Bayes' Theorem, Clearly Explained!!!!

Bayes' Theorem is the foundation of Bayesian Statistics. This video was you through, step-by-step, how it is easily derived and why it is useful.
For a complete index of all the StatQuest videos, check out:
statquest.org/video-index/
If you'd like to support StatQuest, please consider...
Buying my book, The StatQuest Illustrated Guide to Machine Learning:
PDF - statquest.gumroad.com/l/wvtmc
Paperback - www.amazon.com/dp/B09ZCKR4H6
Kindle eBook - www.amazon.com/dp/B09ZG79HXC
Patreon: / statquest
...or...
KZbin Membership: / @statquest
...a cool StatQuest t-shirt or sweatshirt:
shop.spreadshirt.com/statques...
...buying one or two of my songs (or go large and get a whole album!)
joshuastarmer.bandcamp.com/
...or just donating to StatQuest!
www.paypal.me/statquest
Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter:
/ joshuastarmer
0:00 Awesome song and introduction
3:05 A note about notation
5:21 Deriving Bayes' Theorem
9:12 Why Bayes' Theorem is useful
11:39 Another note about notation
#StatQuest #Probability #Bayesian

[@statquest]

Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

[@25BDominique2021]

I just ordered mine. It should be here tomorrow 🥳🎉

[@statquest]

@@25BDominique2021 BAM! :)

[@veeek8]

Just did! Because you are a genius and I finally understand Bayes Theorum!

[@statquest]

@@veeek8 HOORAY! Thank you very much! :)

[@rudraksh111]

Grateful to your animation team kudos to you and your team . You are basically changing the way school and education system worked for more than 150 years.😊😊

[@alexcastillo8507]

Can’t believe I bought three books to figure out what was show to me in two KZbin videos. Fantastic job good sir. Love the content and just became a subscriber.

[@statquest]

bam!

[@txreal2]

I minor in math in college 20 hrs ago and forgot almost everything. This channel makes everything so simple. Thanks Josh!

[@statquest]

@@txreal2 Thank you!

[@hemm2333]

One of the best key points to take is the longer form of representation of conditional probability. Never seen this explained in such great and easy detail than here. The longer notation makes everything so easy and simple to understand. You've a great talent to make the subject easily comprehensible for everyone. No other video in KZbin has put this concept in such a simple way to understand. Thanks & Triple Bam....❤

[@statquest]

Thank you very much! :)

[@johnwig285]

Josh...you have no idea how life changing ur channel is in my journey of exploring data science

[@statquest]

Thanks!

[@hannaabe5188]

one stat quest video a day keeps the failures away! Thanks Josh for the awesome content as always :)

[@statquest]

Thank you!

[@mastadodo]

I really like your videos so far, you are explaining everything enough in detail without making the videos longer than necessary. The clean animations and speaking are also godsent!

[@statquest]

Thank you!

[@riorvall]

Just yesterday I was looking to refresh my knowledge on Bayes theorem when I saw this video appear on my feed. Thank you StatQuest! Best way to learn and review statistics!

[@statquest]

Thank you very much! :)

[@akashkewar]

I am an Indian and I love soda, but I love StatQuest more

[@statquest]

Triple bam!!! :)

[@THEMATT222]

@@statquest Noice 👍 Doice 👍 Ice 👍 you BAMed Throice 👍

[@user-ij2um2oj7g]

Thank you! I didn't understand Bayes while I was studying in high school. Now I understand it! Your explain is so clear!

[@statquest]

Glad it helped!

[@reakal7740]

Right on time 😊 I started studying conditional probability and Bayes' rule just yesterday! Thanks StatQuest!!

[@statquest]

bam!

[@bin4ry_d3struct0r]

This is a much more intuitive explanation of Bayes' Theorem than the one I first learned with terms like hypothesis, evidence, prior and posterior.

[@statquest]

Thank you! :)

[@danief929]

You are amazing! I was not understanding Bayes theorem no matter how I look at and now, after watching the video, I completely understand

[@statquest]

Glad it helped!

[@nemeziz_prime]

Your explanations and animations are simply BRILLIANT 😍

[@statquest]

Thank you!

[@OwenMcKinley]

Thank you, Josh! An excellent 'Quest, indeed 😊

[@statquest]

Glad you enjoyed it!

[@shae6557]

I was struggling to understand Bayes Theorem in my biostats class and this video explained it so well. Thank you Josh!

[@statquest]

Thanks!

[@HeyRemy]

That intro is worth the price of admission alone. Thank you for making this; just subscribed!

[@statquest]

Awesome! Thank you!

[@txreal2]

I minor in math in college 20 hrs ago and forgot almost everything. This channel makes everything so simple. Thanks Josh!

[@statquest]

Thank you very much! :)

[@gyulboxing]

I believe your videos on KZbin could make great substitutes for many of stats course content in universities around the world!

