A major source of inspiration in the development of statistical methods for temporal point processes has been neurophysiological recording. Most of the theory and methodology have involved stationary processes. Many neurophysiological experiments, however, use time-varying stimuli and produce time-varying responses. In addition, a major relatively new direction for the field involves the use of multielectrode recording. Statistical methods are needed for the analysis of single and multiple nonstationary point process data, which is the subject of this proposal. The work proposed here involves probability modeling, Bayesian inference, and the Bootstrap. We have successfully applied a simple model for single-neuron spike-train data, based on a generalization of inhomogeneous Poisson processes that we call inhomogeneous Markov interval (IMI) processes. We propose to further develop and investigate IMI processes, taking advantage of an simulation-based Bayesian approach to nonparametric regression that can be adapted for estimation of the IMI intensity function. This will provide methods for problems where scientific interest focuses on temporal evolution of intensities (neuronal firing rates) and trial-to-trial variability. In addition, we will develop inferential methods via resampling from nonparametric curve fitting, including diagnostics to detect situations where the Bootstrap fails. We will then investigate several possible extensions to the multiprocess case in order to describe correlated activity across processes (that is, among neurons). We will also develop enhanced graphical methods for displaying multiprocess data: these include exploratory methods for detecting subgroups of interacting neurons, and the construction and study of quantitative measures of dependence based on the graphical displays.
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