A Bayesian method for estimating variance components in a mixed linear model with two random vectors is presented. The procedure allows for the estimation of the ratio of variances and of any (monotone, differentiable) function of the ratio, such as heritability h2. Prior information is incorporated into the process of inference in a general manner. The methodology can therefore be used for a wide range of prior beliefs, with no modifications. Point estimators of the variance ratio (or of h2) can be obtained by numerical evaluation of one (or in some cases two) one-dimensional integral. The solution of the eigensystem of a certain positive semi-definite matrix simplifyes computations.

A. L Carriquiry

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume XIII. Plenary lectures, molecular genetics and mapping, selection, prediction and estimation., , 429–432, 1990
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