Statistical Decision Fusion Theory

By combining information theory, statistical decision theory, and maximum entropy to address the decision fusion problems, a statistical decision fusion theory is obtained. The theory explains why decision fusion is so difficult and why the performance of decision fusion systems does not always meet expectations. The theory suggests how statistical decision systems such as the conceptual "Family of Systems" might be designed. The theory clarifies why independent subsystems are desired in data fusion systems. A decision fusion function is obtained from the theory for fusing independent decision subsystems. An examination of the characteristics of the fusion function shows that it can handle decision results from subsystems operating at different hierarchical levels in the sets of decisions and prior classes. This fusion arises naturally without the need to incorporate additional principles to convert decisions and prior classes to other hierarchical levels. In the design of decision fusion systems, the subsystems can be designed to operate at their own natural levels in the set hierarchy while the fusion can be designed to operate at the most descriptive level. The fusion function can also be applied to time evolving decision fusion systems and cast as a Bayes-Markov non-linear filtering process. The resulting process is similar to Kalman filtering and allows for the design of decision systems that de-weights the influence of previous results when new information is processed. In summary, the characteristics of the decision fusion theory have only just begun to be explored and a rich variety of decision fusion system designs await discovery.