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The Likelyhood
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Comments from YouTube:

Irene is me

4y↑7

Thank you for this amazing video!! But i have a quick question: why you are trying to MINIMIZE the negative of that function instead of directly MAXIMIZE that function?

Jeb Hank

@CARLOS PINZON CARRERA Very helpful, cheers!

Warren Ricardo

Instablaster...

Mahmoud Abdelkhalek

4y↑1

Hi, the real reason has to do with the Kullback-Leibler divergence. More details here:
https://wiseodd.github.io/techblog/2017/01/26/kl-mle/

CARLOS PINZON CARRERA

4y↑6

Just note that maximize -f(x) is equivalent to minimize f(x); when you apply the logarithm function to the likelihood function, you get an expression just with negative terms, so the professor just multiply all the log-likelihood function by (-1) so that the negative of the log-likelihood function is now an expression with just positive terms. that's why he minimize this function (all positivities terms) rather than maximizing the original (all negative terms). Hope this help.

Thiago Neubauer

4y↑5

I think this is because of many optimization algorithms are build to minimize functions instead of maximizing these functions. Thus, it's better to put our equations in that form to become more easily adapted to an optimization routine.

Bob Bobbity

5y↑8

Perfect. Thanks

Hussein Sleiman

2y↑1

Hello thanks for the effort. I think you have a mistake when you minimized w.r.t v. the sum part of the denominator must be 4v^2

Hussein Sleiman

2y↑1

but it doesn't matter the answer you reach will be the same.

M. Preacher

3y↑4

why we can directly use the PMF of binomial to calculate the ML instead of using the ML function like the second example?

M. Preacher

@MALLAKBASHEER SYED i read the theory of likelihood function, i think at that time i understood something wrong with the likelihood function. but by the way thanks for the reply

MALLAKBASHEER SYED

hii , we can use the same for the first one but at the end we will end up in finding the same. Suppose consider the case of head and tail in 5 tosses ,and u know that the output is HHTTH (given) and we want to use the concept of ML to find the same , as all are independent events we can write the resultant probability as product of probabilities @ each toss ,so we end up in getting teta^3*(1-teta)^2 and by diff it and equating it to 0 ,we get probability of head as 3/5 which is obviously right(by the usual method) .The same happened with the first problem but order doesnot matter hence considering permutations we could have nck at the front(but we can remove it ,as it is not irritating much)

Aakarsh Nair

2y↑2

OMFG this guy is amazing

Nicolas Bourbaki

4y↑9

Blasphemous negligence of the chain rule when performing that first derivative to find its roots for the maximum estimation on the mean of the random variables in the second example. Good thing the difference is symmetric!

Clyde Xu

by watching the video, not clear to me why the optimal value turns out to maximize the likelihood function.

ArmedPenguins

2y↑1

because think of the Pk expression at the very top to be a curve. If you differentiate it and set it to 0 you get the max or minimum. Now if you rearrange It to find theta you now know what value of theta gives you a max or min

Mehrdad Kazemi

thank you

Senior Muchacho

4y↑1

What is that K letter means?

Thiago Neubauer

4y↑2

The number of heads obtained in our population. he probability of having exactly k successes, our number of heads, is given by the probability function showed in the slide.