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We consider Bayes inference for a class of distributions on orien- tations in 3 dimensions described by 3 3 rotation matrices. Non-informative priors are identied and Metropolis-Hastings within Gibbs algorithms are used to generate samples from posterior distributions in one-sample and one-way random eects models. A simulation study investigates the performance of Bayes analyses based on non-informative priors in the one-sample case, making comparisons to quasi-likelihood inference. A second simulation study investigates the behavior of posteriors for some informative priors. Bayes one-way random eect analyses of orientation matrix data are then developed and the Bayes methods are illustrated in a materials science application.

Bayes one-sample and one-way random effects analyses for 3-D orientations with application to materials science