Random Sampling from the Watson Distribution

Publication: Working/Discussion PaperWU Working Paper

Abstract

In this paper we present and discuss two methods for efficient sampling from the Watson distribution.
The first approach adapts the rejection sampling algorithm from Kent et al. (2018), which originally
samples Bingham distribution using angular central Gaussian envelopes. We show that for the
case of the Watson distribution, this allows for a closed form expression for the parameters that
maximize the efficiency of the sampling procedure, which is then further investigated and bounded
by derived asymptotic results. What is more, we present a sampling algorithm that removes the
curse of dimensionality by a smart matrix inversion, which allows for fast runtimes even for complex
problems with high dimension. The second method relates to Saw (1978), and simulates from a
projected distribution using adaptive rejection sampling. Also for this sampling procedure, the derived
algorithm offers fast sampling for large dimension. This is not the case for similar algorithms in the
field, which usually require an expensive rotation of the sampled results using a QR-decomposition.
Finally, we propose some simple generators for the trivial cases and compare the two main methods
in a simulation study.
Original languageEnglish
Place of PublicationVienna
PublisherWU Vienna University of Economics and Business
Publication statusPublished - 2022

Publication series

NameResearch Report Series / Department of Statistics and Mathematics
No.134

WU Working Paper Series

  • Research Report Series / Department of Statistics and Mathematics

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