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9 votes
2 answers
431 views

Hermite–Fourier expansion for the median

Let $n$ be an odd positive integer. Let $M : \mathbb{R}^n \to \mathbb{R}$ be the median function: $M(x_1,\dots,x_n)$ is the median of $x_1,\dots,x_n$. What can be said about the Hermite–Fourier ...
Gil Kalai's user avatar
  • 24.7k
-1 votes
0 answers
19 views

What is the expected value of the set when N elements are chosen from the same probability distribution?

Suppose we have a parameter that follows some probability distribution $f(x)$. When simulating an $N$-body with that parameter as an attribute, how should values of the parameter be chosen? Let each ...
ksrk's user avatar
  • 1
1 vote
0 answers
41 views

Can conditional distributions with respect to a sufficient sub-$\sigma$-algebra be represented by a single Markov kernel?

Let $(\Omega, \mathcal{F})$ be a measurable space, and let $\mathcal{P}$ be a collection of probability measures on this space. A sub-$\sigma$-algebra $\mathcal{G} \subset \mathcal{F}$ is said to be ...
MrTheOwl's user avatar
  • 111