an:00718757
Zbl 0809.62046
Brunner, Lawrence J.; Lo, Albert Y.
Nonparametric Bayes methods for directional data
EN
Can. J. Stat. 22, No. 3, 401-412 (1994).
00022693
1994
j
62H11 62C10 62G05 62F15
spherical statistics; rotationally symmetric density; unimodal density; mean direction; directional data; posterior distribution; small-sample posterior inference; posterior mean; Markov chain; unknown monotone functions
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.