  Suppose we have a Bayesian model which combines evidence from several
different sources. We want to know which model parameters most affect the
estimate or decision from the model, or which of the parameter uncertainties
drive the decision uncertainty. Furthermore we want to prioritise what further
data should be collected. These questions can be addressed by Value of
Information (VoI) analysis, in which we estimate expected reductions in loss
from learning specific parameters or collecting data of a given design. We
describe the theory and practice of VoI for Bayesian evidence synthesis, using
and extending ideas from health economics, computer modelling and Bayesian
design. The methods are general to a range of decision problems including point
estimation and choices between discrete actions. We apply them to a model for
estimating prevalence of HIV infection, combining indirect information from
several surveys, registers and expert beliefs. This analysis shows which
parameters contribute most of the uncertainty about each prevalence estimate,
and provides the expected improvements in precision from collecting specific
amounts of additional data.
