A SWEEP-PLANE ALGORITHM FOR GENERATING RANDOM TUPLES IN SIMPLE POLYTOPES

A sweep-plane algorithm of Lawrence for convex polytope computation is adapted to generate random tuples on simple polytopes. In our method an affine hyperplane is swept through the given polytope until a rando m fraction (sampled from a proper univariate distribution) of the volu me of the polytope is covered. Then the intersection of the plane with the polytope is a simple polytope with smaller dimension. In the seco nd part we apply this method to construct a black-box algorithm for lo g-concave and T-concave multivariate distributions by means of transfo rmed density rejection.