I know the video is old but I have to agree with the pinned comment. I already knew Bayes Theorem buy as I don't use it often, I have to be constantly refreshing the details in my mind. UA-cam algorithm recommended this video and it's hands down the best I have ever watched.
EXCELLENT EXPLANATION!!! I am learning graphical modeling and a lot of these concepts were a bit unclear to me. Examples given here are absolutely to the point and demystify a lot of concepts. Thank you and looking forward to more videos.
Great example! Very easy to follow and understand. On a side note: I showed your video to my students and some of them objected rather "emphatically". They said it was too sexist. Crazy times we live in....Instead of math and statistics, they wanted to discuss gender roles and stereotypes in a Stat class. Gosh!
Thanks John! I agree with your students. When I watch this now, I cringe. I definitely need to re-do it with a better example, one that doesn't reinforce outdated gender norms.
@@BrandonRohrer No....Please, do not follow the mad crowds... this an innocent, simple math example. People are getting crazy and finding excuses to feel offended and start meaningless fights!
Thank you. Your video has been of great help. I have tried different resources to wrap my head around Bayesian theorem and always got knocked out at the front door. Excellent expalnation
The knowledge that Bayes was a theologian and that his theory requires at least some belief or faith in improbable things earns a "Well played, Mr. Bayes" slow clap. I've been enjoying your videos Brandon, thanks for keeping things approachable!
I’m not sure that Bayesian epistemology requires a belief in improbable things. I love this video, but I think that’s an overstatement. I do think that it requires us to be open to the possibility that improbable things may be true. It does not require me to have faith in anything improbable, but rather to proportion our beliefs to the evidence (probabilities)- which is the antithesis of faith-while accepting the possibility of being wrong. To accept something as true that is improbable… is intellectually irresponsible and lacks due caution and humility. But to withhold belief (proportionally to the evidence) from improbable things is intellectually responsible and does not exclude being open to surprise-to the possibility that something improbable is true. I don’t think Bayesian epistemology intrinsically expects you to hold as true some improbable thing (faith). Abstinence from faith is acceptable in all cases as long as the possibility of error is operative. This suggestion that it’s necessary in Bayesian epistemology to believe something that is improbable was the only sloppy part of the video, no? I’m open to correction…
I think you guys got it the opposite way, the video was trying to say, be open to believe in the improbable things that come from the data (evidence), rather than only holding on a prior belief.
This is fantastic. Thank you so much! I have been exposed to BT before, but have never understood it. As sad as it sounds, I didn't realize it was composed of joint probability which is composed of conditional probability, and marginal probability. Conditional probability and joint probability, and Bayes theorem all just looked the same. This really helped clarify things for me.
Thanks for excellent presentation! One question though: at 17:49 the P(m=[13.9, 14.1, 17.5]|w=17) is factorized as following: P(w=17|m=[13.9, 14.1, 17.5]) = P(m=[13.9, 14.1, 17.5]|w=17) = P(m=13.9|w=17) * P(m=14.1|w=17) * P(m=17.5|w=17) then at 20:47 the P(m=[13.9, 14.1, 17.5]|w=17) * P(w=17) is expanded into: P(w=17|m=[13.9, 14.1, 17.5]) = P(m=[13.9, 14.1, 17.5]|w=17) * P(w=17) = P(m=13.9|w=17) * P(w=17) * P(m=14.1|w=17) * P(w=17) * P(m=17.5|w=17) * P(w=17) how do you get that P(m=[13.9, 14.1, 17.5]|w=17) * P(w=17) is equal to P(m=13.9|w=17) * P(m=14.1|w=17) * P(m=17.5|w=17) * P(w=17)^3 ? Thx in advance!
i hate stats because of those things... my teacher was teaching us utility analysis, and says "satisfaction is measured in utils" to that i ask "tell me how satisfied are you with your job and answer in the form: n-utils...". i still haven't got an answer!
