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Biometrika 1975 62(3):651-654; doi:10.1093/biomet/62.3.651
© 1975 by Biometrika Trust
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A note on partially Bayes inference and the linear model

D. R. COX

Department of Mathematics, Imperial College London

Some results are outlined for estimation in a replicated linear model in which the variance changes from cell to cell in accordance with an inverse gamma prior density. The primary parameters of the linear model are, however, treated as fixed unknown parameters. The analysis thus exemplifies the treatment of problems in which the nuisance parameters have a prior distribution but the parameters of primary interest do not.

Key Words: Ancillary statistic • Behrens-Fisher problem • Conditional estimation • Empirical Bayes • Linear model • Maximum likelihood • Variance heterogeneity


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