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A sweep-plane algorithm for generating random tuples in simple polytopes |
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| Authors: | Josef Leydold Wolfgang Hö rmann |
| Institution: | University of Economics and Business Administration, Department for Applied Statistics and Data Processing, Augasse 2-6, A-1090 Vienna, Austria ; University of Economics and Business Administration, Department for Applied Statistics and Data Processing, Augasse 2-6, A-1090 Vienna, Austria - |
| Abstract: | 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 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 |
| Keywords: | Uniform distributions polytope rejection method multivariate log-concave distributions universal method |
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-concave multivariate distributions by means of transformed density rejection.