97-02-01.ley-wh
#
A Sweep-Plane Algorithm for Generating Random Tuples in Simple
Polytopes

### Abstract

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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Josef.Leydold@statistik.wu-wien.ac.at