Markov models for neural spike trains

Neurons convey information by transmitting action potentials or spikes in a series known as a spike train. The study of these spike trains can lead to a greater understanding of the behavior of neurons and how they interact amongst themselves and with their surroundings. As a result, it is an issue of great interest to develop a model that best describes these spike trains.;Models exist for each of these separate effects. Systems have been proposed to address latency and excitability issues. Kass and Ventura (2001) proposed the inhomogeneous Markov interval (IMI) process model to address the problem of modeling the renewal process of a neuron following a spiking event. Subclasses of this model include the multiplicative IMI model and the time-rescaled renewal process. Methods of addressing the relationship between oscillatory behavior and neural spiking, such as the roseplot, are often crude and lack a proper quantitative explanation. Auto-regressive models have been used to show describe ensemble effects but are often restricted to parametric models. Efforts have been made to address each effect separately, but estimates of the overall fit of a firing rate with associated measures of variance are lacking.;This thesis proposes a non-parametric method of addressing each of these effects simultaneously in a single joint model. It utilizes a spline-based method to estimate the contributions of each factor. We use a Gibbs sampler that contains an adaptation of Bayesian adaptive regression splines (BARS) to provide not only the overall fit to the firing rate but also a fit to each piece of the firing rate along with associated measures of variability. We also propose a second mechanism for fitting the model which the removes the need for the time-intensive Gibbs sampler and BARS application, and the results of the two methods are compared. Simulation studies demonstrate the adequacy of the model and associated mechanism. The model is used to perform a real data analysis of neuronal data that exhibit multiple effects that gradually change over time.;The sequences of spike trains form a temporal point process. The simplest method of modeling these spike trains is with a Poisson process. While this technique may be adequate for examining the firing rate of neurons when the spike trains are pooled across a large number of trials, this method is insufficient in many other cases. Neurons may exhibit variations during repeated trials of an Experiment; these variations are often exhibited in the form of delayed response to stimulus, or latency, or variation in the intensity of the response, or excitability. Also, the firing behavior of a neuron has been observed to be dependent upon its own past spiking history, which leads to non-Poisson behavior. In addition, the firing behavior of a neuron may be correlated to the observed oscillatory behavior associated with neural activity. Neurons within an ensemble can affect the action of other neighboring neurons. These effects can change during repeated experimental trials. A proper model should seek to incorporate each of these effects.