Maximum Likelihood, clearly explained!!!

Рет қаралды 1,377,477

Күн бұрын

If you hang out around statisticians long enough, sooner or later someone is going to mumble "maximum likelihood" and everyone will knowingly nod. After this video, so can you!
Also, some viewers asked for a worked out example that includes the math. Here it is! (you may need to click on the "Show More" button below to see the link) • Maximum Likelihood for...
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0:00 Awesome song and introduction
0:34 Motivation for MLE
1:12 Overview of the Normal Distribution
2:06 Thinking about where to center the distribution
3:25 Using MLE to find the optimal location for the center
4:27 Using MLE to find the optimal standard deviation
5:19 Probability vs Likelihood
#statquest #MLE

Пікірлер: 1 200

@statquest 2 жыл бұрын

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

@rubberlung1 5 жыл бұрын

It is just ridiculous. I paid several thousands USD to my college and end up at getting better education in youtube.

@statquest 5 жыл бұрын

I'm glad to hear this video helped you out! :)

@bharathbhimshetty8926 5 жыл бұрын

But some companies are asking for certifications...damn

@prizmaweb 5 жыл бұрын

It is because I paid several thousand USD for my masters but still felt my education was outdated, that I still come and watch youtube for more ( to sort of recover my investment)

@CRockaell 5 жыл бұрын

no kidding... same here!

@xj-vn4eo 5 жыл бұрын

Getting to college makes me appreciate more of the internet resource.

@Swisspokerboy 6 жыл бұрын

Sometimes I think professors make it extra hard for their students at University by explaining simple things as complicated as possible.Luckily there are guys like Joshua. Great video!

@Quasarbooster 3 жыл бұрын

Kevin H. I couldn't agree more. Thanks Stat-Quest!

@VeganSemihCyprus33 3 жыл бұрын

The untold secret to civilization (a lecture): kzfaq.info/get/bejne/braBZ9an2afKnX0.html

@keronnicholson8313 3 жыл бұрын

I have always said I think the 'community' tries to remain as small and closed as possible by making it hard for people to understand.

@kwartemaaa773 2 жыл бұрын

They themselves do not understand

@MJ-ye7dd 2 жыл бұрын

@@kwartemaaa773 I also think so

@jc_777 3 жыл бұрын

This video has helped distressed students who are awake at night all around the world for over 3 years .... and counting. Joshua can make a religion for students & grad students and it will become a major religion in no time. I mean, he's literally "Joshua". The Holy Book will be named "StatQuest".....

@statquest 3 жыл бұрын

@siddheshzadey9714 4 жыл бұрын

You're a statistical outlier when it comes to teaching! Above 100 SDs on the scale of teaching goodness :)

@statquest 4 жыл бұрын

I love this! Thank you.

@jc_777 3 жыл бұрын

Agreed. It's almost as if college stats professors have some kind of coalition for teaching badly, and somehow Josh wasn't invited.

@kyledampier Жыл бұрын

I literally applied to UNC because of him

@joaoostrowski 5 жыл бұрын

From all statistics courses I've taken so far, I've never heard about the difference between likelihood and probability. As we can expect from any StatQuest, it was clearly explained. Thank you Josh, cheers from Hungary!

@tiankhean 3 жыл бұрын

I just want to tell you how much I appreciate your videos. I am a 74 year old retiree living in Singapore doing time series analysis of financial markets data using NumXL software. For the first time, I understand Maximum Likelihood Estimation. I have signed on as a Member and hope to learn more by watching your unique so-clearly-explained videos. Thanks again.

@statquest 3 жыл бұрын

Wow! Thank you very much for your support!!!

@vishalthakran1743 3 ай бұрын

bro,you just need to chill at that age!!!!

@kellenswain2049 5 жыл бұрын

The "Large-Boned" was priceless. Well done.

@statquest 5 жыл бұрын

Hooray! :)

@snake1625b 3 жыл бұрын

The distribution is bulking

@andrewd1788 3 жыл бұрын

no doubt some people will think that's the actual term for it and will write "large boned" in their coursework lol

@rebelai5981 Жыл бұрын

🤣🤣🤣🤣

@herobrine1847 2 ай бұрын

I totally thought I was misreading it and assumed it was “large bound” before taking my glance off of it… holy shit he actually said it

@mohsenr.estabraq5808 3 жыл бұрын

Whenever I get confused reading Statistics books, I come here. Thanks!

