Chaotic statistics of biomedical time series

New statistical techniques are reviewed that have been developed specifically for the analysis of chaotic systems. These techniques involve new concepts that are largely unrelated to those developed for the analysis of linear systems. Three such techniques are discussed: dimension, entropy, and Lyapunov exponents. All three techniques have a common starting point: embedding the time series. It is shown that artifacts of the chaotic statistical techniques-unimportant aspects of the time series (such as their finite length)-have unintended consequences in the statistical results. There are two widely (but not universally) applicable techniques that can help: randomized time series as controls, and coarsely approximate methods.<
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