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Raiffa and Schlaifer's theory of conjugate prior distributions is here applied to Jeffrey's theory of tests for a sharp hypothesis, for simple normal sampling, for model I analysis of variance, and for univariate and multivariate Behrens-Fisher probelms. Leonard J. Savage's Bayesianization of Jeffrey's theory is given with new generalizations. A new conjugate prior family for normal sampling which allows prior independence of unknown mena and variance is given.
James Dickey (Mon,) studied this question.