Confusion and clairvoyance: some remarks on the composite hypothesis testing problem

This paper discusses issues related to the inherent ambiguity of the composite hypothesis testing problem, a problem that is central to the detection of target signals in cluttered backgrounds. In particular, the paper examines the recently proposed method of continuum fusion (which, because it combines an ensemble of clairvoyant detectors, might also be called clairvoyant fusion), and its relationship to other strategies for composite hypothesis testing. A specific example involving the affine subspace model adds to the confusion by illustrating irreconcilable differences between Bayesian and non-Bayesian approaches to target detection.