A Bayes Approach for Combining Correlated Estimates

Abstract A Bayes solution is supplied for an estimation problem involving a sample from a multivariate normal population having an arbitrary unknown covariance matrix, but a vector mean whose components are all equal. Assuming that a particular unnormed prior density is a convenient expression for displaying prior ignorance, it is then demonstrated that a posterior interval for this common mean can be based on Student's t distribution. If prior information can be conveniently represented by a natural conjugate prior density, the posterior interval will also depend on Student's t. An extension is made to the case of estimating the constant difference between two parallel profiles.