One-sample Bayes inference for symmetric distributions of 3-D rotations. (English) Zbl 1471.62167
Summary: 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.
MSC:
| 62-08 | Computational methods for problems pertaining to statistics |
| 62F15 | Bayesian inference |
| 62H10 | Multivariate distribution of statistics |
| 62H11 | Directional data; spatial statistics |
| 62F12 | Asymptotic properties of parametric estimators |
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