Description

This paper is a theoretical investigation on conservative data-fusion. It provides insights at a fundamental level on what is meant by the term "conservative" in the context of Bayesian estimation. Notably, we are (i) making conservative approximations of known probability distributions, (ii) avoiding double counting of common information, and (iii) providing lower bounds on point-wise probabilities. As a practical conservative fusion rule, the geometric mean density (GMD) is already in common use, especially its Gaussian incarnation: the Covariance Intersection. Our conservativeness results provide a stronger justification of GMD than existed previously, so that practitioners may be confident that it is a principled rule for fusing dependent information.

Abstract

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.

Download

Full paper [pdf] (201 kb)