much better than way too many mumbo jumbo videos out there. This was quite clear.
Yeah you should start a math like you're 5 channel!
Also the explanation was at just the right speed.
Hi Dana,
this was really great. I am going to adapt this for my UK students. Well done for such an informative and well presented vid
Thank you! I used the info you gave for my class project! Hope the professor likes it as well :)
THANK YOU FOR THIS! Subscribed :) I'm a first year music student and your diction videos are also very helpful!
Thank you! This is exactly what I needed for my Machine Learning course
Best video on Bayes' Theorem. Bravo!
Great VIDEO!!! Love that it was made cause of the subreddit, Keep it up!
This is a great explanation! The mathematics of bayes' theorem is really simple but I struggled to get the intuition.
I like it, because it gives me the exact math I need to write in my C++ application. :)
Thanks for sharing that video... It helped me to understand Bayes theorem or the reason why it is famous. Thanks once again.
I wouldn't necessarily explain politics to a five-year-old. Perhaps a more accessible example would be:
Jim doesn't like Apples, they often make him sick. One day, Jim picked a random piece of fruit from his fruit bowl and ate it. The probability of him picking an apple [P(A)] is 20%. If he eats the apple, his chance of being sick [P(S | A)] is 90%. Without eating an apple his chance of being sick [P(S | A')] is 5%. You visit Jim the next day to find him being sick, what is the probability that he picked an apple from his fruit bowl given that he is sick today [P(A | S)]?
Very easy to understand (albeit it was made easier to understand because I had watched the first 15 minutes of Bayesian statistics made (as) simple (as possible)). Thanks.
you think a 5 year old knows what taxes and elections and democrats and republicans are?
Unfortunately, this isn't Bayes Theorem. What was demonstrated was a very good explanation of conditional probability.
I think if you wanna work backwards from B.T.... that's the formula you would use... or isn't it?
Thanks for pointing this out. Care to elaborate?
good explanation with politics example. i struggled a lot to understand the bayes theorem but here got idea. thanks a lot
I really liked the example and the explanation, but I think the slides are moving too fast and not synchronous. If you can improve that, this might be one of the most useful explanations of Bayes Theorem on RUclips. Thanks for doing this! :)
thanks for the video, it is clear and easy to understand , but would also want to know how the Bayes equation comes
Can you break out all of the various formulas for finding the missing probability when you have different pieces of information?
Awesome explanation...very well broken down..thank you
the rage is strong in this one, grasshopper.
Honestly..... It's still better than my professor's explanation of it
Very helpful.Please do other videos like this.
Excellent example! Thanks for making this video. Very helpful!!
This is a video for a 5-year-old _who took Statistics in college._ According to Bayes' theorem, how many possible universes contain people who fit those parameters? :-)
We need more singers with an understanding of Bayes Theorem.
Very helpful, thanks! How do you use this to make a prediction (e.g., how Nate Silver used Bayes to predict the last election by aggregating polls)?
Dana, I appreciate this very much. I am currently doing a probability/statistics course at university and the way you explained this helped me understand things better. Could you do a video on probability using permutations and combinations.
Great video. After tho I went back to the penultimate screens so I could in my head plug in the actual values to see if I could intuit why it was that I am starting with the opposite conditional, multiplying it by the totals probability of one condition, then dviding by the total probability of the other condition.
If you ever make any edits, you should consider stepwise swapping the three symbols for the actual numbers during the video itself. Otherwise great vid, thank you
This comic is very a propos. xkcd.com/1364/
The P(a) = 0.475 + 0.125 at 3.54 is wrong, it should be P(a) = 0.425 + 0.125 (which it later is, but it can be a bit confusing if you tries to follow it as you go).
+Michael Ståhl wrong
Thanks a lot Dana, Bayes theorem was becoming slightly clumsy but you explained it in such lucid fashion and in such a step by step fashion that it is "Crystal Clear" now. Appreciate your effort and heartfelt thanks
Your scenario is so relevant now. How did you know what's coming lol
Doubt a 5yo would get that, but the explanation was great, thank you! How to you feel about Bayesian statistics applied to natural sciences (with null hypothesis significance testing)?
You're incredibly clear in this description. Thanks!
@anvilmaths Thanks! I take requests too so if there's anything else you think could use a similar explanation let me know!
Intuitive and illustrative, great video!
crock1255 - for some reason RUclips wouldn't let me reply to you directly (nor would it let me upvote your comment after I accidentally downvoted it - sorry). The reason your book uses a summation is because the general form includes situations where there are multiple cases. I only talked about two cases - Democrat or Republican - so the single denominator WAS the summation.
Great video, thanks a lot! :) Made me love the Bayes theorem actually
Thank you! Can you tell me why we divide by P(a) to get P(D|a)? I don't get that part.
an honest question- if such a common sense conclusion could have been made without all the math, and the numbers were basically estimates pulled out of thin air anyways, then what exactly does the theorem do for us?
Bayes theorem very often shows us that reality goes against common sense more than you'd think. Look up more examples and experiments. You will be surprised.
She only used an example with a common sense conclusion so that it was easy for the viewer to digest. Bayes' Theorem has real-world applications when you're dealing with probabilities that are based on good evidence, and the conclusions are not obvious.
I know this is 7 months ago, but I happened to come across your comment. I think Dana did a great job explaining the concept, but she picked out a poor example. The 77% to 85% is simply not enough to see a difference. Here's a fairly common example as explained in medicine.
Suppose you know 1% of the population has a disease. You take a test that states it has a 1% false positive rate. That means that 99% of the time, the test is correct and provides a positive when you have the disease, and 99% of the time, the test will be negative if you do not have the disease. Well, if you calculate it all out based on the video, you'll see that your chance of having that disease is really only 50% still. The main point of the theorem is to show that the prior possibilities have an enormous effect on the actual result regardless of any tests/observations. Hope this helps!