4 ms·

> we thinking of cutting slice through a multivariate distribution, and then normalizing. If you have some distribution P(X, Y) where X and Y are both real, the

> we thinking of cutting slice through a multivariate distribution, and then normalizing. If you have some distribution P(X, Y) where X and Y are both real, then its density is like some landscape (i.e. each x,y is associated with some height). P(X | Y=y) is like a slice through that landscape at Y=y, which leaves a 1-D plot of the density along X. If we re-scale it so that the area under it is 1, then it's a well-formed PDF. How intuitive! /s

markisus 3y ago
This is a case where a picture is worth a thousand words. The slicing intuition is quite useful and I imagine quite common for those who have taken calculus. It is the very same mental picture as you would use for computing area using two nested integrals. This video [1] has some nice graphics along these lines. [1] https://www.youtube.com/watch?v=gifQWtTWqEY https://www.youtube.com/watch?v=gifQWtTWqEY