Maximum Likelihood estimation - an introduction part 3

[@johncase9047]

I love twist endings.

[@Alumiss682]

Nearly 20mins worth of derivation only to find out that the estimator = sample mean. #econometrics

[@daniz0rz]

Right... I have an exam on Thursday for a categorical data class and this was never made clear in that class. And he wants us to be able to do this.... I was hoping for more practical applications (I'm an epidemiology major) than theory and derivatives. It's also quite likely I saw a ton of math and blacked out... XD

[@TheBjjninja]

I had a chuckle at the very end also.

[@mihaililiev5932]

LOL, I thought the same. Beautiful derivation but what's the point? But then... there must be something more to the MLE, right? Can Ben perhpas expand a bit more on why is MLE useful?

[@hamza_ME_]

@@mihaililiev5932 ​ I'm learning Artificial intelligence and I can tell you MLE is very useful in forming and working with some algorithms of Machine Learning...

[@lastua8562]

@@hamza_ME_ Good to know! I am starting a research master in economics and consider moving into AI later in case I should dislike writing research papers. Aside from logistic regression, are there any econometrics topics you are particularly recommending to learn for AI?

[@danthemangoman5931]

One hour of college class with 2 hours of tutorials and barely understanding what the simple terms mean to having a full understanding in this. You my friend, is a saint.

[@cliqclaq508]

I can't be the only one who loves it when a complicated function gets canceled out till it's really short. It's like those oddly satisfying videos.

[@pkoomson1]

I am happy i did followed this 3-part series on estimation of ML. Thank you Ben for making this clearer to me.

[@axelboberg9374]

in 10 min you explained MLE better than my text book! Thank you.

[@ovauandjahera8664]

True

[@mpgrewal00]

Many tutors on youtube fail to explain with a simple example. But you didn't do that, you are an Ace.

[@TheTorridestCheese]

Thank you very much for these videos. My statistics professor just breezes by these concepts and I really needed a much slower explanation and you helped a ton.

[@HankWank]

You are a gentleman and a scholar.

[@emielabrahams8475]

Ben Lambert - these videos were awesome. Well explained - thank you kindly

[@nature_through_my_lens]

Amazing. Got it in 15 mins... Watched all three videos at 1.25x. Thank you so much.

[@fmp000]

What a kick-ass video, Ben! You have no idea how much it helped me.

[@MrHugosky1]

Great class! Thank you very much Mr. Lambert. Greetings from Mexico

[@singhay_mle]

Beautiful explanation, i saw like 5 videos none were able to explain like you did..thank you!

[@ravideeplehri]

Thankyou for taking out time to post these wonderful intuitive video lectures

[@deansfa]

So well explained! Thank you very much for this three videos, it was very helpful!

[@0blivisi0n]

You are a rockstar Ben! Greatly explained!

[@SpartacanUsuals]

Hi, thanks for your message, and kind words. Glad to hear that it was useful. Best, Ben

[@alandubackupchannel5201]

Thanks for the video, great explanation. I wish lectures were this clear.

[@Becca01223]

Ben, you're the best. Thank you!

[@daattali]

Great 3-part video, so easy to understand (if you really pay attention and put some thinking into it), thank you!

[@robpatty1811]

Great video, thanks Ben.

[@cnaroztosun9402]

the "i" you wrote at 3:20 is perfect omg

[@askfskpsk]

Great explanation. Thanks Ben.

[@bend.4506]

Thank you! Enjoyed parts 1-3! VERY helpful!

[@pavybez]

Thank you for the clear and concise explanation.

[@pandeyprince25]

an amazing explanation ! you are savior

[@charlesledesma305]

Excellent explanation!

[@seineyumnam4374]

so why aren't college professors this good?

[@barovierkevinallybose1040]

I think some prof like for you t figure it out on ur own

[@lastua8562]

They are more advanced than Ben was at the time (before PhD). It is easier to teach when you know less and are closer to the students.

