Bayes' Theorem - The Simplest Case
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- Опубликовано: 10 июн 2024
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Bayes' Theorem is an incredibly powerful theorem in probability that allows us to relate P(A|B) to P(B|A). This is helpful because we often have an asymmetry where one of these conditional probabilities is easy to compute and the other is not. It let's us treat compute how to update our probabilities given new information.
The formula: P(A|B) = P(B|A)P(A)/P(B)
0:00 Deriving Bayes' Theorem
1:40 The Formula
2:57 First Example
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spent 1 hour reading and trying to understand the textbook, still dont get it. 2 minutes into this video and i understand the whole concept about bayes theorem. thank you sir.
My stats professor must not have understood it, and acted like she had never heard of it -- it was never taught in our class, neither the name nor the math, but we were taught the answer to this kind of problem was 1/2 on the basis that one baby's gender would not influence the other's gender (which is also much more intuitive). So, don't feel bad, you can teach college stats without knowing this.
That's coz you read the book i suppose
that probably was because you put in the initial effort of reading book where you had no idea what bayes theorem was. But when you started watching this video , you already had some idea of Bayes theorem , and his explanation probably caused the chunks that you have gathered to assemble and see you the overall picture .
welcome being enrolled in university of youtube
THIS IS SO TRUE!
You will be the reason I pass my college Stats class, God Bless.
dude im watching this so i can pass my 7th grade math class whats going on
Lol finnely
@@theoandco.5591 the future is now
@@purpurpur2 the times are achanging
Bae's theorem..
I didn't realize how many puns there are for this system
Hahaha
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You bastard,I suddenly miss my ex
😂
In this video I explain what conditional probabilities are and I show how to calculate them in Excel and how to interpret them, using Solver to implicitly apply Bayes' theorem. Though in spanish, subtitles in english are available: ruclips.net/video/rxHd7td6Xo0/видео.html.
It's been 4 years and the knowledge still flows on from here to there. I'm just glad you made this video coz I understand a concept I been struggling to understand in class!👍🏼
Well done, my data science professor spent 2 hours on this and we were all confused! You explained it in 5 minutes, thanks Trefor for sharing knowledge, really appreciated!
Why do you think it is that your professor didn’t communicate the idea well?
Lol I’m learning this in 10th grade😂
@@EmperorsNewWardrobe indeed
@@EmperorsNewWardrobe Giving too much details to someone who's new to a topic is never a good idea. University and college lectures are designed to teach people who studied the topics pretty well. In contrast to that, videos like this on RUclips, however, are made to teach.
@@Max-tk4lj I'm learning this in 7th grade 💀
This is exactly how I prefer to approach Bayes' Theorem: a short and sweet reminder about conditional probability rules so that the formula can be derived from first principles rather than recalled from memory. Most excellent Trefor.
I was trying to understand the formula for a week and almost gave up when I found this video. Now i FINALLY understand it. Thanks so much!! This is the best explanation of Bayes' Rule that I've seen.
I study Probabilities in French and no French video was as helpful as yours, God bless you and thank god i'm bilingual
This is so useful. I sometimes find myself getting stuck because I don’t have “enough information”. This will definitely help in this today’s exam 🔥
I don't usually make RUclips comments but ever since my calculus course went online with no access to video learning, I've been drowning. This video made it so easy to understand. Thanks for posting this.
Your videos literally teach me better than all of my professor's! Great job!!!!! Thank you!
You sir have saved my Math IA singlehandedly. Thank you so much! This video was so simple and easy to understand, it makes me want to learn more!
IB gang, assemble
Thank you for this. Hours of research didn't help but your work was exceptional.
an old video that still has updated timestamps! great work brother!
I'm taking statistics online with TONS of reading and was completely lost before this video. thank you so much!!
Idk what the problem is, but it seems like all teachers/textbooks fail to explain it easily. Thanks for the clear explanation in such little time
Thanks so much. Verifying the Bayes Theorem with the simplest probability formula (i.e Number of favorable outcomes (1- GG) / Number of total outcomes (3 - GG, GB, BG)) was eye opening. Thanks again bro.