[@statquest]

Thank you!

[@veeek8]

Agreed!

[@kwstantinaparadisopoulou7569]

This is the best channel for data science!!

[@statquest]

Wow, thank you!

[@ankithguzz]

I have been waiting for your video on Bayes theorem! So excited :)

[@statquest]

bam!

[@katka7634]

After this video, I wouldn’t say I understand because this is the first time I dove in this topic, but now I certainly have the idea and I’m fascinated! Great video

[@statquest]

Thanks!

[@misterbennnn]

I went headfirst into a grad school cryptography class with zero knowledge of anything math related past high school, and this has helped me out a lot. Thank you!

[@statquest]

Good luck! :)

[@josevaldes7493]

I´m a statistics student from Colombia and I want to tell you Your channel is awesome man. keep it this great job. Thank you. again Googleplex BAM!

[@statquest]

Glad you like StatQuest!!!

[@SaintSaint]

Wow. Thank you so much! I'm not doing anything with Bayesian probability.... but this was so good I had to watch it through! Subbed. I knew how to get a degree of belief and check it... but I didn't know WHY until your video and the "why" is so important.

[@statquest]

Glad you enjoyed it!

[@szemingkoi6927]

thank you, Josh! always had a hard time with stats and bayes' theorem

[@statquest]

Glad I could help! :)

[@user-hv2fr4ec8m]

Greetings from Brazil. You are simply a legend, mr. quest. Love the content and the dorky intros! Thank you for everything! ❤

[@statquest]

Muito obrigado!!! :)

[@koryhardcastle81]

I started this video and instantly jumped to subscribe. I love stats and you are the BEST at teach stats! Had to come back and comment just to make sure you know it :)

[@statquest]

Thank you so much! :)

[@yiangseng]

Unbelievably amazing. Thank you very much for making this channel.

[@statquest]

Thank you! :)

[@theFriendlyGhst]

You're notes about notation really helped me. I think that's where I got confused before seeing this.

[@statquest]

bam!

[@AkshatKalra-gw5cx]

Everyone should watch your videos, loved this derivation of the Bayes theorem ! I wish I'd find you sooner.

[@statquest]

Thanks!

[@johnbarbuto5387]

I'm not a fan of the "bam" technique; but, in my opinion the explanation is actually clearer, and more easily connected to real-world examples, than other videos which seek to explain Bayes' Theorem. Thank you! (Liked and subscribed. Will be looking at other videos of StatQuest.).

[@statquest]

Thank you, but brace yourself for a whole lot of bams! ;)

[@akagordon]

I really like where this is going.

[@statquest]

bam!

[@johnjamesbaldridge867]

Quadruple BAM!

[@tijmentans5174]

rn studying already really long, but your videos make it doable. Thanks

[@statquest]

You got this!

[@adeoyeoladipupoibrahim3066]

You are great. You are really helping build a great future for a lot of people

[@statquest]

Thank you! :)

[@fernunez2131]

This videos help me a lot to understand the concepts, and then when I read the 'technical' definition I don´t get scared. DOUBLE BAM!

[@statquest]

BAM! :)

[@TheRonakagrawal]

Don't know how many ppl relate to it.. but unnecessary optimisations to notations has really screwed up the learning/understanding of concepts. A concrete example is @03:08 This was so spot on!!!

[@statquest]

bam!

[@auzaluis]

Only God knows how much I love this channel

[@statquest]

bam!

[@Iron-Bridge]

I wish you were my lecturer in school and uni. Your material and presentation is that good 👏

[@statquest]

Thank you! 😃

[@RO-gf7je]

You are a blessing to humanity!

[@statquest]

Thanks!

[@PhuongLe-gg4ge]

Easy to remember and understand. Thank you so much !!!

[@statquest]

bam!

[@joaomcarmo]

This might be one of the best things on YT.

[@statquest]

Wow! Thank you very much! :)

[@sdsa007]

another brilliant insightful tutorial, perfectly memorable!

[@statquest]

Thanks!

[@pedrazzinig]

The "slightly" redundant notation is very important and I do agree that it deserves to be there/used. And, the/your explanation is excellent. Thank you.

[@statquest]

Thank you!

[@nickfountain-jones5853]

This is a great intro to the topic!

[@statquest]

Thanks!

[@FengyuanHu]

Dear Josh, your videos are super fun to watch and learn as well as your book, hope you have a chance to revisit the idea of making a series of Bayesian Statistics in 2024. Triple KUDOs to you.

[@statquest]

That would be awesome!

[@nikitasinha8181]

U sing really well brings smile on face before setting mood for lecture

[@statquest]

Thank you!

[@JuanBretti]

Josh, as usual... Great explanation!