@statquest 3 жыл бұрын

Happy to help!

@morningmoon6100 3 жыл бұрын

If you can explain a concept with simple tools, it means you really understand it well, else you are just memorizing ! You are doing a great job !

@statquest 3 жыл бұрын

Noted

@pluetsy2324 4 жыл бұрын

the intro made my day man.I have a shit tone of assignments and i am low on time so really that little guitar gig made me smile.Also great work on the explanations.KEEP it up!!

@statquest 4 жыл бұрын

Thanks and good luck with your assignments. :)

@bennasserchafi304 6 жыл бұрын

you deserve an oscar. i have been struggling for years to understand this thing. and you came from nowhere and explained it in such an easy and beautiful way. i really think you.

@matthewjung5446 3 жыл бұрын

First time on your channel, the intro had me questioning what I was doing. I am eternally thankful I stayed until the end! Cheers mate, great content.

@statquest 3 жыл бұрын

Thanks! :)

@iamgroot3834 4 жыл бұрын

I spent the whole day trying to understand this. Its just now that i found your video on youtube. GOD BLESS YOU. You are greaaattttttttttt.

@statquest 4 жыл бұрын

Hooray! :)

@nimishabunga 3 жыл бұрын

You have made statistics so much better and easy for people like me (who have been avoiding it for so long) , Thankyou ❤

@statquest 3 жыл бұрын

You’re welcome 😊

@fatsquirrel75 6 жыл бұрын

I sat through a 3 hour stats lecture earlier today and had no idea what he was talking about. Thanks to your 6min video actually learned something about likelihood functions today (and it turned out to be so straight forward too). Thanks.

@stylyxmephix2365 24 күн бұрын

Bro wtf this is the revolutionary. This is amazing. Thank you for sharing your knowledge. You made something so clear in six minutes. I am deeply impressed. May fortune be with you.

@statquest 24 күн бұрын

Thank you!

@user-up5kh2mz4n 4 жыл бұрын

The enthusiasm in the video makes the learning experience more motivating!

@statquest 4 жыл бұрын

Thanks! :)

@Latesttechs 3 жыл бұрын

I am doing my Masters in Informatics right now and I feel bad I didn't find you during my Bachelors lol would have cleared so many concepts years ago but better late than never God bless you dude lovely precise explanations to brush up on things and understand them.

@statquest 3 жыл бұрын

Thanks!

@sintumavuya7495 7 ай бұрын

I loved this. You have no idea how I needed this. We just started this chapter this week and just knowing what it is that I'm trying to do is really calming. Now I can listen with understanding.

@statquest 7 ай бұрын

Thanks!

@ThinkingRockh 6 жыл бұрын

Gold content. Can't find anyone on KZfaq really try to explain the phrase "maximum likelihood". Thank you so much!

@fransdany2452 4 жыл бұрын

Sir Josh, you have no idea how helpful your explanations are in your videos. Waaay better and clearer than available statistics textbooks and lecturers. I am wondering if you can make other videos regarding difference between maximum likelihood vs penalized likelihood and the application of penalized likelihood in Firth's Logistic Regression (as well as its interpretation). I encounter a quasi-separation problem after running binary logistic regression while the sample size is not that small (~1800). Any thoughts will be highly appreciated. Best regards

@theq18 4 жыл бұрын

I wish I saw your video 10 years ago during graduate school. I finally understand the maximum likelihood! THANK YOU!

@statquest 4 жыл бұрын

Better late than never! :)

@CainisUponUs 6 жыл бұрын

Such amazing timing! One of my mathematically inclined friends just told me that we could use maximum likelihood to determine how many times I had to conduct an experiment to produce a statistically significant result, but I had no idea what she was talking about till I saw this!

@TheFartoholic 7 ай бұрын

I've been looking for a straightforward approach to explaining this concept - you've provided the perfect blueprint. Thanks!

@statquest 7 ай бұрын

Thanks!

@CocaBrunel Жыл бұрын

Wow! You litterly nailed it first sentence. 'Why' seems to be the most difficult question to ever face statisticians. I've read an entire textbook and still been unable to grasp, Why at an intuitive level. " it's the optimal way to fit a distribution to your data" job done. Thankyou so much.

