Bayes' Theorem EXPLAINED with Examples
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- Опубліковано 2 кві 2023
- Learn how to solve any Bayes' Theorem problem. This tutorial first explains the concept behind Bayes' Theorem, where the equation comes from, and finally how to use the formula in an example. Bayes' Theorem is one of the most common equations covered in Statistics due to its numerous applications to the real world. It is also one of the most misunderstood theorems, but this video will help clear all of that up!
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I don't know how this is not the most viewed Bayes' theorem video because its the most helpful in youtube
That means so so much to me! Thank you for saying that! I appreciate it!
I am Indian I have no words for saying video but I say few word this is very amazing and very helpfull in all students
Indeed, great vid. I also found this one to be very useful:
ua-cam.com/video/1QulO1jS2Hk/v-deo.htmlfeature=shared
I totally agree
because it's not
Thanks a lot for this intuitive example. It helped me a lot to understand this mechanism when I understood that as p(cloudy) becomes smaller, p(rain|cloudy) becomes greater, all else being equal. Since p(cloudy) is the numerator.
This makes sense intuitively, because in a situation clouds are rare (i.e. p(cloudy) is smaller), but when it rains, there were often clouds in the morning (i.e. p(cloudy|rain) is large), the prediction value of it being cloudy in the morning is high.
Reversely, in a climate where it is always cloudy (i.e. p(cloudy) is near one), the fact that it's cloudy in the morning does not tell you much in terms of how much rain you will get.
Probably the clearest explanation of Bayes Theorem I have seen so far. Beautifully done. Got to watch all your videos now.
The best explanation of Bayes' theorem on youtube, thank you
Saying this video is the best is an understatement. Thank you so much for posting this beyond-amazing video!
superb video. How easily the theorem is explained with the help an excellent example...thanks.
This is so beautiful.
I didn't understand it really at first, but after now I have a pretty great idea of it
That's terrific to hear! That is exactly my goal with my videos!
Please make more videos on the probabilities. Thank you so much We appreciate your effort.
Very precisely explained.Thank you Sir❤
Please keep making more videos. I am an MPH student at Harvard, and you make the concepts extremely understable. Sending you a lot of love
Thank you so much for your kind words! I really appreciate it and will keep work on putting out videos.
@@AceTutors1 we need probability testing statistics if possible
This was very helpful am taking statistics class and was so lost. Thanks
That was easy and simple to understand. Master it is another thing, but my guess is that you saved me some precious time with this video. Thank you a lot.
This was super helpful thank you!
Thank you soo much for well explaining this concept. I now can say that I understand it better!
That's amazing to hear! Thanks for watching!
Thanks! Very helpfull and understandable.
Amazing video, thank you for the explanation it finally clicked.
Great videos Mark, you inspire us every day with your slogan "You've big dreams, don't let a class get in your way."
The likelihood of it being rain while picnic seems low, as it's less than 0.5 / 50%. So I think.i would still go on the picnic.
Thank you so much for your kind words and support! Ahh, you might have a higher risk tolerance than me! haha :)
love your work man, keep up the good work!
Thank you so much for the support!
Thanks for your videos. It helped a lot. Please do something on hypothesis. Thanks
Thank you so much for this vid man, your method of explanation was impressive
honestly u did better job than many others
this was great thnx for the example
Super helpful ,Thank you 🌹
Got an exam in 8 min, this was good help
Great explaination sir
Super explanation. Thanks Sir
Good explanation.Thank you
Great videos man they help a lot
Thank you so much! I appreciate it!
THANKS MAN! Tomorrow is my official school graduation exam and honestly i didn't ecen know a word about this concept so i was worried and your video popped up! Thanks a bunch for making me understand it! Ill be back to report my marks if i am reminded of this comment!
P. S: keep doing this. We love it and will support you through the best of our efforts!
Thank you so much for your comment! It's stories like yours that give me the fuel to make these videos. I wish you luck on your exam! And thank you for the support!
