Maximum Likelihood estimation - an introduction part 2

[@Yustiks]

there is a mistake at 6:38: should multiply by N the left part

[@albertogutierrez346]

I can't find the words to thank you Ben, you have no idea of how many times your videos have saved me along graduate school. The simplicity and detail of how you explain is priceless! I owe you big time!! Best wishes from Mexico.

[@SatyaRanjanSahoowmu]

I think the last equation should be logP(N*Xbar) instead of just logP(Xbar)

[@Partho2525]

you are really really good...I never understood this concept this clear.

[@SpartacanUsuals]

Hi Prektesh, glad to hear it was useful! Best, Ben

[@sami-samim]

I love the way you recap previous lectures.

[@internetscheisse]

Thanks alot for this helpful video! But still I got a question. In the last line, shouldn't it be N*mean(x) instead of just mean(x)?

[@SpartacanUsuals]

Hi, thanks for your message - yep you are right - there should be an 'N' before the last mean(x). My apologies for the confusion! Best, Ben

[@YawarSohail]

Oh I was wondering what happened to N. Thanks he asked it.

[@abokbeer]

You are my statistics hero. I shared this with all my colleagues.

[@horsepowerfactorytx]

I want to thank you for such a great explanation. My professor does not teach half as good as you. Cheers.

[@jacquelineoverton8223]

Beautiful explanation of log likelihood! Thank you. This is tremendously helpful!

[@zeeshan008x52]

Rockstar of statistics. U teaching style is very good sir

[@notyouraveragecat97]

This explanation is beyond amazing. Thank you so much.

[@elenae1366]

Great explanation of ML! This whole playlist is very helpful for understanding the intuition behind these concepts, especially since you show the mathematical derivations clearly. Thank you for posting!

[@tsasa192]

watched many videos and so confused. got it know. yours is the best!

[@N.E.Olsson]

Thanks Ben! The lecturerers tend to make it more complicated than it is when they skip this kind of thorough explanation. Big thanks, it is very clear now! // Niklas

[@Simbwhaha]

In my eyes, you obtained “hero status” !

[@charlesledesma305]

Excellent explanation!

[@ArtisticContingent]

Audio needs boosting but this was a very helpful video :) thanks for making it!

[@kikikikikiki7859]

This is really helpful and it really makes sense to me!

[@akjagsdfiausd]

In the end shouldn't it be log(p)Nx(bar) + log(1-p)(N - Nx(bar)) rather than log(p)x(bar) + log(1-p)(N - Nx(bar))? Great video, nonetheless!

[@zangasenor]

The uploader corrected the mistake through annotations at 6:35

[@kamikaze9271]

yeah...since the background is black, it's kind of hard to see the annontation..

[@indragesink]

you can also rewrite L as p^(sumfromi=1ton(xi))*(1-p)^(n-sumfromi=1ton(xi)), which seems (a lot) easy(/ier) but I guess you'll still need the product rule because of p*(1-p) (in the basis).

[@SC-hu2rt]

Thanks a lot for your explanation! Really helpful and encouraging

[@chriskiguongo138]

Saved me on the night before my statistics exam \

[@zarakkhan72]

A very nice explanation. Understood it completely but except for the final line. The same point raised by "dlambriex" in the comments, is my question as well.

[@SpartacanUsuals]

Thanks for your message. Yes, you were correct. That was a mistake. I have now added a note to the video. Best, Ben

[@sardaou3944]

is it possible sir to explain in more detail the fact that differentiate and taking the log leads to the same conclusion Thanks in advance

[@alandubackupchannel5201]

Have you considered the case where X1=M, X2=F, but your sample is X1=F, X2=M, the samples are the same but the likelihood L function doesn't take that into account? Sorry if I'm wrong, I have just began learning this. So, the likelihood estimator is just the chance that you get a particular sample (where the ordering *does* matter)?

[@ScottEdwards2000]

I was thinking the same thing! Yeah it seems like this is calculating the probability of getting this same in this exact order of M's and F's. Is that right?