@statquest Жыл бұрын

Thank you! :)

@lanxizhang2816 4 жыл бұрын

Best teacher in the world! Even English is my second language, I can understand you easily.

@statquest 4 жыл бұрын

Hooray! :)

@joohokim5257 6 жыл бұрын

Very intuitive! I've never found this kind of clear explanation on any other stats textbooks. Thank you! If there's a chance, I'd like to watch a video on Generalized Method of Moments (GMM).

@geraldidzakwan8666 4 жыл бұрын

You saved my life, best plug in principle explanation I've ever watched. I need this to solve a best estimator problem for some probability density function.

@statquest 4 жыл бұрын

I've got a few examples of how to use MLE to estimate the best parameters. Here's an example for the exponential distribution: kzfaq.info/get/bejne/ppmEYMJ9stjacpc.html and here's an example for the normal distribution: kzfaq.info/get/bejne/etRmlZyXqK-5oIE.html

@burninmind 3 жыл бұрын

WOW! it was literally the best explanation of MLE I've ever seen! Well done!

@statquest 3 жыл бұрын

Wow, thank you!

@rameshmaddali6208 5 жыл бұрын

Best thing i found for this week, so clear to understand - lots of appreciation for your lecture.

@statquest 5 жыл бұрын

Thank you! :)

@ElinaGoroshkova 5 жыл бұрын

You make the best videos on statistics. Thank you so much! After your videos I would like to study statistics and data analysis further and further! )))))LOL! And I'm 35 years old woman, and just trying to figure out a few concepts for an IRT course. Very interesting and thank you very much for your genius work!

@tiredkiris 6 жыл бұрын

I don't know how to thank you but this explanation really helps me understand what I'm reading elsewhere. I really appreciate the work and thought you put into teaching us an intuitive approach.

@statquest 6 жыл бұрын

You're welcome! I'm so happy to hear that the video was helpful for your understanding.

@teetanrobotics5363 4 жыл бұрын

I think you're the king in machine learning and statistics on KZfaq. Could you please make a playlist for deep learning as well ?

@statquest 4 жыл бұрын

I'm going to make deep learning videos in the next few months.

@bhumikasoni361 Жыл бұрын

If not a teacher, you could very easily be an awesome songwriter and singer! But, as the luck would have it, you blessed us with the best statistics videos instead :D Thanks Josh for such clear explanation :)

@statquest Жыл бұрын

Thanks!

@dr.ksartplace3785 5 жыл бұрын

Subscribed! I’m so glad I found this channel. I struggled with stats throughout college. To the point that I gave up on the field and avoided it as much as I could. Watch out statisticians. I’m back with “vengeance” to devour this field. :-) Seriously! Thanks for putting these videos together. Highly informative.

@statquest 5 жыл бұрын

Awesome!!!!

@estefaniac8260 5 жыл бұрын

Thank you so much, your explanation was clear, detailed and concise. Exactly what I needed. Your graphic explanation was awesome!

@sherifgerges9316 6 жыл бұрын

Excellent.

@cloveramv 4 жыл бұрын

4:53 BAM!

@ericosa7002 4 жыл бұрын

I am to see your effort of this platform &an excellent videos , please can you show me how R software to teaCh these statistical inference theories

@kallehallden4855 3 жыл бұрын

So in essence the type of distribution is determined by Goodness of Fit and the parameters of distribution are determined by Maximum Likelihood. Thank you professor.

@srishtisingh2170 3 жыл бұрын

Every time I see a video here, it makes me fall in love with statistics a little more...❤️

@statquest 3 жыл бұрын

Wow, thank you!

@ravish6280 5 жыл бұрын

Quality content... short video... no crap talk.... i like it. Keep it up !

@Daniel-to5jd 5 жыл бұрын

best explanation of this topic that I have found so far

@jedidelalog9834 5 жыл бұрын

Wonderful video!! and I spent a lot of time to understand a "silly" formula when it would be enough to see your beautiful video :)

@statquest 5 жыл бұрын

Thanks! I'm glad it was helpful. :)

@Sabu113 4 жыл бұрын

This is so refreshing. I just had to take these things as 'given' in my econometric course.