This is very helpful❤
Amazing video!! thank you:))
Thank you so much. It took 1 video of you understand 3 hours of lecture.
God bless you sir for this video. I HAVE went through few videos on UA-cam and this was one of the best where my mind has understood this fully. Now lets see if you have stuff on Binomial distribution. Thanks just subscribed now
Thank you so very much!
I think the example in this video is better than what 3B1B gave in his Bayes' theorem video. The starting wasn't good because you just spammed the formula but the example and the way you conveyed it is really good. One can understand the principle through your example. Good work!
great, great and best explanation
Omg thank you sir thank you so much ❤ the way u explained it,, cleared my all doubts regarding this topic ❤
That's really awesome to hear! Thanks for the kind words!
Great video thanks
Well done! Excellent Explanation. And I would definitely cancel the picnic I'm worry wart. LOL
Thanks for the concept ☺️ I think I will try to reschedule 😅❤
this helped tonnnnnnn thankyou
Good explanation 🎉
Thank you for creating this theorem, Bae 😍
It indeed helped ! appreciate it gentleman
Great, I'm so glad! Thanks for your support!
I’ve never seen a more clear explanation of how Bayes’ Theorem can be applied. This is extremely helpful! Thank you so much!
Thank you so much for saying that! I really appreciate the support!
Super helpful and straightforward. Thank you sir please keep posting
Pretty helpful!
English is not my first language and you still made it very easy :D
that was so helpful, thanks
You got it! Thanks for watching!
Damn, perfectly explained. Thanksssssssssss!
Thank you so much
THANK YOU!
I was trying to learn Bayes' Theorem off the example of "Go For Broke" the gameshow. 🥵 my brain was twisting in on itself. THIS I can understand.
Thank you NRI ❤
Thank you!
i feel like i want to cry
great vids bro
How you will connect prior and posterior terms with this?
This series is amazing. Must have been hard to make these beautiful animations. Thank you so much❤.
Can you please make two more distributions viz:
1. "Poisson Distribution" and
2. "Exponential Distribution"
And explain the intuition behind the mean and standard deviation in these distributions like you did in Uniform distribution video?
What an example ❤❤
So farthis is the best bayes explanation. Can you explain this thing using a venn diagram and a probability distribution for the cloudy rain example
Thanks so much for your kind words! I'm not sure a probability distribution would help much, but some more Venn diagrams could be helpful! We'll consider this in a follow-up video! Thanks for the feedback!
Thankyou!
Excellent
Which software are you using to make these videos?
Nice explain dear
Hi, so is conditional probability used with limited information in a question, however Bayes theorem can be used to answer a question that has more information? I'm just struggling with which one to use in an exam question
Thank you. I'm still having concept issues. As a teaching technique is it possible for you to summarize the meaning of the numerator and what the denominator accomplishes in the equation
hi I want to ask so in this case what the addictional knowledge? the probability of beibg cloud?
It's awesome 🎉😢
nice example
Can we solve the same example by conditional probability?
you really aced it
Wow fairly good explanation. i just understand it perfectly today. However, in the process, i found another better way to comprehend this theorem.
To those who still do not understand. Read this.
First you must understand what p(a/b) is. It is the probability that a happening when we already know that b happened.
To find p(a/b) we need to find prob that a and b happening at the same time , and divided it by prob of b happening.
To find prob that and b happening at the same time (p (a interect b)), you can find that indirectly from prob that b happening when we already know that a happened multiplied by prob of a happening
Ah.... i need a pen and a paper to convey this concept 🙄
NICE VIDEO
I LOVE YOU GUYS
I'm still puzzeld on which data is A and which is B - and why. Swapping things around changes the outcome of the formula, doesn't it?
it would make me 48% worried about rain and 48% considerable of postponing the picnic
Nice!
Thank you for watching
in need more explanation of this "give" thing
Thus is amazing
This
Can we please have a video about P value and what does it mean?? pretty please
Yes we have some videos on p-value in the works! Great idea!
thankkkkkkkkkkkk youuuuuuuuuuuuuuu !
