Performance bounds for mismatched decision schemes with Poisson process observations

This paper develops a framework for analyzing the performance loss in fixed time interval decision algorithms that are based on observations of time-inhomogeneous Poisson processes, when some parameters characterizing the observation process are not known exactly. Key to the development is the formulation of an analytically computable performance metric which can be used in lieu of the true, but intractable, error probabilities. The proposed metric is obtained by identifying analytical upper bounds on the error probabilities in terms of the uncertain parameters. Using these tools, it is shown that performance degrades gracefully as long as the true values of the parameters remain within a neighborhood of the nominal values used in decision making. The results find direct application to problems of detecting illicit nuclear materials in transit.