We present local Bayesian fusion approaches for the reduction of storage and computational costs of Bayesian fusion which is detached from fixed modelling assumptions. Using local approaches, Bayesian fusion is not performed in detail on the whole space that is spanned by the quantities of interest but only locally - at least in regions that are task relevant with a high probability. These regions are determined using common bounds for the probability of misleading evidence. Coarsening and restriction techniques are then used to create local Bayesian setups in a top-down or a more general bottom-up manner. Distributed local Bayesian fusion is realizable via an agent based fusion architecture.