Much current neurophysiological research concerns the way neuronal activity evolves over time. For static characterizations, standard statistical tools such as Analysis of Variance suffice, but for dynamic studies there is a large neuroscientific payoff for using state-of-the-art, special-purpose statistical methods. In addition, a major relatively new direction for the field involves the use of multielectrode recording. Multielectrode neuronal recording has not only produced new scientific insights, it has also led to development of neural prostheses via brain-computer interface, which are likely to have important clinical applications. There is a widespread perception that there are not yet adequate tools for understanding dynamic responses available from current recording technologies. From a statistical point of view it is natural to view neuron firing events (spike trains) as defining point processes. While there exist rich theory and methods for stationary point processes, nonstationarity is common. Many neurophysiological experiments use time-varying stimuli and produce time-varying responses. Furthermore, there are interesting physiological phenomena that evolve across experimental trials. Thus, statistical methods for the analysis of single and multiple nonstationary point process data are urgently needed. The research to be conducted under this grant emphasizes statistical modeling and inference for point processes, Bayesian sequential modeling, and clustering of functions. Specific aims involve functional data analysis of trial-averaged firing rates;non-Poisson modeling of spike trains for within-trial analysis;multivariate point process modeling of dependency among multiple spike trains;variable clustering methods for identifying clusters of correlated neurons;particle filtering and related methods for decoding of motor cortical signals;and functional goal-oriented clustering for spike sorting in the context of decoding.