Applications of Point Process Modeling to Spiking Neurons

Electrophysiological measurements of neurons recorded individually, collectively, and across brain regions simultaneously have been advancing the study of biophysical properties of individual neurons, information encoding and decoding, and interactions between neuronal ensembles. The recordings are composed of sequences of action potentials, usually referred to as spike trains, which carry signals of neural activity but they are contaminated with ubiquitous Poisson-type noise and the patterns vary from neuron to neuron, time to time, and trial to trial. The discreteness and randomness of the data make point process a suitable tool for understanding the neural signals represented by spike train data. This thesis provides four applications of point process modeling to spiking neurons. The first project addresses stability of fitted point process regression models. In the second project, we aim to bridge biophysical modeling and statistical modeling by describing how ion channel conductance can affect spike train patterns. The third project studies the covariation of time-dependent population firing rate features among interacting brain regions. The fourth project focuses on the inter-spike dependency between brain areas with weak coupling effects.