A hierarchical loglinear model is defined by its domain of means which is a convex polyhedron called the marginal polytope. If the data belongs to the interior of the marginal polytope, Bayesian and frequentist inference goes as usual. However if the data is sparse, geometrically, it will belong to one of the faces of the polytope and to make correct inference, we have to identify the face of the polytope on which the data lies. We will give some methods to find such a face, exactly or approximately.