[@rosamaytapalacios]

Thanks for the explanation. I have a doubt,in which case is it used negative log?

[@dheerajsharma5279]

Hi Ben, Amazing video. Can I please ask if thats nX (bar) in the end.

[@carolinaxlopez7495]

thank you so much for your great videos! i really loved them all! very clrear and simple way to get complicated stuffs :)

[@abhilamsal7185]

Setting fist derivative to zero, might give Maximum or Minimum. So, In my opinion further steps are required like setting second derivative less than zero.

[@comvnche]

or even a local max or min

[@danielbhc]

Thanks a lot! I'm just a little confused. p hat would be an estimator of how many males are in the population. But for a more general MLE understanding, is p hat just the parameter that makes the sample data fit the PDF f(x|p) where p is the unknown parameter? So for example, could you do MLE for a Poisson distribution where the unknown parameter p would be the mean lambda? Could a Possion MLE still be described by f(x|p)? Thanks!

[@lmgpc]

You are great! really helpful

[@ashankavindu2409]

Thank you very much sir ♥

[@dlambriex]

First of all thank you for your videos! They have helped a lot with studying for my econometrics courses! But I have a question regarding the last line in your last simplification. You state that the summation of Xi is equal to N * Xaverage (in yellow on the right). Yet when you erase sum of Xi in the formula you only write Xaverage and not N*Xaverage. While for the second summation you do simplify the that sum of (1-Xi) = N(1-Xaverage). Could you please confirm that this should in fact be N * Xaverage? Thanks ever so much in advance and keep up the good work it is really a lifesaver for me and my fellow students in the Netherlands!

[@zarakkhan72]

Yup i also didn't get that part.

[@SpartacanUsuals]

Hi, Thanks for your messages, and kind words. Yes, it should be N times Xaverage; my apologies for the mistake. I shall add a note to the video now. Best, Ben

[@guilhermearaujo5868]

But how can I be sure that I am maximizing the function? The turning point could be a maximum or minimum, no? The likelihood function doesn't have a minimum ( I imagine it does and its 0), or its minimum is not a turning point?

[@regularviewer1682]

How do you get N(1-xbar) at the very end? I can't figure it out for the life of me, even though I know it's relatively simple!

[@igorrizhyi5572]

i did't get why we can so easily wrap this all into log without worrying about that it will be completely different expression? i see how it makes our calculations much easier but do you have some sources where i can get material about this log function wrapping? thanks

[@igorrizhyi5572]

ok, i think i got it. if somebody will stack into the same problem of understanding this material i can recommend this url - en.wikipedia.org/wiki/Monotonic_function

[@jeongsungmin2023]

In 6:50 shouldn’t sigma Xi equal N*(X bar)?

[@adelinesou8899]

This is so helpful thank you!

[@leojboby]

if log is always increasing, when is the derivative 0?

[@chandnibhudia624]

you are amazing!!

[@SpartacanUsuals]

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

[@khalidmzd]

Excellent

[@SpartacanUsuals]

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

[@anthonymatovu6169]

Thank you very much,

[@endeshawhabte6667]

I MUST THANK YOU!!

[@LovelyWorldFressia]

Thank you so much! I was able to get it fast with this video. (Tried other methods for a day and didn't get it >.

[@bend.4506]

thank you soooo much!!!!

[@jansiranibdumtcs]

The (unobserved) parameters are Θ = (µ1 ,…,µn , σ2) and the parameter space is Ѳ = Rn X R+. (a) Derive the maximum likelihood estimator(MLE) for Θ. Pls answer me for this.

[@user-ck1hh9lh5s]

Why did the xi become a xbar

[@abbe23456789]

It is an error, it is supposed to be N*x_bar

[@lehmann_clips]

awesome

[@SpartacanUsuals]

Hi, many thanks for your message and kind words. All the best with your studies, Ben

[@hashimallawati2828]

great

[@MegaxAT]

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