Neat problem of the week: we have n discrete random variables, X1...Xn. Given any variable, all variables are independent:
∀i:P[X|Xi]=∏jP[Xj|Xi]
Characterize the distributions which satisfy this requirement.
This problem came up while working on the theorem in this post, and (separately) in the ideas behind this post. Note that those posts may contain some spoilers for the problem, though frankly my own proofs on this one just aren’t very good.
Neat problem of the week: we have n discrete random variables, X1...Xn. Given any variable, all variables are independent:
∀i:P[X|Xi]=∏jP[Xj|Xi]
Characterize the distributions which satisfy this requirement.
This problem came up while working on the theorem in this post, and (separately) in the ideas behind this post. Note that those posts may contain some spoilers for the problem, though frankly my own proofs on this one just aren’t very good.