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Theory & Methods: An Empirical Bayes Inference for the von Mises Distribution
Author(s) -
Rodrigues Josemar,
Galvão Leite José,
Milan Luis A.
Publication year - 2000
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00140
Subject(s) - mathematics , von mises distribution , hyperparameter , frequentist inference , empirical distribution function , bayesian linear regression , bayes factor , statistical inference , inference , bayesian inference , bayes' theorem , gibbs sampling , prior probability , econometrics , bayesian probability , von mises yield criterion , statistics , algorithm , artificial intelligence , computer science , physics , finite element method , thermodynamics
This paper develops an empirical Bayesian analysis for the von Mises distribution, which is the most useful distribution for statistical inference of angular data. A two‐stage informative prior is proposed, in which the hyperparameter is obtained from the data in one of the stages. This empirical or approximate Bayes inference is justified on the basis of maximum entropy, and it eliminates the modified Bessel functions. An example with real data and a realistic prior distribution for the regression coefficients is considered via a Metropolis‐within‐Gibbs algorithm.