[@statquest]

Thank you very much! :)

[@whateew]

Studying philosophy of probability, this vid was a massive help for understanding logical theory type stuff !

[@statquest]

Thanks!

[@profh9382]

Beautifully explained, finally, I get Bayesian. Bam 💥 💥

[@statquest]

Hooray!

[@jonathanbernardo3833]

Josh!! Thanks a lot, I love your videos :) Please show us the hypothesis testing in Bayesian perspective. Looking forward to more videos with Bayesian statistics.

[@statquest]

That's the plan. Unfortunately I have to write a book on machine learning first. However, as soon as finish the book I'll do a whole series on Bayesian statistics.

[@jonathanbernardo3833]

@@statquest double bam!! Looking forward for your book also

[@LQNam]

@@statquest Reveal something about your book, please!

[@statquest]

@@LQNam I've got about 70 pages done, and in two weeks I'm going to work on it full time until it is done.

[@The_Bri_Cli]

Hey Josh. This is a great video. You and Brandon Foltz should collaborate. Suggestion: A video applying Bayes Theorem to a continuous dataset would be very interesting.

[@statquest]

I hope to do a full series on Bayesian Statistics as soon as I can.

[@laurelhiatt3398]

Thank you for this and all of your many spectacular videos. I was wondering if you could do a StatQuickie or other such video on z-scores if you don't already have one available?

[@statquest]

I'll keep that in mind.

[@elizabethelson1124]

Your explanation is easily understandable..thank u so much 👍👍👏👏😁

[@statquest]

Thanks!

[@sherriwyatt]

I LOVE this channel:) THANK YOU!

[@statquest]

Glad you enjoy it!

[@oliveros9]

This is the best explanation on Bayes' Theorem ever! However, It is so difficult for me to use the kind of basic examples that ilustrates the theorem, for the particular task of analyzing differential gene expression between samples. There are available several "bayesian methods" to analyze gene expression changes and I can not understand the relationship of these methods with the theorem's formulation based on conditional probability. I am looking forward to see the upcoming videos on the subject. Would you please dedicate some of them to such practical applications of the Bayes' theorem? Thanks a lot!

[@statquest]

Yes, that's the whole idea of Bayesian Statistics and that is what I want to cover in the follow up videos. Unfortunately I have to write a book about Machine Learning first. However, as soon as that is done I'll make the videos about Bayesian Statistics.

[@sumailsumailov1572]

My God, this is amazing content! Need more views!

[@statquest]

Thank you! :)

[@exoticcoder5365]

12:35 it’s tricky, meaning the same thing but with different words, thanks Josh for making it clear

[@statquest]

Thanks! That was probably the most confusing part of Bayes' Theorem when I learned about it on my own.

[@nuwantattygalle5645]

undrestood "BAM" context meaning after watching 5 videos. your videos are super super helpful. thankyou and please keep up. please consider including an example scenario for one sided statistical test

[@statquest]

Thanks!

[@brucekang6474]

I love you man. you saved my life.

[@statquest]

thanks!

[@mohammedfazalkhattal576]

Very good explanation Josh 👍

[@statquest]

Glad you liked it!

[@harziraaa]

so so clear explanation! subscribed!!!!!

[@statquest]

Thanks and welcome!

[@teja_surya]

Great explanation StatQuest 😃. Thanks Josh. Bam!

[@statquest]

Glad you enjoyed it!

[@marvinbcn2]

Excellent video as usual. May I make a wish: would it be possible that you made a video about bayesian vs. frequentist statistics? Every now and then I stumble about this antagonism, but explanations are often kept on a very abstract level. It would be great if you could give a case study which exposed the different (and incompatible?) conclusions these methodologies come to.

[@statquest]

Great suggestion! I hope to do it soon.

[@ellieeeee615]

Great video, thank you so much!!!

[@statquest]

Glad you enjoyed it!

[@elliotyip9844]

Small bam? No. TRIPLE! Thank you for explaining the logic behind Bayesian statistics so clearly.

[@statquest]

Hooray! :)

[@Emundadhu]

Bam is back

[@statquest]

yep! :)

[@jahndoe679]

what is this! this is the most clear explanation! thank you!

[@statquest]

Glad you think so!

[@brihatsharma3452]

Great explanation josh 👍👍

[@statquest]

Thank you!

[@user-or7ji5hv8y]

Lots of great insights.

[@statquest]

Thanks!

[@hemesh5663]

Hands down best channel❣️

[@statquest]

Thank you!

[@hemesh5663]

@@statquest I should be the one thanking you, you are absolute legend, literally I am not lying, I have never seen a lecture as clear as this and thank you for this service.

[@statquest]

@@hemesh5663 bam! :)

[@mikaelbergman2093]

Josh, you need to make hoodies and T-Shirts with Statsquach on. It wold be wery funny!

