Far East Journal of Theoretical Statistics
Volume 9, Issue 2, Pages 143 - 156
(March 2003)
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BAYESIAN MULTIPLE COMPARISONS FOR k MULTIVARIATE NORMAL
VARIANCE-COVARIANCE MATRICES
Myung Cheol Kim (Korea) and Hea-Jung Kim (Korea)
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Abstract: In this article, we suggest a nonparametric Bayesian method
for calculating posterior probabilities for various hypotheses of equality among
k multivariate normal population variance-covariance matrices. This leads
to a simple method for obtaining pairwise comparisons of variance-covariance
matrices in a statistical experiment with a partition on the parameter space
induced by equality and inequality relationships among the matrices. The family
of Dirichlet process priors is applied in the form of baseline prior/likelihood
combination to provide the method. Finding the posterior probabilities are
analytically intractable, we use Gibbs sampling. Two examples are illustrated
for the method. It is seen that the method is straightforward for specifying
distributionally and to implement computationally, with output readily adapted
for required comparison. |
Keywords and phrases: Bayesian multiple comparison, Dirichlet process priors, the Gibbs sampler,
hierarchical model, posterior probabilities. |
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