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One-sample Bayes inference for symmetric distributions of 3-D rotations

Author

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  • Qiu, Yu
  • Nordman, Daniel J.
  • Vardeman, Stephen B.

Abstract

A variety of existing symmetric parametric models for 3-D rotations found in both statistical and materials science literatures are considered from the point of view of the “uniform-axis-random-spin” (UARS) construction. One-sample Bayes methods for non-informative priors are provided for all of these models and attractive frequentist properties for corresponding Bayes inference on the model parameters are confirmed. Taken together with earlier work, the broad efficacy of non-informative Bayes inference for symmetric distributions on 3-D rotations is conclusively demonstrated.

Suggested Citation

  • Qiu, Yu & Nordman, Daniel J. & Vardeman, Stephen B., 2014. "One-sample Bayes inference for symmetric distributions of 3-D rotations," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 520-529.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:520-529
    DOI: 10.1016/j.csda.2013.02.004
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    References listed on IDEAS

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    1. Bingham, Melissa A. & Nordman, Daniel J. & Vardeman, Stephen B., 2010. "Finite-sample investigation of likelihood and Bayes inference for the symmetric von Mises-Fisher distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1317-1327, May.
    2. Bingham, Melissa A. & Nordman, Daniel J. & Vardeman, Stephen B., 2009. "Modeling and Inference for Measured Crystal Orientations and a Tractable Class of Symmetric Distributions for Rotations in Three Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1385-1397.
    3. Nordman, Daniel J. & Vardeman, Stephen B. & Bingham, Melissa A., 2009. "Uniformly Hyper-Efficient Bayes Inference in a Class of Nonregular Problems," The American Statistician, American Statistical Association, vol. 63(3), pages 234-238.
    4. León, Carlos A. & Massé, Jean-Claude & Rivest, Louis-Paul, 2006. "A statistical model for random rotations," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 412-430, February.
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