Distribution of mutual information

In the analysis of time series from nonlinear sources, mutual information ( MI) is used as a nonlinear statistical criterion for the selection of an ap propriate time delay in time delay reconstruction of the state space. MI is a statistic over the sets of sequences associated with the dynamical sourc e, and we examine here the distribution of MI, thus going beyond the famili ar analysis of its average alone. We give for the first time the distributi on of MI for a standard, classical communications channel with Gaussian, ad ditive white noise. For time series analysis of a dynamical system, we show how to determine the distribution of MI and discuss the implications for t he use of average mutual information (AMI) in selecting time delays in phas e space reconstruction. (C) 2001 Elsevier Science B.V. All rights reserved.