No abstract

A.M. Albano et al. Phys. Rev. A 38, 3017 (1988).

Given two time series X and Y, their mutual information, I͑X , Y͒ = I͑Y , X͒, is the average number of bits of X that can be predicted by measuring Y and vice versa. In the analysis of observational data, calculation of mutual information occurs in three contexts: identification of nonlinear correlation, determination of an optimal sampling interval, particularly when embedding data, and in the investigation of causal relationships with directed mutual information. In this contribution a minimum description length argument is used to determine the optimal number of elements to use when characterizing the distributions of X and Y. However, even when using partitions of the X and Y axis indicated by minimum description length, mutual information calculations performed with a uniform partition of the XY plane can give misleading results. This motivated the construction of an algorithm for calculating mutual information that uses an adaptive partition. This algorithm also incorporates an explicit test of the statistical independence of X and Y in a calculation that returns an assessment of the corresponding null hypothesis. The previously published Fraser-Swinney algorithm for calculating mutual information includes a sophisticated procedure for local adaptive control of the partitioning process. When the Fraser and Swinney algorithm and the algorithm constructed here are compared, they give very similar numerical results ͑less than 4% difference in a typical application͒. Detailed comparisons are possible when X and Y are correlated jointly Gaussian distributed because an analytic expression for I͑X , Y͒ can be derived for that case. Based on these tests, three conclusions can be drawn. First, the algorithm constructed here has an advantage over the Fraser-Swinney algorithm in providing an explicit calculation of the probability of the null hypothesis that X and Y are independent. Second, the Fraser-Swinney algorithm is marginally the more accurate of the two algorithms when large data sets are used. With smaller data sets, however, the Fraser-Swinney algorithm reports structures that disappear when more data are available. Third, the algorithm constructed here requires about 0.5% of the computation time required by the Fraser-Swinney algorithm.

Measuring neuronal activity with electrophysiological methods may be useful in detecting neurological dysfunctions, such as mild traumatic brain injury (mTBI). This approach may be particularly valuable for rapid detection in at-risk populations including military service members and athletes. Electrophysiological methods, such as quantitative electroencephalography (qEEG) and recording event-related potentials (ERPs) may be promising; however, the field is nascent and significant controversy exists on the efficacy and accuracy of the approaches as diagnostic tools. For example, the specific measures derived from an electroencephalogram (EEG) that are most suitable as markers of dysfunction have not been clearly established. A study was conducted to summarize and evaluate the statistical rigor of evidence on the overall utility of qEEG as an mTBI detection tool. The analysis evaluated qEEG measures/parameters that may be most suitable as fieldable diagnostic tools, identified other types of EEG measures and analysis methods of promise, recommended specific measures and analysis methods for further development as mTBI detection tools, identified research gaps in the field, and recommended future research and development thrust areas. The qEEG study group formed the following conclusions: (1) Individual qEEG measures provide limited diagnostic utility for mTBI. However, many measures can be important features of qEEG discriminant functions, which do show significant promise as mTBI detection tools. (2) ERPs offer utility in mTBI detection. In fact, evidence indicates that ERPs can identify abnormalities in cases where EEGs alone are non-disclosing. (3) The standard mathematical procedures used in the characterization of mTBI EEGs should be expanded to incorporate newer methods of analysis including non-linear dynamical analysis, complexity measures, analysis of causal interactions, graph theory, and information dynamics. (4) Reports of high specificity in qEEG evaluations of TBI must be interpreted with care. High specificities have been reported in carefully constructed clinical studies in which healthy controls were compared against a carefully selected TBI population. The published literature indicates, however, that similar abnormalities in qEEG measures are observed in other neuropsychiatric disorders. While it may be possible to distinguish a clinical patient from a healthy control participant with this technology, these measures are unlikely to discriminate between, for example, major depressive disorder, bipolar disorder, or TBI. The specificities observed in these clinical studies may well be lost in real world clinical practice. (5) The absence of specificity does not preclude clinical utility. The possibility of use as a longitudinal measure of treatment response remains. However, efficacy as a longitudinal clinical measure does require acceptable test–retest reliability. To date, very few test–retest reliability studies have been published with qEEG data obtained from TBI patients or from healthy contro...