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The main aim of this note is to give a theoretical discussion of Bayesian inference for the von Mises-Fisher distribution. The choice of particular priors is considered and the admissibility of certain Bayesian estimators studied. For the multisample case estimators are given. Some problems of testing hypotheses are summarized in the form of posterior odds against the null hypothesis.
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Mardia et al. (1976) studied this question.
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