Bayes' Theorem EXPLAINED with Examples
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- Опубликовано: 29 сен 2024
- 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 feel like i want to cry
#metoo 😢
Very precisely explained.Thank you Sir❤
Thanks! Very helpfull and understandable.
this helped tonnnnnnn thankyou
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
Fr… my university professor can teach for shit… I have a much better understand how to do these operations and use the formula after watching this 8 minute video and I swear my professor has spent 2 days talking about this… wtf thank you… someone find the probability that my professor won’t teach the students anything something given he can’t teach p(a) = .1 p(b) =.1 p(b|a)= .99.
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:
ruclips.net/video/1QulO1jS2Hk/видео.htmlfeature=shared
I totally agree
because it's not
i have final exams in medicine but studying it to teach my gf whos architect :) worthy baby i love you honey soooo muchhhhh
Teraa bhi cutegaaaaa
@@shubhamsharmavlogs1482 mujhe aasha hai ki prthvee par kisee ko bhee brekap ka anubhav nahin hoga, aapakee haar ke lie khed hai
Which software are you using to make these videos?
How did you made your subscribe button glow at 0:25 ??
it would make me 48% worried about rain and 48% considerable of postponing the picnic
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
Probably the clearest explanation of Bayes Theorem I have seen so far. Beautifully done. Got to watch all your videos now.
Got an exam in 8 min, this was good help
The best explanation of Bayes' theorem on youtube, thank you
Well done! Excellent Explanation. And I would definitely cancel the picnic I'm worry wart. LOL
when they say subscribe, the button will not glow
how?
Probably the algorithm thinks that subscribe is a part of the lecture ig, it needs to be said with enthusiasm
I'd definitely not reschedule if there is a 0.48 chance. I hate my siblings
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
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!
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 :)
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?
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.
Saying this video is the best is an understatement. Thank you so much for posting this beyond-amazing video!
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!
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!
I think the most difficult part overall regarding to probability problems... are the wordings. They seem to be confusing
I would definitely not have my damn picnic >:(
Hahah me neither!
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!
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.
God bless you sir for this video. I HAVE went through few videos on RUclips 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
Please make more videos on the probabilities. Thank you so much We appreciate your effort.
Simple things are best.
You explained without getting complicated.
Thanks.
Loved this, I never really understood until now after watching your tutorial..... Your a genius or just a great teacher, thank you. ❤
It was a good calculation of conditional probability.
But I have come across terms like updating a belief with reference to Bayesian statistics.
How does updating of belief applies here.
Thanks again.
At last! I got it! I wish my professor were so clear. Subscribed.
Im stuck😅 I think my cat got out because I didn’t see her today, so:
P(left|unseen)=(P(unseen|left .80)•P(left .40))/P(unseen .30) and that leaves me with the probability of her having left given that I haven’t seen her at… 1.06?? I must be doing something wrong because I think it’s fair to say there’s a 30% chance I wouldn’t see her today anyway, there’s about a 40% chance she could have gotten out on any given day, and about an 80% chance I wouldn’t see her if she got out (she does come back the same day roughly 20% of the time), but I don’t know about there being a 106% chance she left given that I haven’t seen her today lol what am I doing wrong here?
Please help✌️😅
This is really an excellent explanation of Bayes Theorem.
TL;DR - I would postpone the picnic!
- not rain is 1.08x more likely to cloudy than rain.
- not rain is 24.00x more likely to not cloudy than rain.
- cloudy is 12.00x more likely to rain than not cloudy.
- not cloudy is 1.85x more likely to not rain than cloudy.
- cloudy given rain is 5.23x more likely than cloudy given not rain.
- not cloudy given not rain is 4.24x more likely than not cloudy given rain.
Let’s say the prevalence or prior probabilities for rain is 15.00% (odds of 0.18x or chances of 100 for every 667), and for not rain is 85.00% (5.67x or 100 for every 118), whether or not cloudy. In a world of rain, 80.00% (4.00x or 100 for every 125) is cloudy, let’s say, and 20.00% (0.25x or 100 for every 500) is not cloudy. In a world of not rain, 15.29% (0.18x or 100 for every 654) is cloudy, let’s say, and 84.71% (5.54x or 100 for every 118) is not cloudy. Thus, rain is 5.23x as likely cloudy as not rain. Also, rain is 0.24x as likely not cloudy as not rain. We know this as the Likelihood Ratio, Risk Ratio, or Bayes Factor.
