On the sample-mean method for computing hyper-volumes

Rabiei Nima () and Saleeby Elias G. ()
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Rabiei Nima: Department of Mathematics, The American University of Iraq, Sulaimani, Iraq
Saleeby Elias G.: Mount Lebanon, Beirut, Lebanon

Monte Carlo Methods and Applications, 2019, vol. 25, issue 2, 163-176

Abstract: Estimating hyper-volumes of convex and non-convex sets are of interest in a number of areas. In this article we develop further a simple geometric Monte Carlo method, known also as the sample-mean method, which transforms the domain to an equivalent hyper-sphere with the same volume. We first examine the performance of the method to compute the volumes of star-convex unit balls and show that it gives accurate estimates of their volumes. We then examine the use of this method for computing the volumes of nonstar-shaped domains. In particular, we develop two algorithms, which couple the sample-mean method with algebraic and geometric techniques, to generate and compute the volumes of low-dimensional stability domains in parameter space.

Keywords: Monte Carlo; hyper-volumes; generalized unit balls; stability domains (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/mcma-2019-2034

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