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Objective Bayesian analysis for the normal compositional model

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  • Kazianka, Hannes
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    Abstract

    The issue of objective prior specification for the parameters in the normal compositional model is considered within the context of statistical analysis of linearly mixed structures in image processing. In particular, the Jeffreys prior for the vector of fractional abundances in case of a known covariance matrix is derived. If an additional unknown variance parameter is present, the Jeffreys prior and the reference prior are computed and it is proven that the resulting posterior distributions are proper. Markov chain Monte Carlo strategies are proposed to efficiently sample from the posterior distributions and the priors are compared on the grounds of the frequentist properties of the resulting Bayesian inferences. The default Bayesian analysis is illustrated by a dataset taken from fluorescence spectroscopy.

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    File URL: http://www.sciencedirect.com/science/article/pii/S016794731100315X
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 6 ()
    Pages: 1528-1544

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1528-1544

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Normal compositional model; Spectral unmixing; Jeffreys prior; Reference prior; Frequentist properties;

    References

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    1. Manishi Prasad & Peter Wahlqvist & Rich Shikiar & Ya-Chen Tina Shih, 2004. "A," PharmacoEconomics, Springer Healthcare | Adis, vol. 22(4), pages 225-244.
    2. Hannes Kazianka & Michael Mulyk & J�rgen Pilz, 2011. "A Bayesian approach to estimating linear mixtures with unknown covariance structure," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(9), pages 1801-1817, September.
    3. Berger J.O. & De Oliveira V. & Sanso B., 2001. "Objective Bayesian Analysis of Spatially Correlated Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1361-1374, December.
    4. Xu, Ancha & Tang, Yincai, 2011. "Objective Bayesian analysis of accelerated competing failure models under Type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2830-2839, October.
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