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Objective Bayesian analysis for the normal compositional model

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  • Kazianka, Hannes

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.

Suggested Citation

  • Kazianka, Hannes, 2012. "Objective Bayesian analysis for the normal compositional model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1528-1544.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1528-1544 DOI: 10.1016/j.csda.2011.08.016
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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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