Non-parametric methods for the analysis of neurobiological time-series data

Recent technological advances have led to a large increase in the volume and quality of recordings from the brain. For example, while traditional electrophysiological recordings relied on painstaking observations of single neurons, it is now increasingly possible to record from tens or even a hundred neurons simultaneously. Similarly, electro and magnetoencephalographic recordings are routinely performed with upto three hundred sensors. This increase in data has also led to the need for bringing advanced time series analysis tools to bear on the problems of interpreting this data. In this paper, we illustrate the use of contemporary non-parametric smoothing and spectral estimation techniques in the analysis of data acquired in electrophysiological experiments. In particular, we discuss how local likelihood based methods have been used to model firing rates and how spectra and coherences can be used to assess degrees of association within and between spike trains and local field potentials.