Collections > Electronic Theses and Dissertations > A Statistical Approach to Functional Connectivity Involving Multichannel Neural Spike Trains

The advent of the multi-electrode has made it feasible to record spike trains simultaneously from several neurons. However, the statistical techniques for analyzing large-scale simultaneously recorded spike train data have not developed as satisfactorily as the experimental techniques for obtaining these data. This dissertation contributes to the literature of modeling simultaneous spike train data and inferring the functional connectivity in two aspects. In the first part, we apply a point process likelihood method under the generalized linear model framework (Harris, 2003) for analyzing ensemble spiking activity from noncholinergic basal forebrain neurons (Lin and Nicolelis, 2008). The model can assess the correlation between a target neuron and its peers. The correlation is referred to as weight for each peer and is estimated through maximizing the penalized likelihood function. A discrete time representation is used to construct the point process likelihood, and the discrete 0-1 occurrence data are smoothed using Gaussian kernels. Ultimately, the entire peer firing information and the correlations can be used to predict the probability of target firing. In the second part, we propose a regression spline model, which directly makes use of the neural firing times instead of using the smoothed version of spike train. The primary contribution of the model is that it can both capture the spontaneous dynamics and also infer functional connectivity for an arbitrary number of interactive neurons in a given region or across different regions. In addition, it does not need discretization, relaxes the parametric assumption, and offers high flexibility for estimation via spline functions. The regression spline model selects the optimal spline knots adaptively using the spike train data. Our model incorporates adaptive model selection and is estimated through maximum likelihood. Asymptotic properties of the proposed estimator are investigated as well.