Abstract:

A new inference method has been created for the class of composite hypothesis (CH) testing problems, which arise regularly in real world applications. CH problems involve epistemic unknowns, and this precludes the selection of optimal detectors. The commonly accepted answer to such non-Bayesian problems has been for many decades the generalized likelihood ratio (GLR) test. For each sampled value of a feature vector, the GLR recipe makes an educated guess as to which optimal detector should be employed.

By contrast, a new approach called Clairvoyant Fusion (CF) attacks the CH problem from a new perspective. CF handles ignorance of which optimal detector to use by using them all. It fuses such clairvoyant detectors into a single algorithm, which it applies to all test values of the feature vector. The exact method of fusion is optional, a freedom that produces many CF flavors, all in response to the same ill-posed statistical problem. This flexibility in design affords a unique opportunity for addressing several practical problems in autonomous detection, such the presence of outliers, or the desire to simultaneously discriminate targets from other targets, as well as from clutter. It also allows the sculpting of decision boundaries in cases where reliable probability distributions cannot be devised.

Example applications are described, one class of which demonstrates the unambiguous superiority of CF to GLR. Some theoretical properties of the fusion approach are also discussed. For example, it is shown that whenever an UMP detector exists, one flavor of CF is guaranteed to produce it, a property not shared by the GLR test. It is also shown that the GLR recipe can be generated as merely one particular flavor of Clairvoyant Fusion.