A New Unified Approach for the Simulation of a Wide Class of Directional Distributions

References

• Best, D. J., and Fisher, N. I. (1979), “Efficient Simulation of the von Mises Distribution,” Journal of Applied Statistics, 28, 152–157.
   Google Scholar
• ——— (1986), “Goodness-of-Fit and Discordancy Tests for Samples From the Watson Distribution on the Sphere,” Australian Journal of Statistics, 1, 13–31.
   Google Scholar
• Byrne, S., and Girolami, M. (2013), “Geodesic Monte Carlo on Embedded Manifolds,” Scandinavian Journal of Statistics, 40, 825–845.
   PubMed Web of Science ®Google Scholar
• Chikuse, Y. (2003), Statistics on Special Manifolds, New York: Springer-Verlag.
   Google Scholar
• Fisher, N. I., Lewis, T., and Embleton, B. J. J. (1987), Statistical Analysis of Spherical Data, Cambridge: Cambridge University Press.
   Google Scholar
• Ganeiber, A. M. (2012), “Estimation and Simulation in Directional and Statistical Shape Models,” Ph.D. thesis, University of Leeds.
   Google Scholar
• Green, P. J., and Mardia, K. V. (2006), “Bayesian Alignment Using Hierarchical Models, With Applications in Protein Bioinformatics,” Biometrika, 93, 235–254.
   Web of Science ®Google Scholar
• Habeck, M. (2009), “Generation of Three-Dimensional Random Rotations in Fitting and Matching Problems,” Computational Statistics, 24, 719–731.
   Web of Science ®Google Scholar
• Hoff, P. D. (2009), “Simulation of the Matrix Bingham–von Mises–Fisher Distribution With Application to Multivariate and Relational Data,” Journal of Computational and Graphical Statistics, 18, 438–456.
   Web of Science ®Google Scholar
• Kendall, D. G. (1984), “Shape-Manifolds, Procrustean Matrices and Complex Projective Spaces,” Bulletin of the London Mathematical Society, 16, 81–121.
   Web of Science ®Google Scholar
• Kent, J. T. (1982), “The Fisher–Bingham Distribution on the Sphere,” Journal of the Royal Statistical Society, Series B, 44, 71–80.
   Google Scholar
• ——— (1994), “The Complex Bingham Distribution and Shape Analysis,” Journal of the Royal Statistical Society, Series B, 56, 285–299.
   Google Scholar
• ——— (2012), “Statistical Modelling and Simulation Using the Fisher–Bingham Distribution,” in Bayesian Methods in Structural Bioinformatics, eds. T. Hamelryck, K. Mardia and J. Ferkinghoff-Borg, Berlin: Statistics for Biology and Health, Springer-Verlag, pp. 179–188.
   Google Scholar
• Kent, J. T., Constable, P. D. L., and Er, F. (2004), “Simulation for the Complex Bingham Distribution,” Statistics and Computing, 14, 53–57.
   Web of Science ®Google Scholar
• Kent, J. T., and Ganeiber, A. M. (2012), “Simulation of Random Rotation Matrices,” in Proceedings of the 46th Scientific Meeting of the Italian Statistical Society, Sapienza University of Rome, June 20–22.
   Google Scholar
• Kent, J. T., Ganeiber, A. M., and Mardia (2012), “Simulation of the Bingham Distribution in Directional Data Analysis,” in New Statistics and Modern Natural Sciences, eds. K. V. Mardia, A. Gusnanto, A. D. Riley and J. Voss, Leeds, UK: Leeds University Press, pp. 57–59.
   Google Scholar
• Kent, J. T., and Hamelryck, T. (2005), “Using the Fisher–Bingham Distribution in Stochastic Models for Protein Structure,” in Proceedings in Quantitative Biology, Shape Analysis and Wavelets, eds. S. Barber, P. D. Baxter, K. V. Mardia and R. E. Walls, Leeds, UK: Leeds University Press, pp. 57–60.
   Google Scholar
• Kent, J. T., Hussein, I., and Jah, M. K. (2016), “Directional Distributions in Tracking of Space Debris,” in Proceedings of the 19th International Conference on Information Fusion (FUSION), Heidelberg, Germany: IEEE, pp. 2081–2086.
   Google Scholar
• Kent, J. T., Mardia, K. V., and McDonnell, P. (2006), “The Complex Bingham Quartic Distribution and Shape Analysis,” Journal of the Royal Statistical Society Series B, 68, 747–765.
   Google Scholar
• Kume, A., and Walker, S. G. (2006), “Sampling From Compositional and Directional Distributions,” Statistics and Computing, 16, 261–265.
   Web of Science ®Google Scholar
• ——— (2009), “On the Fisher–Bingham Distribution,” Statistics and Computing, 19, 167–172.
   Web of Science ®Google Scholar
• Kume, A., and Wood, A. T. A. (2005), “Saddlepoint Approximations for the Bingham and Fisher–Bingham Normalising Constants,” Biometrika, 92, 465–476.
   Web of Science ®Google Scholar
• Magnus, J. R., and Neudecker, H. (1999), Matrix Differential Calculus, with Applications in Statistics and Econometrics, Chichester: Wiley.
   Google Scholar
• Mardia, K. V., and Jupp, P. E. (2000), Directional Statistics, Chichester: Wiley.
   Google Scholar
• Mardia, K. V., Kent, J. T., and Bibby, J. M. (1979), Multivariate Analysis, London: Academic Press.
   Google Scholar
• Mardia, K. V., Taylor, C. C., and Subramaniam, G. K. (2007), “Protein Bioinformatics and Mixtures of Bivariate von Mises Distributions for Angular Data,” Biometrics, 63, 505–512.
   PubMed Web of Science ®Google Scholar
• Scealy, J. L., and Welsh, A. H. (2011), “Regression for Compositional Data by Using Distributions Defined on the Hypersphere,” Journal of the Royal Statistical Society, Series B, 73, 351–375.
   Google Scholar
• Ulrich, G. (1984), “Computer Generation of Distributions on the m-Sphere,” Applied Statistics, 33, 158–163.
   Web of Science ®Google Scholar
• Wood, A. T. A. (1987), “The Simulation of Spherical Distributions in the Fisher–Bingham Family,” Communications in Statisics, B16, 885–898.
   Google Scholar
• ——— (1994), “Simulation of the Von Mises–Fisher Distribution,” Communications in Statisics, B23, 157–164.
   Google Scholar