@statquest 4 жыл бұрын

I'm glad my videos are helpful! :)

@harshalpimple3143 Ай бұрын

Thank you so much Joshua for this uniquely-explained video!!!

@statquest Ай бұрын

Thank you!

@rockerjatt 6 жыл бұрын

Mr. Starmer, may I request for a video on MAP (maximum a posteriori) inference? Subsequently, a comparison of MLE vs MAP will also be extremely helpful

@scottgrenestedt9983 Жыл бұрын

Very intuitive. Phenomenal explanation, Mr. StatQuest :)

@statquest Жыл бұрын

Glad you think so!

@archowdhury007 4 жыл бұрын

Excellent video....loved the way you explained it. FINALLY!!!!! I understood what MLE actually means. Great work Josh! :)

@statquest 4 жыл бұрын

Hooray! :)

@BillHaug 2 жыл бұрын

needed a refresher on the concept, was rewarded with the jam... still crushing.

@statquest 2 жыл бұрын

bam!

@MySimpleMe 6 жыл бұрын

This was so necessary and brilliant! Thank you so much!!

@aimeecalepso 4 жыл бұрын

Every time I listen to the intro I can imagine Phoebe singing it. Thanks for the explanation, your channel is the best I found about statistics on youtube and it's helping me analyse results for my thesis

@statquest 4 жыл бұрын

Awesome! If this intro song reminds you of Phoebe, check out this one: kzfaq.info/get/bejne/epaVmat2r9nKeKM.html

@AliAPanahi 6 жыл бұрын

Wow, The simplest explanation I've seen.

@FREELEARNING 3 жыл бұрын

Excellent explanation, I think with all these simplified and clear explanations of many statistical concepts, You may consider making a book that can organize all the wonderful content with all the beautiful illustrations.

@statquest 3 жыл бұрын

Great suggestion!

@abc39722 3 жыл бұрын

Thanks a lot, brother. Ur videos are really easy to follow and comprehensive too.

@statquest 3 жыл бұрын

Thanks!

@grigoryshepelev8149 5 жыл бұрын

Thank you a lot! I'm passing an online course on statistics that has NONE simple graphical representation of terms and teacher always looks at his papers. This sucks. But at least it has some structure on the subject.

@statquest 5 жыл бұрын

Hooray! I'm glad the video is helpful. :)

@koochibabua1904 4 жыл бұрын

Same with me. My course is on Bayesian statistics. The instructor foolishly copies from his notes by looking down all the time.

@NitishPareek 5 жыл бұрын

There could not have been a better explanation of this topic.

@statquest 5 жыл бұрын

Thank you!!!

@MLDawn 6 күн бұрын

I really enjoyed your terminology alert! Good catch!

@statquest 5 күн бұрын

Thank you very much! :)

@karimnaufal9792 4 жыл бұрын

Damn, you know how to sing!!! Love the guitar too :) Thank you, great explanation! I would love to have a Stat Quest on Group Sequential Testing (as opposed to Fixed sample size testing, my interest is in A/B testing)...

@rodrigoos3 4 жыл бұрын

Simple and clear, as it should have always been! Thanks ALOT!

@statquest 4 жыл бұрын

Thanks! :)

@cantkeepitin 5 жыл бұрын

Great explanation. However, from watching to doing is still a big step. I can recommend everyone to also do the calculus, really getting numbers. Maybe for a uniform distribution, having no difficult formulas, like the "normal" distribution has.

@statquest 5 жыл бұрын

I've got a few examples of the calculus in action for the binomial distribution: kzfaq.info/get/bejne/arF7iZyqv6nTfWg.html for the exponential distribution: kzfaq.info/get/bejne/ppmEYMJ9stjacpc.html and the normal distribution (this one is long since the math is messy): kzfaq.info/get/bejne/etRmlZyXqK-5oIE.html

@andreajulieth100 2 жыл бұрын

this is the greatest explanations that I found in all google search great job Josh

@statquest 2 жыл бұрын

Thanks!

@carloschire5777 Жыл бұрын

Thank you, very clearly. It was a good recommendation in a virtual class about Maths for Data Science, greetings from Peru

@statquest Жыл бұрын

Muchas gracias!

@TheDiklovones 2 жыл бұрын

No words to say 😊how easily you explained everything 🤠🤩

@statquest 2 жыл бұрын

Thanks!

