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 different 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 configurations of detectors, varying the distances between the thresholds and the signal, as well as the noise level. The approach generalizes to nonconstant signals.

[1]  Thomas T. Imhoff,et al.  Noise-enhanced information transmission in rat SA1 cutaneous mechanoreceptors via aperiodic stochastic resonance. , 1996, Journal of neurophysiology.

[2]  J. M. G. Vilar,et al.  Stochastic Multiresonance , 1997 .

[3]  R. Z. Khasʹminskiĭ,et al.  Statistical estimation : asymptotic theory , 1981 .

[4]  Frank Moss,et al.  Stochastic Resonance in Ensembles of Nondynamical Elements: The Role of Internal Noise , 1997 .

[5]  Bulsara,et al.  Cooperative behavior in the periodically modulated Wiener process: Noise-induced complexity in a model neutron. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  John P. Miller,et al.  Broadband neural encoding in the cricket cereal sensory system enhanced by stochastic resonance , 1996, Nature.

[7]  D. Politis,et al.  Statistical Estimation , 2022 .

[8]  D. Chialvo,et al.  Stochastic Resonance in Models of Neuronal Ensembles Revisited , 1996 .

[9]  Carson C. Chow,et al.  Aperiodic stochastic resonance in excitable systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Frank Moss,et al.  STOCHASTIC RESONANCE: TUTORIAL AND UPDATE , 1994 .

[11]  Bulsara,et al.  Time-interval sequences in bistable systems and the noise-induced transmission of information by sensory neurons. , 1991, Physical review letters.

[12]  Kurt Wiesenfeld,et al.  Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs , 1995, Nature.

[13]  L. Gammaitoni,et al.  Stochastic resonance and the dithering effect in threshold physical systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Teich,et al.  Information measures quantifying aperiodic stochastic resonance. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  François Chapeau-Blondeau,et al.  Input-output gains for signal in noise in stochastic resonance , 1997 .

[16]  Zhou,et al.  Escape-time distributions of a periodically modulated bistable system with noise. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[17]  F. Moss,et al.  Non-Dynamical Stochastic Resonance: Theory and Experiments with White and Arbitrarily Coloured Noise , 1995 .

[18]  André Longtin,et al.  Stochastic resonance in models of neuronal ensembles , 1997 .

[19]  Bulsara,et al.  Threshold detection of wideband signals: A noise-induced maximum in the mutual information. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Lutz Schimansky-Geier,et al.  Linear response theory applied to stochastic resonance in models of ensembles of oscillators , 1997 .

[21]  W. Pitts,et al.  A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.

[22]  Peter Jung,et al.  STOCHASTIC RESONANCE AND OPTIMAL DESIGN OF THRESHOLD DETECTORS , 1995 .

[23]  Paul Embrechts,et al.  STATISTICAL ESTIMATION: ASYMPTOTIC THEORY: (Applications of Mathematics, 16) , 1982 .

[24]  Anishchenko,et al.  Dynamical Entropies Applied to Stochastic Resonance , 1996, Physical review letters.

[25]  Carson C. Chow,et al.  Aperiodic stochastic resonance. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Ursula U. Müller,et al.  Nonparametric regression for threshold data , 2000 .

[27]  Carson C. Chow,et al.  Stochastic resonance without tuning , 1995, Nature.

[28]  Zoltan Gingl,et al.  A stochastic resonator is able to greatly improve signal-to- noise ratio , 1996 .

[29]  P. Bickel.  Efficient and Adaptive Estimation for Semiparametric Models , 1993 .

[30]  H Sompolinsky,et al.  Simple models for reading neuronal population codes. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[31]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[32]  M. Stemmler.  A single spike suffices: the simplest form of stochastic resonance in model neurons , 1996 .

[33]  François Chapeau-Blondeau,et al.  Noise-enhanced capacity via stochastic resonance in an asymmetric binary channel , 1997 .

[34]  Luca Gammaitoni,et al.  Stochastic resonance in multi-threshold systems , 1995 .