Summary
Two independent random samples of sizesN 1 andN 2 from multivariate normal populationsN p (θ1,∑1) andN p (θ2,∑2) are considered. Under the null hypothesisH 0: θ1=θ2, a single θ is generated from aN p(μ, Σ) prior distribution, while underH 1: θ1≠θ2 two means are generated from the exchangeable priorN p(μ,σ). In both cases Σ will be assumed to have a vague prior distribution. For a simple covariance structure, the Bayes factorB and minimum Bayes factor in favour of the null hypotheses is derived. The Bayes risk for each hypothesis is derived and a strategy is discussed for using the Bayes factor and Bayes risks to test the hypothesis.
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Nel, D.G., Groenewald, P.C.N. A Bayesian approach to the multivariate Behrens-Fisher problem under the assumption of proportional covariance matrices. Test 2, 111–124 (1993). https://doi.org/10.1007/BF02562671
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DOI: https://doi.org/10.1007/BF02562671