Maximum Likelihood - Cramer Rao Lower Bound Intuition

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Maximum Likelihood - Cramer Rao Lower Bound Intuition

Рет қаралды 129,351

Күн бұрын

This video provides some intuition behind the idea that the Cramer-Rao Lower Bound is inversely related to the variance of a maximum likelihood estimator.
Check out oxbridge-tutor.... for course materials, and information regarding updates on each of the courses. Check out ben-lambert.co... for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: ben-lambert.co... Accompanying this series, there will be a book: www.amazon.co....

Пікірлер: 63

@AndrewCarlson005 5 жыл бұрын

THIS MAKES SO MUCH SENSE!! Thank you so much for explaining this more clearly in a few minutes than my textbook could do in a few hours!

@Borey567 8 жыл бұрын

I think this small video worth few 2hrs lectures in a university.

@dragosmanailoiu9544 4 жыл бұрын

lmao true

@123456789arty 4 жыл бұрын

I just watched a 1 hour lecture about Cramer-Rao Lower Bound and you are totally right :P this was waaay more informative.

@oscarlu9919 4 жыл бұрын

This explanation is excellent. It is crystal clear to explain why is the inverse relationship between variance and second derivative, and why is second derivation, and plus why it is negative! Bravo, Prof.Ben!

@satltabur4597 2 жыл бұрын

In 7m and 59s you explained it better and more clearly than many 2h university lectures combined.

@jaymei2532 5 жыл бұрын

Like everyone else said, very well explained. I feel way less jittery about this whole entire concept. Thank you in 2019!

@accountname1047 Жыл бұрын

This was my intuition when studying ML estimators in statistics, but never got a straight answer about it from my teachers. Happy to see others think of it through a geometric lens! Great video

@andrewedson7010 4 жыл бұрын

Studying for actuarial exams and the material just throws Fisher Information at you with no context. This will help me understand exactly what we are expected to do in the calculations. Thank you

@mehinabbasova5013 5 ай бұрын

This makes so much more sense now, thank you!

@LongyZ13 10 жыл бұрын

Really appreciate videos like this where the aim is to provide an intuitive explanation of the concepts as opposed to going into detail on the maths behind them. Thanks.

@GuppyPal 3 жыл бұрын

Damn. You explained this so well. I never have any idea what my professor is talking about, but videos like this help SO MUCH. Thank you!

@yukew4106 4 жыл бұрын

Hi Mr. Lambert, I just want to take a moment to thank you for taking the time to make these videos on KZfaq. They are very easy to understand and by watching your videos I have been able to understand my statistical theory and bayesian statistics courses more as an undergrad. Thanks a lot and I wish you all the best!

@HappehLlama 9 жыл бұрын

This was a fantastic intuitive explanation - thank you!

@ishaansingh1789 7 ай бұрын

Beautifully explained my friend- intuition is almost always as important as the actual proof itself

@johannaw2031 Жыл бұрын

This video makes me very clear about one thing, that I find it strange how hard it obviously is for professors to provide some clear intuition. Why must it be so hard to be pedagogical when you really know something, which I expect a professor does. This is a working day of headache over horrible handouts made understandable in 5 mins.

@Trubripes 3 ай бұрын

High curvature -> sharp -> concentrated -> low variance. Makes sense.

@tomthefall 2 жыл бұрын

this is the best video ive seen on this topic, very well done

@fancy841014 4 жыл бұрын

The point of view in curvature is soooo great!

@cecicheng5791 9 жыл бұрын

wow finally get the idea about this relationship between covariance matrix and hessian

@wahabfiles6260 4 жыл бұрын

so in otherowords the covariance matrix is hessian of maximum likellihood?

@irocmath9727 4 жыл бұрын

Wow! This clarifies a good week or two from last year's lectures. I wish I had seen these videos when I was taking the course last year.

@OtakuRealist 28 күн бұрын

Thank you so much. This explains so much.

@MrYahya0101 3 жыл бұрын

you said we add the negative sign, because the second derivative is negative after a certain value, and the negative sign is added to correct for that negative. what about when the second derivative is positive? doesn't the negative sign make the second derivative negative then? of what use will that be?

@aartisingh1387 8 ай бұрын

Thank you for this video. I have watched this video many times over the years. The simplicity, intuition, visuals, clarity, and ease, are nothing less than brilliant. It has always helped whenever things get fuzzy. Just a small request or a question if you may: Calling vertical axis "likelihood of the data" makes it a bit confusing! Instead, should it not be "likelihood of the parameter" that is L( theta; data). And this "likelihood of the parameter" then happens to be equivalent to f(data|theta)? So, y axis should not be called L(data|theta)?

@jubachoomba 3 жыл бұрын

Those tangents illustrate the convexity... Jensen!

@unnatishukla8513 Жыл бұрын

Awesome awesome awesome video....Thankyou so much!

@achillesarmstrong9639 5 жыл бұрын

OK 3 months ago, I thought I understood this video. After I learned more statistic. Now I understand what is going on. I didn't quite understand the concept 3 months ago.

@leza7584 Жыл бұрын

This helps so much. very simple explanation

@michaelmalone7614 4 жыл бұрын

Wow, that makes things so much clearer. Thank you.

@johanjjager 3 жыл бұрын

Isn't the variance of theta hat also dependent on n, the number of observations which constitute the likelihood function?

@kimchi_taco 5 жыл бұрын

Kudos man! most intuitive explanation ever!

@1024Maverick 6 жыл бұрын

You just saved my semester (again) GGWP

@fengdai2304 4 жыл бұрын

Ben, you are amazing!

@filipposchristou441 6 жыл бұрын

thanks. Good explanation. I guess you saved me hours of searching.

@vitorjung 3 жыл бұрын

Excellent video, congratulations!

@jorgebretonessantamarina18 7 жыл бұрын

Wonderful video. Thank you very much!

@madhurasutar5332 3 жыл бұрын

Well explained man!!! Thanks a million 🙏

@pumpkinwang548 3 жыл бұрын

Thank u Ben, it was quite helpful

@coopernfsps 7 жыл бұрын

Great video, as always. Helped me out a lot!

@archangel5437 3 жыл бұрын

You da best!

@davidpaganin3361 5 жыл бұрын

Many thanks, much appreciated!

@hankyang7466 5 жыл бұрын

wonderful video, thank you!

@bgheyer 3 жыл бұрын

Thank you so much!

@charlesity 7 жыл бұрын

Thank you very much!

@lucystruthers7876 3 жыл бұрын

Hi ben, thank you so much for your videos, i am studying quantitative ecology and do not have a strong mathematical background - your lessons really help! May I ask how the different values of theta are generated (along the x axis)? I assume the MLE expression stays constant and that the parameter estimates vary due to sample variation but in my case I only have one sample. I am a bit confused whether variance of the MLE is actually referring to variance in the parameter estimate due to sampling error. Secondly, in order to calculate the variance, must the 2nd derivative be evaluated for the value of theta which gives the MLE? I hope these questions make sense!

@flo6033 6 жыл бұрын

Thanks, very intuitive. [Subscribed]

@alecvan7143 4 жыл бұрын

Awesome video!!

@wildboar3170 8 жыл бұрын

Hi Ben find your tutorials very easy to follow- thanks. What software are you using? Especially like the coloured pens on black background.

@atfirstiamhuman9183 6 жыл бұрын

i dont know hat he is using but I sometimes use app.liveboard.online/ . It also allows you to chose different backgrounds for a board and different colors and to livestream your drawing from your tablet/smartphone to PC which i often use as it is better to draw by hand/pen then by mouse.

@lastua8562 4 жыл бұрын

You can check his website for info.