Bayesian data fusion with shared priors

The integration of data and knowledge from several sources is known as data fusion. When data is available in a distributed fashion or when different sensors are used to infer a quantity of interest, data fusion becomes essential. In Bayesian settings, a priori information of the unknown quantities is available and, possibly, shared among the distributed estimators. When the local estimates are fused, such prior might be overused unless it is accounted for. This paper explores the effects of shared priors in Bayesian data fusion contexts, providing fusion rules and analysis to understand the performance of such fusion as a function of the number of collaborative agents and the uncertainty of the priors. Analytical results are corroborated through experiments in a variety of estimation and classification problems.