0:40 Bayes wrote 2 books one about theology and one about probabilty. He planed to write a third book infering the existence / non existence of God with probability (likelihood distribution = humanity, Prior distribution= miracles !
I was looking for intuitive content to introduce me about essence of Bayes theorem in statistics, thanks for this. Luckily I found your blog about machine learning and robotics. That's all what I wanted under a roof, robotics, data science and machine learning.
Excellent. For those for whom this is the first lesson on Bayes, you've left out a few steps here and there. But still excellent. It's difficult to make things understandable. You're excellent at it.
Thanks Dov! And good callout - this focuses on the concepts and doesn't tell you quite enough to code it up. That will be the subject of a future course on e2eml.school
Brandon, 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 UA-cam explanation I am excited about the possibilities and understand the way it works - cool stuff! Thank you for all you do!!!
I believe you don't know much about statistics (the impossible thing), but I do believe you really know how to explain Bayesian Inference. Great video.
Excellent explanation. At the 15:20 and beyond is when everything really started to come together. Also thanks for deriving the formula at the 7:10 mark.
I found this quite helpful in giving Bayesian probability a more intuitive appeal. Bayes idea had previously been presented to me as "a priori probability", and I had always been troubled by the a priori part. But I guess a good way to think about it is like this: When we say, "All else, being equal, such-and-such is the case," we mean (or ought to mean) "Assuming that the variables which we have not measured or aren't even aware of have the values they most likely have when our one measured variable has the value measured or assumed by us, then such-and-such is most likely the case."
Thank you for the video, it helped me understand the concept of Bayesian inference. The concept is simple. In a nutshell, you have an idea about what the quantity is and then you use the measurements to sharpen your assumption.
Please consider doing a longer version of the video as its a nice way you have introduced this concept and you'll miss the intended audience who's not well versed with Bayesian statistics to go along with the pace of this video. I have some basics but I still had to pause the video a lot to be able to read the material before it changed to next slide and also listen to what you are saying. Also if you had a cursor or pointer that would also improve the experience.
GOD THANKS FOR EXISTING. Finally somebody that fucking breaks down the most important part of it (namely, how the do you calculate the likelyhood in practice). I hope life rewards you beautifully.
_" When you have excluded the impossible, whatever remains, however improbable, must be __-the truth-__ _*_possible_*_ "_ There 'ya go Sheerluck Holmes, I've fixed it for 'ya : )
Great video!! Very nice and easy to digest explanation of Bayes theorem! Thank you very much for sharing this excellent material. I have got a better understanding on how to apply it to my problems. Keep the great work!
Wow can't believe I only came across this video now. This is by far the best explanation on Bayes with great examples! Thanks @BrandonRohrer !! Love the example with the weight of puppy! May I ask if you have codes to deal with multiple priors/ multiple events? Say such as an extension of the weight of the puppy, if the weight change is more than one pound, plus she may be showing some other symptoms (say losing appetite), the likelihood of her being sick from something is x. Or even, losing appetite can be just due to weather being too hot. So the lost of weight of one pound from the last vet visit and losing appetite may not be significant at all and doesn't warrant multiple expensive test suggested by the vet.
Awesome! She told me to tell you that she is very flattered. Hopefully your cocktiel will not earn her name by eating an entire bowl of salt water taffy, including the wrappers.
More helpful than most! I will say though that the distribution for heights is really funny, unless you're crazy enough to think that the most common measurement would be in the 185 cm range, which is around 6'1"....which is taller than around 90% of men in the west and 95% of men globally.
