[myWindoonn]

On the horizon, algebraic geometry and category theory have opened up new ways to think of posets, and posets are in correspondence with DAGs. We can talk about mappings between Bayesian networks, as well as sheaves which encode the logical restrictions and can be further linearized or categorified.

You're right that it seems like not much attention is paid to this stuff. At a lecture a few years ago, it was pointed out that sheaves on Bayesian networks seem interesting, but that nobody seems to be working directly on applying the maths to existing problems.

[jesuslop]

I am aware of the categorical treatment and that's how I think about Bayesian nets, but would like to know something about the sheaf-theory aspect of it. Also: it puzzles me that Algebraic Geometry is mentioned in this context, how's that?