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Abstract This article deals with the use of prior beliefs in the estimation of regression coefficients; in particular, it considers the problems that arise when the residual variance of the regression equation is unknown and it offers a large-sample solution. Additional contributions deal with testing the hypothesis that prior and sample information are compatible with each other; and with a scalar measure for the shares of these two kinds of information in the posterior precision.
H. Theil (1963) studied this question.