Linearized Bayesian estimation of network flows

Suppose we have an imprecise estimate of arc flows in a given network, either through prior measurements under similar conditions, or through observation of related phenomena; how can we use imprecise measurements of boundary flows into and out of the network to improve our original estimate? This is a problem in Bayesian regression that is difficult to carry out, in general. However, by using a linearized approach due to credibility theory that is similar to results in linear filter theory, one can find interesting and useful estimates using only first and second moments of the prior and observation error distributions. This result has application in road and communication traffic measurement, statistical auditing, and nuclear material accountability problems.