Title: Algebraic Factor Analysis: Tetrads, Pentads and Beyond
Speaker: Bernd Sturmfels

Abstract:
This talk is based on the paper with Mathias Drton and Seth Sullivant
which is posted at  http://front.math.ucdavis.edu/math.ST/0509390.
Factor analysis refers to a statistical model in which observed variables
are conditionally independent given fewer hidden variables, known as
factors, and all the random variables follow a multivariate normal
distribution. The parameter space of a factor analysis model is a
subset of the cone of positive definite matrices. This parameter space
is studied from the perspective of computational algebraic geometry.
Grobner bases and resultants are applied to compute the ideal of all
polynomial functions which vanish on the parameter space. These polynomials,
known as model invariants, arise from rank conditions on a symmetric matrix
under elimination of the diagonal entries of the matrix. Besides revealing
the geometry of the factor analysis model, the model invariants also
furnish useful statistics for testing goodness-of-fit.