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Abstract:
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One-way ANOVA model is of substantial importance in contemporary statistical theory and application. It could be used to data fusion for analyzing data from different resources. It allows us to assess differences and correlations among different groups or resources. One primary interest is to estimate unknown overall mean and two covariance components (matrices). The usual MLE and moment estimators for some covariance component may not exist. Bayesian analysis under various subjective and objective priors is explored. For two covariance components, a new class of commutative priors is also proposed. Interestingly, it is also a conjugate class. Propriety and moment existence are derived for both the prior and posterior. Simulation and real data analysis show the advantages of commutative priors.
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