SPEAKER: Serkan Hocsten (SFSU) <br>

<br>

TITLE: The Maximum Likelihood Degree <br>

(joint with F. Catanese, A. Khetan and B. Sturmfels)

<br>

ABSTRACT: Maximum likelihood estimation in statistics leads to the
problem of maximizing a product of powers of polynomials.  The maximum
likelihood degree is the algebraic degree of the critical equations of
this optimization problem. This degree is related to the number of
bounded regions in the corresponding arrangement of hypersurfaces,
and, under suitable hypotheses, it equals the top Chern class of the
sheaf of differential forms with logarithmic singularities.  We will
give exact formulas in terms of degrees and Newton polytopes for
polynomials with generic coefficients, and we will present further
exact formulas for linear (not necessarily generic) polynomials.