Practical building of subjective covariance structures for large complicated systems

Summary.  In many practical problems it is necessary to specify prior beliefs about large numbers of related quantities. In Bayes linear systems this consists of specifying means, variances and covariances. Likewise standard probabilistic Bayesian approaches often lead to prior representations involving systems of Gaussian unknowns which require similar moment specifications. In practice, the specification of such collections of beliefs may seem daunting to non-specialists if no help or guidance is given. However, such assistance can be provided through the use of structured graphical models and some simple devices to make the task manageable. These ideas are illustrated by some practical examples. In particular, a computer system, designed for sales forecasting in supply chain management, is described. This system includes a graphical interface for building and editing belief specifications.