Easiest way to weigh your dog is to first weigh urself, then hold ur dog and weigh again. Then you subtract your weight from dog+yourweight = dog weight
Bayes Theorem (1) only describes 2 events A and B that overlap (A+B). Bayes Theorem states that independent of the magnitude of A+B, the relationship between the proportion of A= P(A) and the proportion of B = P(B) is always the inverse of the conditional proportions being P(A | B) and P(B | A) or P(A) / P(B) = P(A | B) / P(B | A) (1) So if we know in your example the proportion: P(A) = P(M) = 0.50 P(B) = P(LH) = 0.25 than P(A) / P(B) = 0.50/0.25 = 2:1 which is true for any P(A+B) then according to (1): P(A | B) / P(B | A) = P(A) / P(B) P(A | B) / P(B | A) = 2/1 when P(B|A) = P(LH | M) = 0.04 the equation can be solved P(A | B) = P(M | LH) / 0.04 = 2 / 1 P(M | LH) = 0.08
Wow best explanation and example ever I saw ^^ Fantastic.
Excellent
exactly. These pacient disease examples were driving me nuts.
this is by far the most accessible explanation of Bayes theorem. Well done Brandon!
Best explanation of Bayes theorem I have seen. Fantastic teaching.
This is the most accessible explanation about Bayesian Inference. Thank you Brandon for the time taken to prepare this video. You rock !
I know the video is old but I have to agree with the pinned comment. I already knew Bayes Theorem buy as I don't use it often, I have to be constantly refreshing the details in my mind. UA-cam algorithm recommended this video and it's hands down the best I have ever watched.
Thank you. I really appreciate that.
Brandon I just want to tell you that you are a fantastic teacher.
Thank you very much Shirshanya. That is a huge compliment. I'm honored.
Please make more statistics videos! I have suggested your channel to my biostat teacher.
Wow! One of the clearest explanations of Bayes Theorem I’ve come across!
Thanks!
i don't know what to say, i'm a computer science student and i have never seen an explanation better than this ... thank you veryyyyy much
Excellent explanation ! This is the manner in which mathematics must be explained. With cases of practical applicability. Good job mr. Brandon !
Thanks Razvan. I'm so happy you enjoyed it.
This is the first time I've felt like I've actually understood this... and it's such a simple concept! Thank you!
Loved the analogies with real life philosophies, brilliant!
The way you connect things with appropriate easy to examples...Amazing...
EXCELLENT EXPLANATION!!! I am learning graphical modeling and a lot of these concepts were a bit unclear to me. Examples given here are absolutely to the point and demystify a lot of concepts. Thank you and looking forward to more videos.
Thank you for this excellent explanation. You are a patient and well-spoken teacher.
Great example! Very easy to follow and understand. On a side note: I showed your video to my students and some of them objected rather "emphatically".
They said it was too sexist. Crazy times we live in....Instead of math and statistics, they wanted to discuss gender roles and stereotypes in a Stat class. Gosh!
Thanks John! I agree with your students. When I watch this now, I cringe. I definitely need to re-do it with a better example, one that doesn't reinforce outdated gender norms.
@@BrandonRohrer No....Please, do not follow the mad crowds... this an innocent, simple math example. People are getting crazy and finding excuses to feel offended and start meaningless fights!
So sad. Long hair and standing in the womens restroom line and we cant even use Bayes' thereom to assume its a woman 😂
Thank you. Your video has been of great help. I have tried different resources to wrap my head around Bayesian theorem and always got knocked out at the front door. Excellent expalnation
The knowledge that Bayes was a theologian and that his theory requires at least some belief or faith in improbable things earns a "Well played, Mr. Bayes" slow clap. I've been enjoying your videos Brandon, thanks for keeping things approachable!
I’m not sure that Bayesian epistemology requires a belief in improbable things. I love this video, but I think that’s an overstatement. I do think that it requires us to be open to the possibility that improbable things may be true. It does not require me to have faith in anything improbable, but rather to proportion our beliefs to the evidence (probabilities)- which is the antithesis of faith-while accepting the possibility of being wrong. To accept something as true that is improbable… is intellectually irresponsible and lacks due caution and humility. But to withhold belief (proportionally to the evidence) from improbable things is intellectually responsible and does not exclude being open to surprise-to the possibility that something improbable is true. I don’t think Bayesian epistemology intrinsically expects you to hold as true some improbable thing (faith). Abstinence from faith is acceptable in all cases as long as the possibility of error is operative. This suggestion that it’s necessary in Bayesian epistemology to believe something that is improbable was the only sloppy part of the video, no? I’m open to correction…
I think you guys got it the opposite way, the video was trying to say, be open to believe in the improbable things that come from the data (evidence), rather than only holding on a prior belief.
