  A likelihood function on a smooth very affine variety gives rise to a twisted
de Rham complex. We show how its top cohomology vector space degenerates to the
coordinate ring of the critical points defined by the likelihood equations. We
obtain a basis for cohomology from a basis of this coordinate ring. We
investigate the dual picture, where twisted cycles correspond to critical
points. We show how to expand a twisted cocycle in terms of a basis, and apply
our methods to Feynman integrals from physics.
