A Bayesian detection model is formulated for a distributed system of sensors, wherein each sensor provides the central processor with a detection probability rather than an observation vector or a detection decision. Sufficiency relations are developed for comparing alternative sensor systems in terms of their likelihood functions. The sufficiency relations, characteristic Bayes risks, and receiver operating characteristics provide equivalent criteria for establishing a dominance order of sensor systems. Parametric likelihood functions drawn from the beta family of densities are presented, and analytic solutions for the decision model and dominance conditions are derived. The theory is illustrated with numerical examples highlighting the behavior of the model and benefits of fusing the detection probabilities.
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