Definitely the best explanation of the theorem told in an easily understandable way, I can find in the internet...
This is the best explanation yet, it helped me get a greater intuitive sense of Bayesian inferences.
Yes it was great. It seems running into Feigenbaum maths or simular
Stop looking for a descent tutorial... this one is the best!
when your teacher don't make sense, had to go through teaching videos online and came across this one...
Lucky lucky lucky! Thank you Mr!
hey man,this is the one good explanation for conditional prob i had ever heard
Thanks!
There are never lines at the men's room.
haha.
lol
Unless it's cocaine.
So the probability of this sample being true is 0%, hahhaha
You have never been to developer conferences :)
I have been struggling with bayesian inference and your tutorial makes it so easy to understand! Thank You! Keep up the good work.
I'm very happy to hear it Fahad. Thanks.
For 5 years i kept Bayes aside , you are the guru in teaching stuff.. God bless you Brandon
This is fantastic. Thank you so much! I have been exposed to BT before, but have never understood it. As sad as it sounds, I didn't realize it was composed of joint probability which is composed of conditional probability, and marginal probability. Conditional probability and joint probability, and Bayes theorem all just looked the same. This really helped clarify things for me.
I have viewed many explanations about Bayes rule but this is no doubt the best! Thanks Brandon
I was reading about Bayes Theory for months ! And this is the first time I understand the concept!! Wow!! such an amazing way of teaching!!
I'm so happy to hear it Taghreed. That was exactly my hope.
Great explanation and simplification of a difficult concept. The three quotations at the end are poetic and purposeful. Thanks
I found them surprising relevant too. Thanks Sridhar.
I must say, this is the explanation of Bayes theorem, I have ever seen..... PERFECT!!!!!
Thanks for excellent presentation! One question though:
at 17:49 the P(m=[13.9, 14.1, 17.5]|w=17) is factorized as following:
P(w=17|m=[13.9, 14.1, 17.5])
= P(m=[13.9, 14.1, 17.5]|w=17)
= P(m=13.9|w=17) * P(m=14.1|w=17) * P(m=17.5|w=17)
then at 20:47 the P(m=[13.9, 14.1, 17.5]|w=17) * P(w=17) is expanded into:
P(w=17|m=[13.9, 14.1, 17.5])
= P(m=[13.9, 14.1, 17.5]|w=17) * P(w=17)
= P(m=13.9|w=17) * P(w=17) *
P(m=14.1|w=17) * P(w=17) *
P(m=17.5|w=17) * P(w=17)
how do you get that P(m=[13.9, 14.1, 17.5]|w=17) * P(w=17) is equal to P(m=13.9|w=17) * P(m=14.1|w=17) * P(m=17.5|w=17) * P(w=17)^3 ? Thx in advance!
i hate stats because of those things... my teacher was teaching us utility analysis, and says "satisfaction is measured in utils" to that i ask "tell me how satisfied are you with your job and answer in the form: n-utils...".
i still haven't got an answer!
I wish everyone taught like this. Your presentation was awesome. Thank you
0:40 Bayes wrote 2 books one about theology and one about probabilty.
He planed to write a third book infering the existence / non existence of God with probability (likelihood distribution = humanity, Prior distribution= miracles !
I was looking for intuitive content to introduce me about essence of Bayes theorem in statistics, thanks for this. Luckily I found your blog about machine learning and robotics. That's all what I wanted under a roof, robotics, data science and machine learning.
Excellent. For those for whom this is the first lesson on Bayes, you've left out a few steps here and there. But still excellent. It's difficult to make things understandable. You're excellent at it.
