  Maximum likelihood estimation is a fundamental computational problem in
statistics. In this note, we give a bound for the maximum likelihood degree of
algebraic statistical models for discrete data. As usual, such models are
identified with special very affine varieties. Using earlier work of Franecki
and Kapranov, we prove that the maximum likelihood degree is always less or
equal to the signed intersection-cohomology Euler characteristic. We construct
counterexamples to a bound in terms of the usual Euler characteristic
conjectured by Huh and Sturmfels.
