On conservative fusion of information with unknown non-Gaussian dependence

This paper examines the notions of consistency and conservativeness for data fusion involving dependent information, where the degree of dependency is unknown. We consider these notions in a general sense, for non-Gaussian probability distributions, in terms of structural consistency and information processing, in particular the counting of common information. We consider the role of entropy in defining a conservative fusion rule. Finally, we investigate the geometric mean density (GMD) as a particular fusion rule, which generalises the Covariance Intersection rule to non-Gaussian pdfs. We derive key properties to demonstrate that the GMD is both conservative and effective in combining information from dependent sources.