Jensen's Inequality as an Intuition Tool (2021)

Post by Ey7NFZ3P0nzAe » Mon, Sep 16, 2024, 11:00 AM UTC

raziel2701 wrote: post #17

I have no idea what Jensen's inequality means. Goes to wikipedia "In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906,[1] building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in 1889.[2] Given its generality,…

Post by [deleted] » Mon, Sep 16, 2024, 2:58 PM UTC

programjames wrote: post #20

raziel2701 wrote: post #17

I have no idea what Jensen's inequality means. Goes to wikipedia "In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906,[1] building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in 1889.[2] Given its generality,…

A convex function is open to the top, like this: \ / \ / \ / \/ If you connect any two points, it lies outside the curve. Which is basically the intuition for Jensen's inequality: if you go partway between two points it's above the curve, so the weighted average of the curve at those two points is bigger than the curve at their weighted average.