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Suppose that n multivariate observations are available with the uth such observation Yu = (Y1u, Y2u …, Yku) recordmg the values of k different responses, such as the yields of k different products of a chemical reaction at the uth set of experimental conditions. Suppose that the k expected values E(Y1u), E(Y2u), …, E(Yku) can be represented by k known functions involving m common parameters θ1 θ2, …, θm. For example, the chemical yield of the k products might be expressed by k different functions of the basic rate constants of the system. In attempting to estimate the θ's and make inferences concerning them we naturally wish to combine appropriately the relevant information from the different responses. In this paper the appropriate Bayesian techniques are worked out and examples are given.
Box et al. (Wed,) studied this question.