@joeaustinathimala768 4 жыл бұрын

How the hell did I not know you before ? Excellent video. Kudos man.

@statquest 4 жыл бұрын

Thanks! :)

@ql8137 5 жыл бұрын

You made stats so easy! I wish I watched your videos back in college.

@statquest 5 жыл бұрын

Thank you! :)

@themlongplays4961 5 жыл бұрын

I feel like professors don't do a great job at bridging the gap between theory and practice especially in the later upper division stats classes so I end up knowing how to calculate things but I have trouble understanding why. That's why I love this video. Thank you!

@statquest 5 жыл бұрын

Hooray!! I'm glad the video was helpful. :)

@maurolarrat 5 жыл бұрын

In 3:33 and forward, in each step we calculate the product operator for all gaussian functions taking the data as input. The resulted product with the highest value will indicate which gaussian function to choose. am I wrong?

@statquest 5 жыл бұрын

I believe you are correct. At the first step, we have a gaussian function on the far left side of the screen - and to calculate the likelihood of that specific function (with the mean over on the left side), we calculate the product of the likelihood of that function given the first datapoint times the likelihood of that function given the second data point times the likelihood of that function given the third data point, etc. Then we shift the distribution to the right a little bit and calculate the same product using the new mean, etc. Until we find the mean that results in the largest product.

@maurolarrat 5 жыл бұрын

StatQuest with Josh Starmer Thank you very much.

@statquest 5 жыл бұрын

Hooray! :)

@andreyko3yrev 5 жыл бұрын

When you say "probability or likelihood" you effectively make these terms mean the same thing, while the whole point is that they are different.

@TheFKPM 5 жыл бұрын

Love you Josh! This is how concepts should be taught

@statquest 5 жыл бұрын

Thank you so much!! :)

@haleemaghafoor2147 3 жыл бұрын

LOVE THE WAY YOU EXPLAINING THE CONCEPT

@statquest 3 жыл бұрын

Thank you! :)

@awfominaya 5 жыл бұрын

Finally clicked for me after years of trying to figure this stuff out.

@statquest 5 жыл бұрын

Hooray!!! :)

@aaronpedraza8974 3 жыл бұрын

Same case Adam, that's great!

@user-ll4cj2gl2v 4 жыл бұрын

I'm doing a masters degree and yet youtube is a better teacher

@statquest 4 жыл бұрын

Thank you! :)

@ruchitagarde4642 3 жыл бұрын

@StatQuest I have started making searches on your channel rather than on youtube search bar whenever I have a question. Please do something on Conditional Random Field (CRF). Amazing work!

@statquest 3 жыл бұрын

I'll keep that topic in mind.

@ondiekpaul3982 6 жыл бұрын

Wow.You just nailed it. Th explanation is vivid.

@SupremeChickenx 3 жыл бұрын

'large boned' HAHAHAHA this guy sounds 5% sarcastic at all times i love it

@statquest 3 жыл бұрын

@indieelectroworks 6 жыл бұрын

Great video. Keep up the good work!

@raoufzanati7532 6 жыл бұрын

Sir, thank you, your explanation is amazing

@pite9 4 жыл бұрын

I'm just here for the song intros.

@statquest 4 жыл бұрын

Awesome! :)

@spaceymchaggis1792 6 жыл бұрын

I just tune in for the intro ;)

@spaceymchaggis1792 6 жыл бұрын

Joshua Starmer And you're doing awesome. You videos have already helped me a lot with my work!

@spaceymchaggis1792 6 жыл бұрын

Joshua Starmer absolutely! Going through my books and R scripts can be quite dry and you videos provide another view onto certain topics. They are great!

@stekim 4 жыл бұрын

Thanks statquest, grad student here and this was clearer than what I get currently at school.

@statquest 4 жыл бұрын

Hooray!!! :)

@isaacadjetey9618 Жыл бұрын

Intuitive way of teaching yields better understanding than the so called “robustness “……Make concepts intuitive to me in simple terms and robustness will be nothing but mere usage of dense notations. God bless you StatQuest!

