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Nonparametric Bayes methods for directional data. (English) Zbl 0809.62046
Summary: A model for directional data in \(q\) dimensions is studied. The data are assumed to arise from a distribution with a density on a sphere of \(q - 1\) dimensions. The density is unimodal and rotationally symmetric, but otherwise of unknown form. The posterior distribution of the unknown mode (mean direction) is derived, and small-sample posterior inference is discussed. The posterior mean of the density is also given. A numerical method for evaluating posterior quantities based on sampling a Markov chain is introduced. This method is generally applicable to problems involving unknown monotone functions.

MSC:
62H11 Directional data; spatial statistics
62C10 Bayesian problems; characterization of Bayes procedures
62G05 Nonparametric estimation
62F15 Bayesian inference
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