The Relative Risk Increase is 423.22%, and the Absolute Risk Increase is 64.71% (1.83x or 100 for every 155). The prevalence of cloudy, or not cloudy, regardless of rain or not rain, is 25.00% (0.33x or 100 for every 400), and 75.00% (3.00x or 100 for every 133), respectively.
Therefore, which is more likely? In a world of cloudy, the posterior probability of rain is 48.01% (0.92x or 100 for every 208), and not rain is 51.99% (1.08x or 100 for every 192). In a world of not cloudy, the posterior probability of rain is 4.00% (0.04x or 100 for every 2500), and not rain is 96.00% (24.00x or 100 for every 104).
That's an Attributable Risk or Risk Difference of 44.01% (0.79x or 100 for every 227). The Accuracy Rate (that is, 'true-positive' and 'true-negative') is 84.00% (5.25x or 100 for every 119), and the Inaccuracy Rate (that is, 'false-positive' and 'false-negative') is 16.00% (0.19x or 100 for every 625). The probability of rain, and cloudy is 12.00% (0.14x or 100 for every 833). The probability of rain, and not cloudy is 3.00% (0.03x or 100 for every 3333). The probability of not rain, and cloudy is 13.00% (0.15x or 100 for every 769). The probability of not rain, and not cloudy is 72.00% (2.57x or 100 for every 139).
Sensitivity analysis:
What would the prevalence or prior probabilities for rain, and not rain, whether or not cloudy, need to be such that in a world where rain given cloudy, and not rain given cloudy, that both these posterior probabilities are equally likely? In other words, we’d be indifferent? The prevalence of rain would need to be 16.05% (0.19x or 100 for every 623), and not rain would need to be 83.95% (5.23x or 100 for every 119), all else being equal.
Similarly, what would the prevalence or prior probabilities for rain, and not rain, whether or not not cloudy, need to be such that in a world where rain given not cloudy, and not rain given not cloudy, that both these posterior probabilities are equally likely? In other words, we’d be indifferent? The prevalence of rain would need to be 80.90% (4.24x or 100 for every 124), and not rain would need to be 19.10% (0.24x or 100 for every 524), all else being equal.
What would the consequent probabilities or likelihoods for cloudy given rain, and not cloudy given rain, need to be such that in a world where rain given cloudy, and not rain given cloudy, that both these posterior probabilities are equally likely? In other words, we’d be indifferent? The likelihood of cloudy given rain would need to be 86.64% (6.49x or 100 for every 115), and not cloudy given rain would need to be 13.36% (0.15x or 100 for every 749), all else being equal.
Similarly, what would the consequent probabilities or likelihoods for cloudy given not rain, and not cloudy given not rain, need to be such that in a world where rain given cloudy, and not rain given cloudy, that both these posterior probabilities are equally likely? In other words, we’d be indifferent? The likelihood of cloudy given not rain would need to be 14.12% (0.16x or 100 for every 708), and not cloudy given not rain would need to be 85.88% (6.08x or 100 for every 116), all else being equal.
What would the consequent probabilities or likelihoods for cloudy given not rain, and not cloudy given not rain, need to be such that in a world where rain given not cloudy, and not rain given not cloudy, that both these posterior probabilities are equally likely? In other words, we’d be indifferent? The likelihood of cloudy given not rain would need to be 96.47% (27.33x or 100 for every 104), and not cloudy given not rain would need to be 3.53% (0.04x or 100 for every 2833), all else being equal.
Using the Wald test, the relationship or association between rain or not rain, and cloudy is statistically significant (n=10,000). Odds Ratio (OR) = 22.16, p < .001, 95% Confidence Interval (CI) [19.27, 25.48]. We can say the same between rain or not rain, and not cloudy. OR = 0.05, p < .001, 95% CI [0.04, 0.05]. By changing P(E|H') of 15.29% such that the OR would be 19.27 - 25.48, then P(H|E) = 45.10% - 50.99%. Therefore, I would postpone the picnic!
