On conjugate families and Jeffreys priors for von Mises-Fisher distributions

Kurt Hornik; Bettina Grün

doi:10.1016/j.jspi.2012.11.003

On conjugate families and Jeffreys priors for von Mises-Fisher distributions

Kurt Hornik, Bettina Grün

Publication: Scientific journal › Journal article › peer-review

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Abstract

This paper discusses characteristics of standard conjugate priors and their induced
posteriors in Bayesian inference for von Mises-Fisher distributions, using either the
canonical natural exponential family or the more commonly employed polar coordinate
parameterizations. We analyze when standard conjugate priors as well as posteriors are
proper, and investigate the Jeffreys prior for the von Mises-Fisher family. Finally, we
characterize the proper distributions in the standard conjugate family of the (matrixvalued)
von Mises-Fisher distributions on Stiefel manifolds.

Original language	English
Pages (from-to)	992 - 999
Journal	Journal of Statistical Planning and Inference
Volume	143
Issue number	5
DOIs	https://doi.org/10.1016/j.jspi.2012.11.003
Publication status	Published - 1 Feb 2013

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abstract = "This paper discusses characteristics of standard conjugate priors and their induced posteriors in Bayesian inference for von Mises-Fisher distributions, using either the canonical natural exponential family or the more commonly employed polar coordinate parameterizations. We analyze when standard conjugate priors as well as posteriors are proper, and investigate the Jeffreys prior for the von Mises-Fisher family. Finally, we characterize the proper distributions in the standard conjugate family of the (matrixvalued) von Mises-Fisher distributions on Stiefel manifolds.",

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AB - This paper discusses characteristics of standard conjugate priors and their induced posteriors in Bayesian inference for von Mises-Fisher distributions, using either the canonical natural exponential family or the more commonly employed polar coordinate parameterizations. We analyze when standard conjugate priors as well as posteriors are proper, and investigate the Jeffreys prior for the von Mises-Fisher family. Finally, we characterize the proper distributions in the standard conjugate family of the (matrixvalued) von Mises-Fisher distributions on Stiefel manifolds.

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