A Multivariate Statistical Inference for the Analysis of Neuronal Spiking Rates
Authors:Reina Galvez, Antouneo Kassab, Duy Ngo
Mentor:Sam Behseta, Professor of Mathematics, California State University Fullerton
In this work, we propose a series of comparative statistical inferences that may be used to: a – distinguish the firing patterns of a population of neurons recorded under two experimental conditions, b – classify neurons based on their differential intensity rates. To approach these objectives, we rely upon the asymptotic properties of the curves fitted to the histograms resulted from accumulating spiking occurrences over multiple trials. Specifically, we borrow from the existing features of multivariate Gaussian distributions and hierarchical clustering techniques. This allows us to simulate a large number of firing intensity curves from the underlying multivariate distributions for further inferential steps.
Applying the proposed simulation-based methods in this work, we were able to construct a 95% confidence interval for the differences between two curves fitted to each neuron. Additionally, we found out that a considerable portion of 139 studied neurons demonstrated significant differences throughout the entire experimental time window with the highest percentage of significance around the 200 ms mark. Moreover, using two different metrics of distance between the simulated curves, a Kullback-Leibler divergence, and a binwise method, we constructed a 95% confidence interval for the mean of six clusters of the 139 difference curves.
Our methods are quite robust in that they do not rely on a large body of theoretical results. More importantly, the main simulation technique in this work is computationally inexpensive and thus can be easily programmed through R, the most commonly used computational tool in the statistical community. We are planning to extend this work to two situations: 1 – a fully non-parametric method, free of all distributional assumptions, 2 – an unsupervised learning classification method through which the optimal number of clusters is obtained.