One of the most important techniques in learning about the functioning of healthy and diseased brains has involved examining neural activity in laboratory animals under varying circumstances. Fundamental knowledge has been obtained by determining experimental conditions, often intended to mimic pathological states, during which neurons in a particular location become increasingly active or inactive. Neural information is represented and communicated through series of action potentials, or "spike trains," and interest often centers on the evolution of neural activity over time in response to some stimulus or behavior. The primary focus of this research is development of methods for analysis of neural spike train data within the statistical framework of nonstationary (time-varying) point processes (processes involving sequences of event times, here spikes). New high-dimensional generalized regression methods will allow characterization of high-dimensional neural stimulus effects that evolve across time, and will allow many diverse effects on neural firing to be considered simultaneously. More powerful use of the data will come from a new variation on statistical clustering in which a covariate is involved-this will combine physiological goals (producing the covariate) with the process of spike identification known as "spike sorting" (which involves clustering). Neuroscientific experiments often produce nonstationary time series, but very frequently these are observed across many repeated trials. By taking advantage of this special circumstance new hierarchical Bayesian models will be developed to reduce dimensionality of complicated tasks, and to reduce the complexity of simultaneously-recorded neural signals. New multiple point process methods based on continuous-time loglinear modeling, conditional-intensity modeling, and functional clustering will provide descriptions of interactions among neural spike trains at multiple time scales. This research will produce a set of tools for identifying change in neural network function following experimental manipulations, such as those producing the cognitive deficits seen in psychiatric disorders.
Neurophysiological experiments increasingly rely on sophisticated statistical analysis of neural activity. By creating new statistical tools for neural data analysis, this research will help advance the understanding of diseases of the nervous system, including those involving cognitive impairment associated with psychiatric disorders.
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