Novel sampling method for the von Mises–Fisher distribution
Abstract
The von Mises–Fisher distribution is a widely used probability model in directional statistics. An algorithm for generating pseudo-random vectors from this distribution was suggested by Wood (Commun Stat Simul Comput 23(1):157–164, 1994), which is based on a rejection sampling scheme. This paper proposes an alternative to this rejection sampling approach for drawing pseudo-random vectors from arbitrary von Mises–Fisher distributions. A useful mixture representation is derived, which is a mixture of beta distributions with mixing weights that follow a confluent hypergeometric distribution. A condensed table-lookup method is adopted for sampling from the confluent hypergeometric distribution. A theoretical analysis investigates the amount of computation required to construct the condensed lookup table. Through numerical experiments, we demonstrate that the proposed algorithm outperforms the rejection-based method when generating a large number of pseudo-random vectors from the same distribution.
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© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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Kluwer Academic Publishers
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Publication History
Published: 26 March 2024
Accepted: 29 February 2024
Received: 22 June 2023
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