[@adauche4875]

Awesome video; very easy to understand. I like your explanations so much. Please when you get a chance, can you make a video on Maximum a Posteriori Probability Estimation. Thank you

[@burninmind]

Awesome explanation! It was really helpful for me

[@frogger832]

sorry if this is a dumb question, but I am still confused as to why we need this. why go through all the math just to get x bar? are there any examples where we actually need to perform this and the estimator is not intuitive or listed somewhere?

[@SpartacanUsuals]

+Froggy Hi, thanks for your message. There are quite a few examples where it is difficult to intuitively work out what might be a good estimator. For example, look at section 4 here: times.cs.uiuc.edu/course/410/note/mle.pdf Understanding how likelihoods work is also very important for Bayesian statistics, see the playlist here: kzbin.info/aero/PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm Best, Ben

[@sunnyhours84]

Hi Ben! I have a follow-up question! When I learn math I always try to fit the topic in a historical perspective. And seeing that the "method of moments" estimator also gives the exact same answer, namely 'x bar', one starts to wonder what came first?? Did people deal with these kinds of problem (ages ago) intuitively, or did they first work out all these different estimators only to find out that they produced intuitively answers? Who came up with e.g. "method of moments" and "maximum likelihood", and what did people use before? All I know is that the field of statistics is relatively young, compared to say Algebra and Analysis. (I haven't had time to read the pdf you linked to, maybe there is an answer there..)

[@Muuip]

Notabot I am trying as well to grasp the benefits of complex calculations trying to estimate probabilities based on sample values. If a sample is too small, any inference/estimate by complex calculations won't be accurate. Only a bigger sample will raise the accuracy.

[@XxAbZzXx100]

You are the man! Thanks Ben.

[@unclecode]

Beautiful. Would you please share what hardware and software u r using for writing your lecture notes in these videos and recording ur screen? Thx

[@tianshili7649]

Hello, Ben! You made an excellent video about MLE and it really helps me understand the subject. But I have a question: what should I do if I don't know the distribution of the samples? For example, it's clear that in your case here it's a binary distribution. But what will you do to a population which you don't know what kind of distribution it has in advance?

[@62294838]

You involved the asymptotic argument (Ie central limited theorem) for it

[@62294838]

Some times , you will encounter something call the pseudo-true parameter. See Wooldrige cross sectional and Panel data textbook

[@muhammadzhafranbahaman6401]

Hi Ben, I would like to clarify is the P-hat is equivalent to tita-hat which is the point estimator for the parameter P which is simply pie(population proportion)?

[@josemanuelromerogonzalez6084]

Not all the heroes wear a coat. Thank you a lot!

[@allall02]

Great explanation, thank you!

[@muhammadzhafranbahaman6401]

Hi Ben, For this example, is the random variable follows Binomial distribution?

[@Muuip]

Thanks for your presentation! At 2:40 you said "x bar times p hat times x bar" but wrote "x bar MINUS p hat times x bar". I assume "minus" is correct? Thank you.

[@kingsleymichael7533]

This really helped me alot. Thank you very much.

[@CharlieFreakin]

Thank you! Very clear and understandable.

[@leojboby]

Does this work if x_i is not equal to 1 for male? This whole thing was to say that if we use MLE to determine the population parameter that defines the probability of Y in the population, that we should use the mean of whatever we obtain from the sample... However, it says nothing about N...? Are there other ways to determine such a population parameter?

[@Robertianocockrell]

do you have videos on method if moments for the gamma function and binomial?

[@lastua8562]

So we are using Log as Ln here, why are they equivalent in this case?

[@ZishanAnsari]

Thanks for the great video Ben. So this means that the maximization function will always find the P_hat value to be same as the value of X_bar. For logistic regression model the probability cut-off that I get using Sensitivity and Specificity crossovers is always close to the value of X_bar. Is this the reason?