Thanks Dov! And good callout - this focuses on the concepts and doesn't tell you quite enough to code it up. That will be the subject of a future course on e2eml.school
Brandon, 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 UA-cam explanation I am excited about the possibilities and understand the way it works - cool stuff! Thank you for all you do!!!
You're very good at explaining and also you go in some details which is nice. Too often youtube tutorials are too simple. keep going.
now that you have said that (an year ago), i kinda feel like finding the probability of likelihood of a youtuber making too simple tutorials!
I believe you don't know much about statistics (the impossible thing), but I do believe you really know how to explain Bayesian Inference. Great video.
Great explanation and video lesson production. Best Bayesian lesson I've found on youtube
You're so much better than my Statistics teacher, thank you so much for this explanation!
Thanks Mathias!
I thought this was not only a great example of Bayes but also a nice intro for Cox's Theorem. Nice jobQ
* quickly looks up Cox's Theorem *
Why, yes it does Donna. Thank you! :)
Best video I found with all the information that I needed at one place.
Thanks.
This was the best explanation of Bayes I've ever heard, I had such a hard time wrapping my head around it from other sources
this was very intuitive explanation, man do more!
Amazing. I already knew what Bayes theorem was, but you have an awesome intro to Bayes. Thanks for the video.
Excellent explanation. At the 15:20 and beyond is when everything really started to come together. Also thanks for deriving the formula at the 7:10 mark.
This video deserves more thumbs up. I understood a lot on a lazy sunday evening :) great explaination.
I am from Brazil. What a fantastic explanation!
Thanks Jose! Welcome to the channel
i like the quotes you put at the end and how you reword them
I found this quite helpful in giving Bayesian probability a more intuitive appeal. Bayes idea had previously been presented to me as "a priori probability", and I had always been troubled by the a priori part. But I guess a good way to think about it is like this: When we say, "All else, being equal, such-and-such is the case," we mean (or ought to mean) "Assuming that the variables which we have not measured or aren't even aware of have the values they most likely have when our one measured variable has the value measured or assumed by us, then such-and-such is most likely the case."
hands down best explanation i've seen, thank you
I have been searching for explanation like this for sometime and a big WOW to this guy. Wonderful explanation!!
Superb lecture - esp. the MLE explanation!
Amazing explanation and graphics!
Thanks!
Thank you for the video, it helped me understand the concept of Bayesian inference.
The concept is simple. In a nutshell, you have an idea about what the quantity is and then you use the measurements to sharpen your assumption.
best explanation on youtube so far
Brandon, this was great, thank you. Very easy to follow and really interesting and concise!
Thanks Erin!
Absolutely brilliant! Your presentation, examples, etc. were perfect and applicable! Thanks!
Thank you very much :)
such a well-thought -through video, very good explanations for every instance, the ending was the bonus, loved it, thank you
Thank you Lilit! I appreciate that.
the best explanation I ever seen! Super clear.
Please consider doing a longer version of the video as its a nice way you have introduced this concept and you'll miss the intended audience who's not well versed with Bayesian statistics to go along with the pace of this video. I have some basics but I still had to pause the video a lot to be able to read the material before it changed to next slide and also listen to what you are saying. Also if you had a cursor or pointer that would also improve the experience.
Thank you sooo much Brandon for explaining the concepts so clearly.
Dude your analogies are on point.
Thanks Julian
"...one of the top 10 math tattoos of all time." 😂
Thumbs up after watching the first 3 minutes. Finally, the "prior" make sense to me!!!!!!
the best explanation i hv seen about bayes theorem... awsome... thnx a ton....
best explanation I found on the topic so far. great work!!!
Thank you for this excellent presentation!
Simply the best ! Thank you Brandon
GOD THANKS FOR EXISTING. Finally somebody that fucking breaks down the most important part of it (namely, how the do you calculate the likelyhood in practice). I hope life rewards you beautifully.
That was fantastically done.
