This project addresses the mathematical representation of arrays of biological neurons that are firing simultaneously with the goal of inferring their causal connections or influence diagram on the basis of firing times. The methodology of point processes of several types will be extended to include full likelihood and second-order procedures to extend the results from social scientists' path analysis and causal modeling. For small net works of two or three neurons, partial coherence analysis and threshold modeling have proved effective; however, for data for a larger network with eight neurons, nontrivial extensions are needed for display and for analysis. Physiologically, neurons communicate with each other via spike trains, emitting pulses that go on to influence other neurons; and the neurons are themselves influenced. The goal of this research is to infer the connection lines or "wiring diagram" of a network of neurons by observing their individual firing times.
