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

Leydold, Josef and Hörmann, Wolfgang (1997) A Sweep-Plane Algorithm for Generating Random Tuples in Simple Polytopes. Preprint Series / Department of Applied Statistics and Data Processing, 18. Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, Vienna.

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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. (author's abstract)

Item Type: Paper
Additional Information: published in: Mathematics of Computation 67, 1998, pp. 1617-1635
Keywords: Uniform distributions / polytope / rejection method / multivariate log-concave distributions / universal method
Classification Codes: MSC 65C10
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 10 Jul 2006 13:21
Last Modified: 06 Feb 2015 10:10
Related URLs:
URI: http://epub.wu.ac.at/id/eprint/476

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