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Spectral and coherence methodologies are ubiquitous for the analysis of multiple time series. Partial coherence analysis may be used to try to determine graphical models for brain functional connectivity. The outcome of such an analysis may be considerably influenced by factors such as the degree of spectral smoothing, line and interference removal, matrix… (More)

If, as is widely believed, schizophrenia is characterized by abnormalities of brain functional connectivity, then it seems reasonable to expect that different subtypes of schizophrenia could be discriminated in the same way. However, evidence for differences in functional connectivity between the subtypes of schizophrenia is largely lacking and, where it… (More)

Complex-valued Gaussian distributions occur frequently in signal processing. We derive a simple statistic, independent of any complex-valued correlation, for testing for the equality of variances using a sample drawn from such a bivariate distribution. The percentage points of the distribution are easy to compute. The power of the test is determined and… (More)

We derive important and useful new statistical properties of the estimated degree of polarization in the two-dimensional case. We find its distribution function and show how it may be used to construct confidence intervals. We also find an expression for any moment of the distribution, and derive an exact unbiasing formula for the estimator of the squared… (More)

We calculate the frequency-dependent variance of the log spectral ratio for correlated time series. This is used to produce a weighted least-squares approach to attenuation estimation, with weights calculated from estimated coherence. Applications to synthetic and real data illustrate that, for correlated series, the method improves significantly on… (More)

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