A Sweep-Plane Algorithm for Generating Random Tuples in Simple Polytopes

Josef Leydold and Wolfgang Hörmann


A sweep-plane algorithm by 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 random fraction (sampled from a proper univariate distribution) of the volume of the polytope is covered. Then the intersection of the plane with the polytope is a simple polytope with smaller dimension. In the second part we apply this method to construct a black-box algorithm for log-concave and T-concave multivariate distributions by means of transformed density rejection.

Mathematics Subject Classification: 65C10 (Random Number Generation)

Key Words: Uniform distributions, polytope, rejection method, multivariate log-concave distributions, universal method

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