IDEAS home Printed from https://ideas.repec.org/p/trn/utwprg/2015-02.html
   My bibliography  Save this paper

Approximate likelihood inference for the Bingham distribution

Author

Listed:
  • Marco Bee
  • Roberto Benedetti
  • Giuseppe Espa

Abstract

Likelihood inference for the Bingham distribution is difficult because the density function contains a normalization constant that cannot be computed in closed form. We propose to estimate the parameters by means of Approximate Maximum Likelihood Estimation (AMLE), thus bypassing the problem of evaluating the likelihood function. We study the impact of the input parameters of the AMLE algorithm and suggest some methods for choosing their numerical values. Moreover, we compare AMLE to the standard approach consisting in maximizing numerically 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

  • Marco Bee & Roberto Benedetti & Giuseppe Espa, 2015. "Approximate likelihood inference for the Bingham distribution," DEM Working Papers 2015/02, Department of Economics and Management.
    • Handle: RePEc:trn:utwprg:2015/02
    as

    Download full text from publisher

    File URL: http://web.unitn.it/files/download/39673/demwp2015_02.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    4. R. Arnold & P. E. Jupp, 2013. "Statistics of orthogonal axial frames," Biometrika, Biometrika Trust, vol. 100(3), pages 571-586.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Ian L. Dryden, 2014. "Comment on Geodesic Monte Carlo on Embedded Manifolds by Byrne and Girolami," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 8-9, March.
    3. Hornik, Kurt & Grün, Bettina, 2014. "movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i10).
    4. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    5. Fernández-Durán Juan José & Gregorio-Domínguez MarÍa Mercedes, 2014. "Modeling angles in proteins and circular genomes using multivariate angular distributions based on multiple nonnegative trigonometric sums," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(1), pages 1-18, February.
    6. Arnold, R. & Jupp, P.E. & Schaeben, H., 2018. "Statistics of ambiguous rotations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 73-85.
    7. Christophe Ley & Thomas Verdebout, 2014. "Skew-rotsymmetric Distributions on Unit Spheres and Related Efficient Inferential Proceedures," Working Papers ECARES ECARES 2014-46, ULB -- Universite Libre de Bruxelles.
    8. Jean-Luc Dortet-Bernadet & Nicolas Wicker, 2018. "A Note on Inverse Stereographic Projection of Elliptical Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 138-151, February.
    9. Jupp, P.E. & Regoli, G. & Azzalini, A., 2016. "A general setting for symmetric distributions and their relationship to general distributions," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 107-119.
    10. Pami Dua & Divya Tuteja, 2021. "Regime Shifts in the Behaviour of International Currency and Equity Markets: A Markov-Switching Analysis," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 309-336, December.
    11. Ley, Christophe & Verdebout, Thomas, 2017. "Skew-rotationally-symmetric distributions and related efficient inferential procedures," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 67-81.
    12. Jes Frellsen & Ida Moltke & Martin Thiim & Kanti V Mardia & Jesper Ferkinghoff-Borg & Thomas Hamelryck, 2009. "A Probabilistic Model of RNA Conformational Space," PLOS Computational Biology, Public Library of Science, vol. 5(6), pages 1-11, June.
    13. Kume, A. & Walker, S.G., 2014. "On the Bingham distribution with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 345-352.
    14. J. Fernández-Durán & M. Gregorio-Domínguez, 2014. "Distributions for spherical data based on nonnegative trigonometric sums," Statistical Papers, Springer, vol. 55(4), pages 983-1000, November.
    15. Davy Paindaveine & Thomas Verdebout, 2017. "Detecting the Direction of a Signal on High-dimensional Spheres: Non-null and Le Cam Optimality Results," Working Papers ECARES ECARES 2017-40, ULB -- Universite Libre de Bruxelles.
    16. Tamio Koyama & Akimichi Takemura, 2016. "Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables," Computational Statistics, Springer, vol. 31(4), pages 1645-1659, December.
    17. Kume, A. & Wood, Andrew T.A., 2007. "On the derivatives of the normalising constant of the Bingham distribution," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 832-837, April.
    18. Marc Hallin & H Lui & Thomas Verdebout, 2022. "Nonparametric Measure-transportation-based Methods for Directional Data," Working Papers ECARES 2022-18, ULB -- Universite Libre de Bruxelles.
    19. Angela Montanari & Daniela Calò, 2013. "Model-based clustering of probability density functions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(3), pages 301-319, September.
    20. David Simoncini & Francois Berenger & Rojan Shrestha & Kam Y J Zhang, 2012. "A Probabilistic Fragment-Based Protein Structure Prediction Algorithm," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-11, July.

    More about this item

    Keywords

    Directional data; Simulation; Intractable Likelihood; Sufficient statistics;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:trn:utwprg:2015/02. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: roberto.gabriele@unitn.it (email available below). General contact details of provider: https://edirc.repec.org/data/detreit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.