@statquest Жыл бұрын

Thank you very much! :)

@hellasleepypal 4 жыл бұрын

I can’t wait to present at a conference and use “large boned” without giggling

@statquest 4 жыл бұрын

That will be a funny day. :)

@Anonymous-54545 4 жыл бұрын

I would be really careful. Weight isn't a federally protected characteristic but we're getting there. I wouldn't joke about anything that alludes to demographical features of humans and/or their sensitivity about it (which is what "big boned" means-- euphemism for fat bc people are embarrassed to say they're fat) in academia. No one's going to care in a math dept / conference but if it's mixed field with undergrads there? Ehhhh.

@hellasleepypal 4 жыл бұрын

S. E. Z thank you for pointing that out I wouldn’t use big boned, I was just kidding. Loll

@VictorOrdu 5 жыл бұрын

Woah! Do they intentionally obfuscate this knowledge with all those formulae?

@statquest 5 жыл бұрын

That is a great question! It's not nearly as complicated as a lot of people make it seem.

@maxxpro4 5 жыл бұрын

yes

@ivomitdiamonds1901 5 жыл бұрын

Did you intentionally obfuscate this comment with the use of the word obfuscate? I think the answer to your question is the question itself. 1. You knew the word and understood and hence assumed that everyone else would. (The professors might do the same with the formulae.) 2. You just wanted to show off your vocabulary (The professors are human too.) Haha, just a thought, I know what you mean though. Cheers, Ani,

@waterspray5743 3 жыл бұрын

So weird. My textbook says nothing about MLE being the mean of the distribution. Why can't the authors just be clear and direct instead of making us read between the lines and figure out what they mean.

@prabhatgoelshanky3701 6 жыл бұрын

Best explanation of MLE, Thanks a ton.

@andersonbessa9044 4 жыл бұрын

Best explanation for maximum likelihood ever! Thanks so much

@statquest 4 жыл бұрын

Thank you! :)

@petretrusca2 4 жыл бұрын

You saved me, from the terrible explanation of my teacher.

@statquest 4 жыл бұрын

Bam! :)

@bigfriki 2 жыл бұрын

Weirdest intro ever, but well explained.

@statquest 2 жыл бұрын

@yashodperera 3 жыл бұрын

The best statistic tutorials from youtube. Thank you

@statquest 3 жыл бұрын

Wow, thanks!

@alexmihai649 3 жыл бұрын

I guess they're right...if you cannot explain it simply, you don't understand it well enough. Thank you for this video!

@statquest 3 жыл бұрын

You're welcome!

@alecvan7143 4 жыл бұрын

"or large boned"

@statquest 4 жыл бұрын

yessssssss! :)

@dilshand.5127 6 жыл бұрын

*Large Boned*

@herobrine1847 2 ай бұрын

Good video! I was personally looking to get a rigorous mathematical understanding of how MLE is actually carried out (points on the probability plot where the gradient is zero or something like that), but this is a great introduction to those who aren’t even sure what the term means.

@statquest 2 ай бұрын

If you would like to see the rigorous math behind MLE in action, check out these videos: kzfaq.info/get/bejne/ppmEYMJ9stjacpc.html kzfaq.info/get/bejne/arF7iZyqv6nTfWg.html kzfaq.info/get/bejne/etRmlZyXqK-5oIE.html

@amalluminati 4 жыл бұрын

Awesome work Josh ! Keep em coming

@statquest 4 жыл бұрын

Thank you! :)

@batman76781 5 жыл бұрын

What is the probability distribution of people who like the weird ass intro song the statQuest videos start with? It's distributed by Uniform(0,0).

@statquest 5 жыл бұрын

Dang....

@o.biertrinker9649 5 жыл бұрын

Aman, you are just an outlier among the smart people. But if you try hard maybe one day you'll touch the lower fence.

@pewpew7108 5 жыл бұрын

Very clearly explained, but man, the little intro songs are cringey

@statquest 5 жыл бұрын

@weixu553 6 жыл бұрын

always enjoy your videos, nice voice!

@rikawrites7104 25 күн бұрын

ABSOLUTELY ASTOUNDED BY THE WAY YOU TAUGHT ME THIS. thank yaaaa

@statquest 25 күн бұрын

Thanks! :)

@dpm2213 3 жыл бұрын

Did you go back to old vids and give your timelines subsections when that feature came out? What a legend.

@statquest 3 жыл бұрын

The feature came out a few months ago. I went back and added subsections to a bunch (but not all) of my old videos. It's something I do when I can't sleep at night.