  Consider the problem of searching a large set of items, such as emails, for a
small set which are relevant to a given query. This can be implemented in a
sequential manner whereby we use knowledge from earlier items that we have
screened to help us choose future items in an informed way. Often the items we
are searching have an underlying network structure: for example emails can be
related to a network of participants, where an edge in the network relates to
the presence of a communication between those two participants. Recent work by
Dimitrov, Kress and Nevo has shown that using the information about the network
structure together with a modelling assumption that relevant items and
participants are likely to cluster together, can greatly increase the rate of
screening relevant items. However their approach is computationally expensive
and thus limited in applicability to small networks. Here we show how Bayes
Linear methods provide a natural approach to modelling such data; that they
output posterior summaries that are most relevant to heuristic policies for
choosing future items; and that they can easily be applied to large-scale
networks. Both on simulated data, and data from the Enron Corpus, Bayes Linear
approaches are shown to be applicable to situations where the method of
Dimitrov et al. is infeasible; and give substantially better performance than
methods that ignore the network structure.