Bayes’ Rule: P(H|E) = P(H) x P(E|H) / P(H) x P(E|H) + P(H’) x P(E|H’)
Contingency Table:
||H|H’|Total|
|:-:|-:|-:|-:|
|E|1200|1300|2500|
|E'|300|7200|7500|
|Total|1500|8500|10000|
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
Dude, when the guy says hit the subscribe button, the button lights up. I noticed it just now
Amazing video, thank you for the explanation it finally clicked.
Thank you so much. It took 1 video of you understand 3 hours of lecture.
Great video! The perfect first step to understanding Bayes' Theorem.
I'm still struggling... please can somehow help me with this example:
1. If someone is white and male, I can detect lies 80% of the time.
2. The chances of someone being white where I live is 81.7%.
3. The chances of someone being male where I live is 49%.
What is the probability of me detecting a lie in these conditions? Please can you include it into the formula to help me apply it?
English is not my first language and you still made it very easy :D
Rescheduling due to anything less than 99.5% proability of rain is for NERDSSSS
.48 is still less than likely, so I wouldn’t change my plans, but it’s still good to know the probability of such a thing occurring.
Likely to postphone but otherfactors like family and children force to go out. May go out for picnick
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.
Thanks for your videos. It helped a lot. Please do something on hypothesis. Thanks
Do you use the Python library called "manim" to create these beautiful animations for your great videos.
We humans do fear water than anything
Nobody likes a rainy picnic!
I would have liked if you incorporated dark clouds vs white clouds in the calculation.
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!
How you will connect prior and posterior terms with this?
legend
0:35 - I think this joke went over most people's heads 🤣
Seeing these comments bring me some comfort and some fear
Thank u for getting me
good sleep
This was very helpful am taking statistics class and was so lost. Thanks
honestly u did better job than many others
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!
Mesmerizing awesome for beginners
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.
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?
Did the video used manim
So you telling me some dude form the 1700 made our lives this hard? 🤣🤣🤣
Bayes' in a nutshell: (what you're looking for)/((what you're looking for + not what you're looking for with the same condition)).
What you're looking for goes in the numerator and the denominator. The only tricky bit is what you add to the denominator. That's whatever has the same condition as the thing you're looking for.
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
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 🙊
Great videos man they help a lot
Thank you so much! I appreciate it!
OMG I do not understand this!!!!!! I am failing my Statistics class!
So why would i tap the like and subscribe before i even watch the show? What do you think is the probability of me doing that?
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!
This should not be confused with the old bays theorem, which states old bays seasoning tastes good on everything.
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.
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 🙄
Thanks for the concept ☺️ I think I will try to reschedule 😅❤
cancel the picnic , instead go for lunch at a restaurant
I'm on board with that! That sounds perfect!
That's so helpful ❤🤝
Why would i tap the like button before i watch this video?Why would anyone do that?
hi I want to ask so in this case what the addictional knowledge? the probability of beibg cloud?
thankkkkkkkkkkkk youuuuuuuuuuuuuuu !
clearly understandable
Can we solve the same example by conditional probability?
On the last slide with example it should be “when it rains”, not where.
love your work man, keep up the good work!
Thank you so much for the support!
You did great. 👍🏻
This is the best RUclips video I've ever seen on bayes theorem I don't think I've ever understand bayes theorem as much as this before❤ 0.48 is not enough to make me cancel my picnic I think I will go for the picnic since it's 0.48% chance of rain 🌧️ ☔
It's 48% chance of rain.
How did u understand anything if you don t even know that 0.48 is 48%
this was great thnx for the example
Thank you so much for this vid man, your method of explanation was impressive
It indeed helped ! appreciate it gentleman
Great, I'm so glad! Thanks for your support!
Thank you for creating this theorem, Bae 😍
Thank you NRI ❤
you really aced it
I would proceed with the picnic only if I do not see clouds.
That's great when the example gives what P A|B is
Amazing video!! thank you:))
yuh i'd reschedule