[@statquest]

That's a great idea!!! YES!!!! If I do, I'll send you one. BAM! :)

[@mn.v.3447]

Duuuude, i want one

[@nonamenoname1942]

Sorry, I prefer... TRIPLE BAM!!!

[@joelduranB52441]

Me encantan sus videos. Saludos desde Costa Rica!

[@statquest]

Muchas gracias!!!

[@badrinathsvn8634]

Today on wards, I am going to be one of your virtual students through out my life...

[@statquest]

bam!

[@tamuman93]

@Badrinath SVN - I see what you did there. Clever ;)

[@nonameneeded7996]

you are the best! now im going to BAM the subscribing button

[@statquest]

Wow, thanks!

[@lashlarue7924]

You are such a great teacher. Any uni should be bending over backwards to put you on tenure track just for the clinical brilliance alone.

[@statquest]

Maybe one day!

[@charlesrambo7845]

I'm looking forward to more Bayesian statistics videos :-)

[@statquest]

Me too! Unfortunately I have to write a book on machine learning between now and then....

[@ad2181]

Thanks for showing the omission in the equation.

[@statquest]

bam!

[@yashvora3099]

Great video. Struggled to understand this all my life. I am from India and we LOVE soda.

[@statquest]

BAM! :)

[@wolfywolfgang2498]

I needed this , hope you talk about natural language processing , I cant find any good resource

[@statquest]

I hope to soon.

[@kwok603]

Wonderful, wonderful, wonderful!!!

[@statquest]

Many thanks!!

[@somdeepkundu2506]

Thank you so much professor ♥️🙏

[@somdeepkundu2506]

Sir, i like to learn about AI, I'm not a very good student.. where to start..?

[@statquest]

Thanks! If you want to learn more, just pick a topic and this map will tell you where to start: app.learney.me/maps/StatQuest

[@escape0707]

At 3:05, I immediately endorsed the video and went to watch the previous video.

[@statquest]

BAM!

[@GoddamnAxl]

I know this might be a new viewer thing, but BAM definitely makes bayes theorem more clear to me

[@statquest]

bam! :)

[@diegobuenovillafane869]

Your videos are the best!! One question relatively unrelated... What software do you use for your videos?? THANKS!!!

[@statquest]

I answer that question in this video: kzbin.info/www/bejne/maOviX19Yqp0ns0

[@eddpalenciavanegas6739]

I watch your videos just for the fun of it hahaha.... Awesome content!

[@statquest]

bam! :)

[@Mars7822]

Brilliant as always.....

[@statquest]

Thank you!

[@Lemurai]

Statsquatch 😂😂😂boy I have to take my hat off to this guys creativity.

[@statquest]

Thanks!

[@hamman_samuel]

Waiting for those StatSquatch t-shirts 😁

[@statquest]

They are in the works!!!!

[@dipankarmandal9442]

Thank You so much.

[@statquest]

Welcome!

[@JohnLegaspi-bl3wu]

Thank you! This helped me understand generating artificial data :D

[@statquest]

Bam! :)

[@shillawolf4686]

I have an exam tomorrow and there is a big chance this is comming back and i didn't completely get is so this really helped :D

[@statquest]

Hooray! Good luck with your exam! :)

[@shillawolf4686]

@@statquest Thank you sir, your videos were a great help to me and other students from my course ^^

[@shillawolf4686]

@@statquest Good news, i passed :D With a 6/10. There were a few questions in there about random forest and PCA etc, and i was able to clearly explain it thnx to your videos. I now have machine learning and your videos are agian a great help. You channel trully is a gold mine for people who need to learn statistics ^^

[@statquest]

@@shillawolf4686 Congratulations!!! Triple BAM!

[@rjeption]

watching this before my stat final... wish me luck!

[@statquest]

Good luck! :)

[@EVERYTHIN_007]

You are a legend.❤️ from India

[@statquest]

Thank you!

[@Theakaiproject]

Top notch professor!!

[@statquest]

Thank you!

[@tirsapambayun3539]

Thank you so much

[@statquest]

bam!

[@sandeepsingh-ly9nh]

Watching statsquest is like quench your thirst with glucose water. ✌️✌️

[@statquest]

bam!

[@ashleyibarra4927]

I LOVE STATQUEST!!!!

[@statquest]

Hooray! :)

[@chadx8269]

Excellent. Thank for clearing up the P(A!B) should be P(A&B!B). This has confused me for years. I would drop in "given" and replace it with "in". P(A!B) becomes P of getting an A in the domain B.

[@statquest]

Noted

[@dlsgaming18]

Dude how do you do this? You save my nearly 50 hour of time.

[@statquest]

Thanks!

[@anuragguptamr.i.i.t.2329]

LOVED IT.

[@statquest]

Thank you! :)