The Bayesian estimation of common parameters from several responses

Abstract

Suppose that n multivariate observations are available with the u th such observation Y u = ( Y 1u , Y 2u …, Y ku ) recordmg the values of k different responses, such as the yields of k different products of a chemical reaction at the u th set of experimental conditions. Suppose that the k expected values E ( Y 1u ), E ( Y 2u ), …, E ( Y ku ) can be represented by k known functions involving m common parameters θ 1 θ 2 , …, θ m . 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.