  We give a numerical algorithm computing Euler obstruction functions using
maximum likelihood degrees. The maximum likelihood degree is a well-studied
property of a variety in algebraic statistics and computational algebraic
geometry. In this article we use this degree to give a new way to compute Euler
obstruction functions. We define the maximum likelihood obstruction function
and show how it coincides with the Euler obstruction function. With this
insight, we are able to bring new tools of computational algebraic geometry to
study Euler obstruction functions.
