Title: The algebraic geometry of Ornstein--Uhlenbeck processes in equilibrium
Abstract: The goal of this talk is to explain a few recent results about a class of statistical models. While these results answer statistical questions, their proofs are carried out entirely in terms of algebraic geometry. I will explain the applied motivation behind all this and show how to carry out such a translation (which is typical for Algebraic Statistics); no knowledge of stochastic processes is required.
More precisely, we associate to each directed acyclic graph G = (V, E) a statistical model M(G) (consisting of equilibrium distributions of |V|-variate Ornstein--Uhlenbeck processes whose drift matrices are supported on the edge set E of G). The set M(G) is the image of a basic open semialgebraic set under a rational map. Ignoring the inequalities, M(G) is an irreducible affine algebraic variety. By tying the structure of the function field of M(G) to properties of the graph G, we obtain a complete combinatorial characterization of when two graphs induce the same model. This is joint work with Carlos Améndola, Benjamin Hollering, and Pratik Misra.
The advanced seminar begins at 11:00 am s.t..