Love youuuuuu. This was short, easy-to-understand and many more! Thanks for the timestamps! These are helpful.
THank you!
Thank you so much. You explained it so good that I won't forget it. You reasoned it so well. Thank you.
I was going to teach this theorem to my students for machine learning model and you made it easy for me to explain .
I have been scratching my head for hours and searching everywhere to understand this and I almost quit, but you sir are a legend. Thank you for the video.
You're very welcome!
The most simplistic and understandable explanation.
Really appreciate your way of teaching! Thanks a lot
Wow. Now I'm in love with this video. I've been watching every Short video on RUclips about naive Bayes, and this is the easiest to understand. Thanks
This is very helpful. Thank you for making it!!
Finally I can recall the bayes theorem perfectly, thanks to your video!!!
The simplest way to explain Baye's theorem. Excellent.
Thank you! A million times thank you! I spent all of my day yesterday pouring over textbooks and RUclips videos getting more and more confused by this theorem. Even Khan Academy had me scratching my head (which they're usually extremely helpful); I was wondering was Sal was on while doing his videos of conditional probability & Bayes' Theorem.
1 minute into your explanation (literally) and it made sense! I just might owe you my midterm mark!
This is the BEST VIDEO on Bayes Theorem. Thank you so very much for such a wonderful video. I saw so many videos but this is the ultimate. Thank you very much. My gratitude for posting such a well made video. Excellent way to explain.
Oh man I'm teaching myself probability and this video was so helpful!!! I couldn't understand the textbook at all. Thanks!
Your passion for teaching is so wonderful, thank you!
Hi, thanks for the video. What I wonder is, what are " default priors" when it comes to bayesian inference? As I understand, the priors are specific to each hypothesis or data, so how come some packages include these defaults? What do these priors entail?
FINALLY some sensible explanation. thank you very much!
Way better than the stuff I’ve been reading, thank you so much 🗣
one of the best videos on bayes' theorem... just loved it!!!!
my favorite tv show is now bayeswatch
Dem 2G looking good
HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAH
ba dum tsss
ohh amazing finally found someone teaching in English.... grt sir needed in this lckdwn time
Spent hours everywhere but could not understand. You sir, are exceptional.
I just stumbled upon your channel. Amazing videos dude, interesting and informative. Thanks a lot.
A very nice way of Explanation for Bayes Theorem so far.
Wow...this is the best video to learn the concept of Bayes Theorem....thanks Trefor :)
Best video on bayes theorem on yt so far
Subbed :D
if we had a math teacher like you, I would have never unloved maths
Thank you for the video. I was scared about the topic before but now your light came. thanks!
i feel like crying, had a hard time before this video. you sir explained it very clear giving the most simple example.
Thank you!
I hate math and have avoided all math heavy areas of Computer Science, until now where one of my courses is data mining.
This helped immensely!
Good video my man. Good presentation, you seem very enthuastic which makes statistics more bearable for us students! :D
Thank you for giving me an easy explanation of Bayes' Theorem.
These are the kind of videos which save you when u are starting to lose it while studying maths. Thank You Sir.
The way you sillify some things through your body language makes learning easy.
Super Saver for my tomorrow's Exam!!!! THANKYOU SIR
Excellent video! Thank you so much. God bless you sir!
Today I studied it at college, not able to understand and it suddenly appeared on recommended. Thank God.
Fantastic explanation. Bravo!
WOW man , you just made this concept so easy ! keep up the good work :D
Amazing explanation. Thank you
hi, by the look of the question, how do u figure out which theorem or formula u gotta use? im super confused in the sense that i dont even know how to start my question.
I'm also using different formula
you made it so obvious and intuitive, that it no longer seems to deserve being called "Bayes Theorem", as if he had to spend years working it out :-)
Very helpful thanks for watching sir i have understood.
