TY - JOUR

T1 - Distribution of mutual information

AU - Abarbanel, Henry D.I.

AU - Masuda, Naoki

AU - Rabinovich, M. I.

AU - Tumer, Evren

N1 - Funding Information:
This work was supported in part by the U.S. Department of Energy, Office Science, Division of Engineering and Geosciences, under grant DE-FG03-90ER14138, and in part by National Science Foundation grant NCR-9612250. Support was also received from the U.S. Army Research Office under contract No. DAAG55-98-1-0269, MURI Program in Chaotic Communications. E.T. acknowledges support from NSF Traineeship DGE 9987614.

PY - 2001/4/2

Y1 - 2001/4/2

N2 - In the analysis of time series from nonlinear sources, mutual information (MI) is used as a nonlinear statistical criterion for the selection of an appropriate time delay in time delay reconstruction of the state space. MI is a statistic over the sets of sequences associated with the dynamical source, and we examine here the distribution of MI, thus going beyond the familiar analysis of its average alone. We give for the first time the distribution of MI for a standard, classical communications channel with Gaussian, additive white noise. For time series analysis of a dynamical system, we show how to determine the distribution of MI and discuss the implications for the use of average mutual information (AMI) in selecting time delays in phase space reconstruction.

AB - In the analysis of time series from nonlinear sources, mutual information (MI) is used as a nonlinear statistical criterion for the selection of an appropriate time delay in time delay reconstruction of the state space. MI is a statistic over the sets of sequences associated with the dynamical source, and we examine here the distribution of MI, thus going beyond the familiar analysis of its average alone. We give for the first time the distribution of MI for a standard, classical communications channel with Gaussian, additive white noise. For time series analysis of a dynamical system, we show how to determine the distribution of MI and discuss the implications for the use of average mutual information (AMI) in selecting time delays in phase space reconstruction.

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U2 - 10.1016/S0375-9601(01)00128-1

DO - 10.1016/S0375-9601(01)00128-1

M3 - Article

AN - SCOPUS:0035794835

SN - 0375-9601

VL - 281

SP - 368

EP - 373

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 5-6

ER -