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Bayesian analysis for bivariate von Mises distributions

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  • Kanti Mardia

Abstract

There has been renewed interest in the directional Bayesian analysis for the bivariate case especially in view of its fundamental new and challenging applications to bioinformatics. The previous work had concentrated on Bayesian analysis for univariate von Mises distribution. Here, we give the description of the general bivariate von Mises (BVM) distribution and its properties. There are various submodels of this distribution which have become important and we give a review of these submodels. Also, we derive the normalizing constant for the general BVM distribution in a compact way. Conjugate priors and posteriors for the general case and the submodels are obtained. The conjugate prior for a multivariate von Mises distribution is also examined.

Suggested Citation

  • Kanti Mardia, 2010. "Bayesian analysis for bivariate von Mises distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 515-528.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:3:p:515-528
    DOI: 10.1080/02664760903551267
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    References listed on IDEAS

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    1. Peter J. Green & Kanti V. Mardia, 2006. "Bayesian alignment using hierarchical models, with applications in protein bioinformatics," Biometrika, Biometrika Trust, vol. 93(2), pages 235-254, June.
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    3. D. J. Best & N. I. Fisher, 1979. "Efficient Simulation of the von Mises Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(2), pages 152-157, June.
    4. Kanti V. Mardia & John T. Kent & Gareth Hughes & Charles C. Taylor, 2009. "Maximum likelihood estimation using composite likelihoods for closed exponential families," Biometrika, Biometrika Trust, vol. 96(4), pages 975-982.
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    6. Lennox, Kristin P. & Dahl, David B. & Vannucci, Marina & Tsai, Jerry W., 2009. "Density Estimation for Protein Conformation Angles Using a Bivariate von Mises Distribution and Bayesian Nonparametrics," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 586-596.
    7. Michael Habeck, 2009. "Generation of three-dimensional random rotations in fitting and matching problems," Computational Statistics, Springer, vol. 24(4), pages 719-731, December.
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    1. Anahita Nodehi & Mousa Golalizadeh & Mehdi Maadooliat & Claudio Agostinelli, 2021. "Estimation of parameters in multivariate wrapped models for data on a p-torus," Computational Statistics, Springer, vol. 36(1), pages 193-215, March.

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