Introduction to neural spike train data for phase-amplitude analysis

Statistical analysis of spike trains is one of the central problems in neural coding, and can be pursued in several ways. One option is model-based, i.e. assume a parametric or semi-parametric model, such as the Poisson model, for spike train data and use it in decoding spike trains. The other option is metric-based, i.e. choose a metric for comparing the numbers and the placements of spikes in different trains, and does not need a model. A prominent idea in the latter approach is to derive metrics that are based on measurements of time-warpings of spike trains needed in the alignments of corresponding spikes. We propose the use of ideas developed in functional data analysis, namely the definition and separation of phase-amplitude components, as a novel tool for analyzing spike trains and decoding underlying neural signals. For concreteness, we introduce a real spike train dataset taken from experimental recordings of the primary motor cortex of a monkey while performing certain arm movements. To facilitate functional data analysis, one needs to smooth the observed discrete spike trains with Gaussian kernels.