Department of Mathematics Colloquium


Abstract 

Algebraic statistics applies algebraic
geometry, combinatorics, and commutative algebra to the study of
statistical models. In this talk, we will introduce algebraic
statistics through the following problem: Given aligned DNA sequences
from a collection of species, find the tree that best describes their
evolutionary history. One method for inferring phylogenetic trees uses
phylogenetic invariants, polynomials that vanish on the variety defined
by the model. As an example of the algebraic geometry involved, the
projectivization of the variety defined by the general Markov model is
a secant variety of a Segre variety. In this talk, we will describe the
general and group‐based Markov models, their defining polynomials, and
their connections to tensors, hypergraphs, and toric algebra. We will
end the talk by looking at statistical models with similar algebraic
properties as such as Holland and Leinhardt’s p1 model for social
networks.