[@SpartacanUsuals]

Hi, thanks for your message. Yes, the Maximum Likelihood estimator for the proportion of data which are of one type is always just the sample mean of the data in the binary case. It makes sense that the proportion of cases identified correctly as positive should mirror the actual value of X_bar heuristically. However, I'm not sure of a theorem etc. that would necessarily demonstrate this. Sorry I can't be of more help! Best, Ben

[@ankurgangwar3622]

in the second part there was log on left hand side , where is the log here

[@TheTehnigga]

You could have explained with a graphical example what is small l. That part was quite confusing to understand.

[@kennzinga]

omg thank you so much. It helped a lot.

[@GiuseppeRomagnuolo]

Thanks Ben for these videos, are incredibly useful. I assume that by log(p_hat) we are referring to the natural logarithm ln(p_hat) and not the log_base10(p_hat)?

[@SpartacanUsuals]

+Giuseppe Romagnuolo Yes, that's correct. Glad to hear the videos have been useful. Best, Ben

[@Connor0isdabest]

does anyone know what video he proves why dL/dp = 0 is the same as dl/dp = 0?

[@SpartacanUsuals]

Connor0isdabest It is this video: kzbin.info/www/bejne/mpXUn6xplr-Bhrs

[@Connor0isdabest]

so simple! thanks so much

[@goldfishyzaza5770]

I do not understand the differentiation part of the log likelihood function. Where did p-hat suddenly come in? Have you just substituted p for p-hat?

[@SpartacanUsuals]

Hi, thanks for your message. After differentiating the log likelihood with respect to p, this leaves a function of p. However, to find the maximum likelihood estimator for p - which I call p hat - it is necessary to set this derivative to zero. This defines p-hat. I hope that helps. Best, Ben

[@Jessica5587]

Hi ! Great videos, thanks a lot ! There's just one thing I couldn't quite get: the minus at the end, I know you explained it, but I'm lacking some basics in maths and I can't understand where it's coming from, sorry: N X_bar / P_hat MINUS ... Would it be possible for you to give me the name of the rule applied here (you say chain rule, I'm used to it in a probabilistic context (mostly Markov Models), and I just don't get it here...) Sorry about that, otherwise awesome video, thanks for uploading it here ! :)

[@fmp000]

when you differentiate log(1-p), through the chain rule you get 1/(1-p)*(-1). This "(-1)" comes from the differentiation of (1-p)

[@benernest7896]

Basic question from a non-math person. How did N*X_bar*log(P_hat) become N*X_bar/P_hat? Thanks.

[@SpartacanUsuals]

Hi, thanks for your message. It became that after differentiating, since log(x) goes to 1/x. Hope that helps! Cheers, Ben

[@manx306]

Isn't the derivative of log x 1/(x(ln 10))? I'm still confused by this step in the video

[@133TME]

Hey, I know you posted this a couple of months ago, but just in case you never figured it out the reason is that Ben used e as the 'default' base for log. This is actually pretty common once you get into more advanced math, my CS lectures basically never use log_10 for instance. Any time log is used, the base is e unless otherwise specified. I find it annoying, as it is not was I taught in high school, but it is what is is. Pretty much, whenever he writes log, just substitute it with ln or log_e.

[@manx306]

That is really helpful. Thanks!

[@Pumbelchook]

This was so helpful! Thanks :)

[@HKNAGPAL7]

Which editor/ software you use to make this video?

[@alirezagyt]

So remind me again how finding P^_ML is helping us with P?

[@flyingpinkyfish]

this is great, thank you

[@roottwo5459]

take my upvote

[@hugoirwanto9905]

Yeayy! Thank you

[@ulisesperez1241]

thanks bro

[@itbeginx]

Thanks!

[@bunkerputt]

Seven thumbs up.

[@chrisie1997]

ty

[@jameshurliman8951]

3 videos of dense calculus later... "Yeah it's just the average"

[@EmperorDraconianIV]

+Ben Lambert thank you my brother. If i ever become a billionaire i will gift your family a huge fortune.

[@gonulakn387]

What the fuck did you do at last

[@trzmaier]

so much faffing for something this trivial

[@Myndir]

It's nice to know that there is solid algebra behind the intuition.

[@ligapis]

Ty