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Nonparametric Bayes methods for directional data
Author(s) -
Brunner Lawrence J.,
Lo Albert Y.
Publication year - 1994
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315601
Subject(s) - posterior probability , mathematics , nonparametric statistics , bayes' theorem , markov chain monte carlo , markov chain , monotone polygon , sample (material) , distribution (mathematics) , statistics , statistical physics , mathematical analysis , bayesian probability , geometry , physics , thermodynamics
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.