Stochastic modeling of neurobiological time series: Power, coherence, Granger causality, and separation of evoked responses from ongoing activity

In this article we consider the stochastic modeling of neurobiological time series from cognitive experiments. Our starting point is the variable-signal-plus-ongoing-activity model. From this model a differentially variable component analysis strategy is developed from a Bayesian perspective to estimate event-related signals on a single trial basis. After subtracting out the event-related signal from recorded single trial time series, the residual ongoing activity is treated as a piecewise stationary stochastic process and analyzed by an adaptive multivariate autoregressive modeling strategy which yields power, coherence, and Granger causality spectra. Results from applying these methods to local field potential recordings from monkeys performing cognitive tasks are presented.