Summary
A standard improper prior for the parameters of a MANOVA model is shown to yield an inference that is incoherent in the sense of Heath and Sudderth. The proof of incoherence is based on the fact that the formal Bayes estimate, sayδ 0 , of the covariance matrix based on the improper prior and a certain bounded loss function is uniformly inadmissible in that there is another estimatorδ l and an ɛ>0 such that the risk functions satisfyR(δ l ,Σ)⩽R δ 0 ,Σ)−ε for all values of the covariance matrix Σ. The estimatorδ I is formal Bayes for an alternative improper prior which leads to a coherent inference.
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Research supported by National Science Foundation grants DMS-89-22607 (for Eaton) and DMS-9123358 (for Sudderth).
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Eaton, M.L., Sudderth, W.D. The formal posterior of a standard flat prior in MANOVA is incoherent. J. It. Statist. Soc. 4, 251–270 (1995). https://doi.org/10.1007/BF02589105
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DOI: https://doi.org/10.1007/BF02589105