OOOOH! So much better those other videos with overly excessive abstraction.
Great video. Clear and concise. Gave me more insight than 2b1b
Thank you so much, very helpful, very clear explanation
Thanks never taught in such an interesting way in college.
They teach this to you in college?
You made it so simple. Thanks
The probability of having one girl in the denominator is 0.5 and not 3/4, because that is the marginal, not conditional probability of 1G (just the probability of having a kid and that that kids sex is girl, not conditioned to any other event). Actually that is the main point of the Bayes theorem.
P(2G|1G) = P(1G|2G)P(2G)/P(1G) = 1*0.25/0.5 = 0.5
P(1G) = 0.5, given that the two (marginal) possible outcomes are just B or G
If you think logically for a second, you will very fast realize that given that a couple has a daughter, it does not make any sense to expect that the probability of the next kid being a girl is only 1/3. It must obviously still be 1/2 since it is just a new different kid, different from the sister.
This probability for each individual kid being a girl lowering with each kid you get would mean something like I am running out of female sperms or so, which is nonsense. If you have 99 daughters, the chance for your next kid to be a girl is still 50%
We're not told which child is the girl, the first or the second. If we're discussing all possible outcomes, we're talking about permutations, so order matters. The possible outcomes including at least one girl are: GG, GB, BG. So 1/3 is the answer.
if P(2G)=0.25, then it makes sense the P(1G)=3/4
@@nicholasjones5995 Tom has 2 children, one of them is a girl. What is the probability they're both girls?
Awesome way of explaining.
thank you so much sir this is so easy to understand ..
Another question is how would you tackle the same 1 girl problem from a frequentist approach?
Good explanation and good delivery I like it!
very nice explanation. Thank you
Timeless. Thank you!
Thanks , that's simple to understand
Thank you for creating this valuable channel. I can learn all the statistics things in easiest way. Could you please make videos about posterior probability, logistic regression and step-wise regression in future??
Hello! Quick question! Why isn't the P(1G) value of 1/2?
Since P(2G) comes from pool of GG, GB, BG, and BB, shouldn't P(1G) be coming from pool of G or B?
P(1G) is in the sense that probability of atleast 1 girl
At 4:50 why are we told there are 4 initial possibilities rather than 3: BB, GG, BG... what possible difference could the order BG or GB make to the calculation when the question is just about the pairing and not the order?
Hi! I'm little bit confused. I thought P(2G)=1/3 and P(1G)=1 because there's at least 1 girl. Why don' t we exclude the BB situation? So it becomes (1*1/3)/1= 1/3. The results are the same though.
I was wondering the same thing.
Excellent explanation thanks
You are really awewome Sir!!
Your explanation level is better than Khan Acadamy👍❤🙏
Let's pay him back by watching the adds on his videos don't skip adds please
simple explanation but really helpful
Very nice video, thank you for your efforts!
You seem like a really cool guy, keep it up
This video is very useful and easy to understand the theroem😉
you really are wonderful. i love your energy and enthusiasm throughout the lesson. definatley helped me. i
I'm so glad!
you just saved my grades!!! thank you SO much 😭😭
that example at the end was really helpful
Hi, the graphic is so interesting. It looks like chalk board. May I know what’s the name of the application so you use?
Thanks for your great explanation :)
Great lectures
Man you are legend !
I spent a lot of time understanding this shit but you explained it in 5 min !
that was very helpful! thanks 😊
It is interesting and clear! I like this video!
Sir you are masterpiece
I saw many videos but know one said how this theorem derived and you maid it so easy
I wish you get at least 100K subscriber by the end of this year
Thank you sir
Wonderful effort
Thanks
Ur examples r great....
very useful video thank you so much
how do I know when to apply baye's theorem though? whenever I see problem with the word "given " I know conditional probability should be used, but how do I know when to use the normal conditional probability and when to use baye's theorem ?
hmmm this is very good advice
Where can I find this video in his playlist... I need related video of probability problem
Thanks for great explanation