Thank you :)
Wonderful explanation. Thank you. The Mark Twain quote at the end is apocryphal though.
Thanks Matthew. I'll have to asterisk that. :)
Start with more slides like your last two. Thanks this was insightful.
thank you so much. you expained it in an awesome way and saved my exam.
Glad to hear it
You deserve many more subscribers dude
That's the best explanation ever❤️❤️❤️❤️
_" When you have excluded the impossible, whatever remains, however improbable, must be __-the truth-__ _*_possible_*_ "_
There 'ya go Sheerluck Holmes, I've fixed it for 'ya : )
The best explaination on youtube
thank you man
Nothing much to say only thank you! you may have helped me in clearing my exam!
Hi Brandon, your video was simple, superb, and stupendous!
Great video!! Very nice and easy to digest explanation of Bayes theorem! Thank you very much for sharing this excellent material. I have got a better understanding on how to apply it to my problems. Keep the great work!
great video presentation Brandon. please try to apply more videos on other machine learning algorithms
What a stunning explanation. Speechless
💜 🧡 🖤 💚 🤎 💛 💙
Excellent examples and explanation! Now everything is so much clearer. :)
Wow can't believe I only came across this video now. This is by far the best explanation on Bayes with great examples! Thanks @BrandonRohrer !! Love the example with the weight of puppy! May I ask if you have codes to deal with multiple priors/ multiple events? Say such as an extension of the weight of the puppy, if the weight change is more than one pound, plus she may be showing some other symptoms (say losing appetite), the likelihood of her being sick from something is x. Or even, losing appetite can be just due to weather being too hot. So the lost of weight of one pound from the last vet visit and losing appetite may not be significant at all and doesn't warrant multiple expensive test suggested by the vet.
we got a cocktiel bird in our house but we don`t know what to name it, your dog`s name gave me a good idea!
Awesome! She told me to tell you that she is very flattered. Hopefully your cocktiel will not earn her name by eating an entire bowl of salt water taffy, including the wrappers.
Terrific examples and terrific explanation down to such applicable quotes!
absolutely amazing explanation
Hi! This was such a clear explanation. It would be great if you could make one on hidden markov models.
Thanks Rachel! Hidden Markov Models are an excellent idea. I'll put it in my to do list.
When you said small human, I imagined a small adult
Imagining calling Tyrian cute
An unforgettable example
More helpful than most! I will say though that the distribution for heights is really funny, unless you're crazy enough to think that the most common measurement would be in the 185 cm range, which is around 6'1"....which is taller than around 90% of men in the west and 95% of men globally.
Easiest way to weigh your dog is to first weigh urself, then hold ur dog and weigh again. Then you subtract your weight from dog+yourweight = dog weight
Amazing explanations
Superb explanation Sir
Bayes Theorem (1) only describes 2 events A and B that overlap (A+B).
Bayes Theorem states that independent of the magnitude of A+B,
the relationship between the proportion of A= P(A) and the proportion of B = P(B)
is always the inverse of the conditional proportions being P(A | B) and P(B | A) or
P(A) / P(B) = P(A | B) / P(B | A) (1)
So if we know in your example the proportion:
P(A) = P(M) = 0.50
P(B) = P(LH) = 0.25
than P(A) / P(B) = 0.50/0.25 = 2:1
which is true for any P(A+B)
then according to (1):
P(A | B) / P(B | A) = P(A) / P(B)
P(A | B) / P(B | A) = 2/1
when
P(B|A) = P(LH | M) = 0.04
the equation can be solved
P(A | B) = P(M | LH) / 0.04 = 2 / 1
P(M | LH) = 0.08
Thanks for the excellent video. A good refresher! Keep up the good work!
Hey @Brandon Rogers,
At 18:12, y axis is likelihood not probability. Probability is area under curve for this graph.
6:04 Okay, I wasn't expecting the milk and jelly donut. Now I've got a craving.
Thank you very much for the best explanation, It's very interesting