| Model-based approaches to electrophysiological signal processing provide low-variance estimates of the activity and relationships within neurological systems. In this dissertation, we develop a method for testing consistency of modeling of neurological signals across different data acquisition systems, introduce a new measure for modeling causality in mean between sets of signals, and construct a fast method for modeling causality in variance.;For testing consistency of signals across different acquisition systems, we use statistical resampling and estimation techniques to assess the similarity of activity estimated from recordings on two different systems. Using this methodology, we can determine what preprocessing and postprocessing steps are advisable for non-invasive studies of brain electrical activity, for example. We can also determine which models are most robust across data acquisition systems.;For causality in mean, we develop a new model of causality between sets of signals inspired by properties in electrophysiological signals. Since nearby sensors are often sensitive to the same information, grouping sensors into regions of interest can increase signal-to-noise ratio. We exploit this property to form a new measure of causality called canonical Granger causality (CGC), which trades off spatial resolution to increase the ability to find short, dynamic connections that are causal in mean.;For causality in variance, we introduce a new method to more quickly estimate the effect of one signal on another signal's variation. This causality is estimated by fitting a conditional heteroscedasticity model to signals using a maximum-likelihood approach. We introduce a new method for this maximum-likelihood problem which uses variable splitting and the alternating direction method of multipliers, avoiding the computational cost of traditional gradient descent methods. The significant gains in speed allow us to analyze dynamic changes in causality in variance with a now-reasonable runtime.;Along with each project we provide applications of these methods to MEG recordings, local field potentials on the macaque brain and intracranial voltage recordings on the resting-state human brain. |
