Statistical analysis and stochastic modeling of neuronal spike-train activity

Considerable attention has been paid in the literature to the development of biologically interpretable mathematical models of spontaneous stationary neuronal spike-train activity. However, these models work poorly in applied spike-train analysis. In order to improve matters, we need (1) to select appropriate statistical techniques, and (2) to fit the models into the semialternating renewal (SAR) framework. In the present study, biologically interpretable models, the SAR framework, and relevant statistical techniques are integrated in a form which suits the practical research worker. The theory is illustrated with reference to the analysis of a number of spike trains.