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Approximate maximum likelihood estimation of the Bingham distribution

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  • Bee, Marco
  • Benedetti, Roberto
  • Espa, Giuseppe

Abstract

Maximum likelihood estimation of the Bingham distribution is difficult because the density function contains a normalization constant that cannot be computed in closed form. Given the availability of sufficient statistics, Approximate Maximum Likelihood Estimation (AMLE) is an appealing method that allows one to bypass the evaluation of the likelihood function. The impact of the input parameters of the AMLE algorithm is investigated and some methods for choosing their numerical values are suggested. Moreover, AMLE is compared to the standard approach which numerically maximizes the (approximate) likelihood obtained with the normalization constant estimated via the Holonomic Gradient Method (HGM). For the Bingham distribution on the sphere, simulation experiments and real-data applications produce similar outcomes for both methods. On the other hand, AMLE outperforms HGM when the dimension increases.

Suggested Citation

  • Bee, Marco & Benedetti, Roberto & Espa, Giuseppe, 2017. "Approximate maximum likelihood estimation of the Bingham distribution," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 84-96.
    • Handle: RePEc:eee:csdana:v:108:y:2017:i:c:p:84-96
    DOI: 10.1016/j.csda.2016.11.004
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    References listed on IDEAS

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    1. Kume, A. & Walker, S.G., 2014. "On the Bingham distribution with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 345-352.
    2. A. Kume & Andrew T. A. Wood, 2005. "Saddlepoint approximations for the Bingham and Fisher–Bingham normalising constants," Biometrika, Biometrika Trust, vol. 92(2), pages 465-476, June.
    3. J. Møller & A. N. Pettitt & R. Reeves & K. K. Berthelsen, 2006. "An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants," Biometrika, Biometrika Trust, vol. 93(2), pages 451-458, June.
    4. Peel D. & Whiten W. J & McLachlan G. J, 2001. "Fitting Mixtures of Kent Distributions to Aid in Joint Set Identification," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 56-63, March.
    5. Bee, Marco & Espa, Giuseppe & Giuliani, Diego, 2015. "Approximate maximum likelihood estimation of the autologistic model," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 14-26.
    6. Thomas Hamelryck & John T Kent & Anders Krogh, 2006. "Sampling Realistic Protein Conformations Using Local Structural Bias," PLOS Computational Biology, Public Library of Science, vol. 2(9), pages 1-13, September.
    7. R. Arnold & P. E. Jupp, 2013. "Statistics of orthogonal axial frames," Biometrika, Biometrika Trust, vol. 100(3), pages 571-586.
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