Exact Bayesian inference for the Bingham distribution

Fallaize, Christopher J.; Kypraios, Theodore

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

Citation

Fallaize, C. J., & Kypraios, T. (in press). Exact Bayesian inference for the Bingham distribution. Statistics and Computing, 26(1), https://doi.org/10.1007/s11222-014-9508-7

• Journal Article Type: Article
• Acceptance Date: Aug 20, 2014
• Online Publication Date: Jan 1, 2016
• Deposit Date: Jul 14, 2016
• Publicly Available Date: Jul 14, 2016
• Journal: Statistics and Computing
• Print ISSN: 0960-3174
• Electronic ISSN: 1573-1375
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 26
• Issue: 1
• DOI: https://doi.org/10.1007/s11222-014-9508-7
• Keywords: Directional statistics; Bayesian inference; Markov Chain Monte Carlo; Doubly intractable distributions
• Public URL: https://nottingham-repository.worktribe.com/output/978876
• Publisher URL: http://link.springer.com/article/10.1007/s11222-014-9508-7
• Additional Information: The final publication is available at Springer via http://dx.doi.org/0.1007/s11222-014-9508-7/
• Contract Date: Jul 14, 2016