State-space modeling of neural signals

Neural systems encode representations of biological signals in the firing patterns of their spike trains. Spike trains are point process time-series and their codes are both dynamic and stochastic. Although the signal is often continuous, its representation in the nervous systems is as a high-dimensional point process time-series. Because neural spike trains are point processes, standard signal processing techniques for continuous data are of limited utility in the analysis of neural systems. Accurate processing of neural signals requires the development of quantitative techniques to characterize correctly the point process nature of neural spiking activity. We discuss our research on the use of the state-space paradigm for point process observation to characterize neural systems and discuss three applications characterizing: the response threshold of neurons in primary auditory cortex; the dynamics of subthalamic nuclei neurons in patients suffering from Parkinson's disease; and how ensemble spiking activity of rat hippocampal neurons maintain a dynamic representation of the animal's position in its environment. Brain dynamics can also be measured indirectly at the scalp through the brain's electrical and magnetic fields. As a final example, we present a high-dimensional EM algorithm for a state-space model and use it to compute simultaneous state (dipole sources) and parameter estimates for magnetoencephalography (MEG) inverse problems.