Local Computation Aspects of Bayes Linear Kinematics

Goldstein and Shaw (2002) developed Bayes linear kinematics describing how a Bayes linear analysis should be carried out when we only receive partial information which changes our beliefs about a vector of random quantities in some generalised way. In this paper we explore principles of local computation for Bayes linear kinematic updates. This theory is illustrated by the Bayes linear Bayes models introduced by Goldstein and Shaw (2002), showing how the conditional independence structure of the Bayes linear graphical model may be exploited. A local computation algorithm for revising our beliefs over the Bayes linear graphical model following observations in the Bayesian graphical models is given. The theory is illustrated by an example in partition testing. A second set of models are introduced, where conditional on an element within a partition, the model is a Bayes linear Bayes model. We discuss updating in such models and an example, involving the modelling of a software action, provided.