Statistical Analysis of Stochastic Resonance in a Simple Setting

A subthreshold signal may be detected if noise is added to the data. We study a simple model, consisting of a constant signal to which at uniformly spaced times independent and identically distributed noise variables with known distribution are added. A detector records the times at which the noisy signal exceeds a threshold. There is an optimal noise level, called stochastic resonance. We explore the detectability of the signal in a system with one or more detectors, with dierent thresholds. We use a statistical detectability measure, the asymptotic variance of the best estimator of the signal from the thresholded data, or equivalently, the Fisher information in the data. In particular, we determine optimal congurations of detectors, varying the distances between the thresholds and the signal, as well as the noise level. The approach generalizes to non-constant signals. AMS 1991 subject classications. Primary 62F12; secondary 62P10. Key words and Phrases. EÆcient estimator, maxim..