  This paper develops a mathematical and computational framework for analyzing
the expected performance of Bayesian data fusion, or joint statistical
inference, within a sensor network. We use variational techniques to obtain the
posterior expectation as the optimal fusion rule under a deterministic
constraint and a quadratic cost, and study the smoothness and other properties
of its classification performance. For a certain class of fusion problems, we
prove that this fusion rule is also optimal in a much wider sense and satisfies
strong asymptotic convergence results. We show how these results apply to a
variety of examples with Gaussian, exponential and other statistics, and
discuss computational methods for determining the fusion system's performance
in more general, large-scale problems. These results are motivated by studying
the performance of fusing multi-modal radar and acoustic sensors for detecting
explosive substances, but have broad applicability to other Bayesian decision
problems.
