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Exact Bayesian inference for the Bingham distribution

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Abstract

This paper is concerned with making Bayesian inference from data that are assumed to be drawn from a Bingham distribution. A barrier to the Bayesian approach is the parameter-dependent normalising constant of the Bingham distribution, which, even when it can be evaluated or accurately approximated, would have to be calculated at each iteration of an MCMC scheme, thereby greatly increasing the computational burden. We propose a method which enables exact (in Monte Carlo sense) Bayesian inference for the unknown parameters of the Bingham distribution by completely avoiding the need to evaluate this constant. We apply the method to simulated and real data, and illustrate that it is simpler to implement, faster, and performs better than an alternative algorithm that has recently been proposed in the literature.

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Notes

  1. Our code is available upon request.

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Acknowledgments

The authors are most grateful to Richard Arnold and Peter Jupp for providing the earthquake data and John Kent for providing a Fortran program to compute moments of the Bingham distribution. Finally, we would like to thank Ian Dryden for commenting on an earlier draft of this manuscript and Andy Wood for helpful discussions.

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Correspondence to Theodore Kypraios.

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Fallaize, C.J., Kypraios, T. Exact Bayesian inference for the Bingham distribution. Stat Comput 26, 349–360 (2016). https://doi.org/10.1007/s11222-014-9508-7

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  • DOI: https://doi.org/10.1007/s11222-014-9508-7

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