| Magnetoencephalography (MEG) provides a non-invasive measurement of the magnetic field emitted by populations of synchronously engaged neurons associated with cortical sulci. The technique is advantageous for its high temporal resolution allowing, in principle, the study of relatively fast dynamics on the order of milliseconds. The characterization of the nonlinear stochastic/deterministic dynamical structure within MEG signals remains a hard problem.;Existing methods use nonlinear test statistics as a means of characterizing the nonlinear features of a time series. The use of moving window analyses using an arbitrary test statistic can reveal the stationarity of the underlying system with respect to some characteristic nonlinear feature. The question of identifying linear-nonlinear partitions from such time-varying estimates of nonlinear features remains challenging.;This dissertation offers a novel resampling approach for characterizing linear-nonlinear partitions via a mixture surrogate model. The distribution of a nonlinear test statistic with respect to a two-component mixture model, conditional on the mixing parameter, is defined using a nonlinear reference function with properties similar to those of the true nonlinearity within the raw signal. From this resampled mixture distribution, it is possible to estimate the partition uncertainty intrinsic to partitions inferred from the use of various nonlinear test statistics. The partition uncertainty is defined here as the likelihood of the mixing parameter, which gives an estimate of the most probable linear-nonlinear mixing ratio based on the observed time-varying point-estimate of the test statistic within the signal. The applications of this work are diverse, although the present context focuses on neuromagnetic signals. |
