This is my intuition for why Jensen's inequality is true: For E[X^2], the bigger values of x are more important because they get much bigger when you square them, and similarly, the smaller values of x are less important. For E[X]^2, every value of x gets equal importance. Since E[X^2] gives less importance to small values and more importance to large values, it ends up being larger overall.
@MTGandP I also think the intuition for why it's true isn't nearly as important as why we care that it's true. Like I've watched two videos about it now, and I'm fairly confident that I understand the mechanics of it. I could work out my own problem, but hand or in Python. But so what? I can work this out very well and good, but this doesn't explain why anybody should care that it's true.
This inequality, for no bias reason atall, is the best inequality out there
Lol
I don't think this gives any intuition as to why this inequality is generally true, you just worked out an example.
This is my intuition for why Jensen's inequality is true:
For E[X^2], the bigger values of x are more important because they get much bigger when you square them, and similarly, the smaller values of x are less important. For E[X]^2, every value of x gets equal importance. Since E[X^2] gives less importance to small values and more importance to large values, it ends up being larger overall.
@MTGandP I also think the intuition for why it's true isn't nearly as important as why we care that it's true. Like I've watched two videos about it now, and I'm fairly confident that I understand the mechanics of it. I could work out my own problem, but hand or in Python. But so what? I can work this out very well and good, but this doesn't explain why anybody should care that it's true.
The average of many (convex) function evaluations is usually greater than the function evaluation of an average
That's what I needed
Super simple and way more helpful than the dry formulations in my class slides..thank you!!
Super intuitive, very helpful. Thanks!
Amazing , very helpful
Nice video but where's the intuition part
Thanks, really clear
thanks!
Who is here because of the book called antifragile?
Lol yup
2:55 Oups?
thanks mate
Awesome
Hi what about concave function
Darkmatter 476 same argument but the inequality is reversed
Thank you so much, it helped a lot
And so what?