Robust Statistical Modeling of Neuronal Intensity Rates
Mentor:Sam Behseta, Professor, Department of Mathematics, California State University Fullerton
A dominating theory in neuroscience disassociates the primary motor cortex (M1) as a mere executioner of movements from storing and retaining motor movements. Matsuzaka et al. (2006) conducted a scientific study where M1 neuronal activities of Macaque monkeys were recorded in correspondence with hand and digit muscle reactions to two types of visual stimuli – random sets and repeated patterns. In this work, we develop a statistical hypothesis testing paradigm based on a nonparametric resampling technique to compare neuronal firing intensity functions obtained from the two experimental conditions. We devise two resampling tests: with and without replacement. We hypothesize that both approaches will yield the same statistical hypothesis test, either of which can be used to detect the nuances between the spiking patterns of the two conditions.
Our methods are structured around resampling neuronal spike trains, recorded during various trials of an experimented task. The neuronal spiking activity is mapped out with the aid of raster plots and Peri-Stimulus Time Histograms and is eventually modeled using Bayesian Adaptive Regression Splines (DiMatteo, 2001). Thereby, the null hypothesis reflecting no statistical differences between the fitted curves to the two conditions (H0: f1-f2=0) is tested nonparametrically. Moreover, our proposed methodology would allow investigators to calibrate the differences between firing intensity rates both locally and globally.
We examine our methods on the firing activities of a group of neurons and note that our method is capable of detecting all local and global firing fluctuations. The statistical detection of differences between the firing patterns of M1 neurons gives way to further investigations associated with the role of M1 in the execution and planning of fully-learned movements as opposed to semi-learned or unlearned movements. Additionally, our method serves the purpose of screening out those neurons that remain unresponsive to the mechanics of the two experimental tasks.