Uniform efficiency of the Ulrich-Wood sampler for the von Mises-Fisher distribution

Sam Power

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arXiv · 2609.27884

Uniform efficiency of the Ulrich-Wood sampler for the von Mises-Fisher distribution

Sam Power

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Abstract

The standard approach to stochastic simulation from the von Mises-Fisher distribution is a rejection sampler proposed by Ulrich and Wood. This note provides a theoretical justification of its efficiency, lower-bounding its acceptance probability uniformly over the dimension and concentration parameter. A novel interpretation of the proposal is given which provides some intuition for this efficiency.

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Sam Power. 2026-08-20. Uniform efficiency of the Ulrich-Wood sampler for the von Mises-Fisher distribution. https://arxiv.org/abs/2609.27884

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