Abstract Bayes' Formula and Conditional Expectation

Рет қаралды 4,214

3 жыл бұрын

Table of contents:
08:28 - A gentle introduction of Bayes’ formula
10:17 - Interpreting the Abstract Bayes’ in terms of Conditioning on Events
13:45 - An intuitive introduction of Abstract conditional expectation
16:56 - Interpreting the Conditional Expectation in terms of Conditioning on Events
20:48 - Interpreting the Cond Expectation in terms of Conditioning on Random Variable
24:14 - Formal definition of Conditional Expectation
28:23 - Definition of abstract Conditional Probability
30:50 - Formal proof of Bayes’ Formula
A correction: At 27:43 when it says \mu is absolutely continuous with respect to P, the reason should be: P[G]=0 means \mu[0]=0, and also at 26:11 please ignore the statement saying weaker/stronger!

Пікірлер: 11

@CONGKAMAEL 2 жыл бұрын

The intro music worked better than my morning coffee for waking me up. ^.^

@quantpie 2 жыл бұрын

Haha avoid watching after 5pm! Many thanks!

@Heygodfrey 3 жыл бұрын

this excellent material with only 1XXX views!?

@quantpie 3 жыл бұрын

Haha good observation! We and the KZfaq algorithm don’t get along! But then as Shakira put it: algorithms don’t lie! May be the channel is more specialised or too random!

@Zorothustra 3 жыл бұрын

Wow, is this a brand new series? what will be the future topic(s)? MCMC? looking forward to see more episodes on these topics! BTW, wish you all a Merry Christmas! Thanks for sharing so many high quality videos!

@quantpie 3 жыл бұрын

thanks! A very diverse set of videos, but hopefully will come together. Thanks a lot of ideas but we are prioritising topics which get relatively more interest. MCMC is definitely on the list! Merry Xmas and a happy New Year to you too!

@arjaninabil7328 3 жыл бұрын

Thanks ❤️

@quantpie 3 жыл бұрын

You are welcome! many thanks!

@tidminglee766 3 жыл бұрын

good job！

@quantpie 3 жыл бұрын

Thank you! Cheers!

@WajidAli-dv6cb 2 жыл бұрын

Hi! How can we define conditional expectation when the (abstract) probability of X and Y are given? Let say random variable X takes values from {0, 1,2,...N}. Define a probability p_n(t)=Pr(X(t)=n) and the exaptation would be E_p=sum_{n=0}^N(nP_n(t). Now define a conditional probability q_n(t)=Pr(X(t)=n| Y=1,2,3...N), We can see that p_Y(t)=1-p_0(t). So q_n(t)=p_n(t)/(1-p_0(t)). I define E_q=Sum_{n=0}^N nq_n(t)= E_p/(?). So what will be in the denominator?