I would have liked if you incorporated dark clouds vs white clouds in the calculation.
Genius!
I am from Bangladesh, have started to learn machine learning. For which I have to learn probability and statistics.
I have clear out all the topics on probability by 11-12th books. But BAYES' THEOREM was seemed to tough to understand.
So I came to UA-cam and saw lots of videos which was even approximately half an hour! Although they tried for a long time, they all were gloomy to understand.
But your 8 minute video is so effective than all those videos. Thanks. I have subscribed your channel. I will visit again if any other topics I have to understand in future.
That's great when the example gives what P A|B is
I think the most difficult part overall regarding to probability problems... are the wordings. They seem to be confusing
Do you use the Python library called "manim" to create these beautiful animations for your great videos.
Depends on how much you like picnics, how often you want to go on picnics, if you think rain ruins it and maybe you might already think a cloudy day isn't nice for picnics.
But before we think about that, let's think about the ethics of holding a picnic and it's core components. We NEED to apply divide and conqure on this problem before we could even start to make a decision.
We might even need to apply derivatives to calculate the slope at how long the picnic takes (x) and how much fun it is (y). Then we can decide the optimal time to hold the picnic 🙊
So what you’re saying (if I pause the video @6:23) is:
If the probability of it being cloudy outside is 4 times greater if it also rains that day, then the probability of it raining on any given day is also 4 times greater if it happens to be a cloudy day?
I essentially just pretended that P(cloudy) was equal to 0.2 instead of 0.25, and then I just isolated the ratio of: P(cloudy/rain)/P(cloudy)
Given the statement "it’s 4 times more likely to be cloudy outside, given it is also raining," we can express this as:
P(Cloudy | Rain) = 4 * P(Cloudy)
Substituting this into the Bayes' theorem equation, we get:
P(Rain | Cloudy) = (4 * P(Cloudy) * P(Rain)) / P(Cloudy)
The P(Cloudy) term cancels out, resulting in:
P(Rain | Cloudy) = 4 * P(Rain)
So, yes, from a simple Bayesian probability standpoint, if it's 4 times more likely to be cloudy outside given that it's raining, then it's 4 times more likely to rain given that it's cloudy outside.
Ive seen bayes theorem be written as P(Ei|A) = P(Ei)P(A|Ei) / ∑ P(Ek)P(A|Ek)
can you explain this version?
Great point! This version is a more general formula if there are more than 2 events being considered. In this video, we just used the simplified version of 2 events to make it easier.
I think this solution is incorrect actually. We should have calculated P(C) with the rainy days' 0.85 ratio with the formula : P(C)=P(C∣R)×P(R)+P(C∣¬R)×P(¬R) where C is being cloudy and R is rainy. So it would be 0.12 for P(C∣R)×P(R) and 0.215 for P(C∣¬R)×P(¬R) and the calculations made it's 0.36. Can you clarify please
if one knows that there are 12 rainy cloudy days (the 80% of 15) in 100 days and 25 cloudy days in total why one can’t just calculate 12/25= 0.48, without all the machinery and the language that the Bayes formula brings along? Is there something wrong in just applying the definition of probability?
CAN YOU EXPAIN THE TIME SERIES
That's definitely a topic we plan to cover in the future! Thanks for the feedback!
On the last slide with example it should be “when it rains”, not where.
Dude, when the guy says hit the subscribe button, the button lights up. I noticed it just now
You explain very well but it would be more helpful if you broke down how to determine step by step which is a and which is B.
How did you made your subscribe button glow at 0:25 ??
Definitely reschedule the picnic
It is observed that 76% of Group A favors the product, 47 % of Group B favors the
product and 54% of Group C favors the product. A random sample of 105 people
with 35 from group A, 28 from Group B and 42 from Group C, was chosen and
polled. A random vote from the poll suggests that the product is preferred. What is
the probability that this vote belongs to a person from group B? Can anyone tell me the answer for this?
20.17% or 47/233
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