Maximum likelihood identification of neural point process systems (Q1111960)

The theory of stochastic point processes is used to describe and to detect functional relationships between two neurons. The representation of the point processes involved by the stochastic intensity is used. For the form of the stochastic intensity assumed the maximum likelihood estimates are derived and their asymptotic properties are presented in the form of two theorems. The model is a version of the additive risk model presented by \textit{O. Aalen}, Ann. Stat. 6, 701-726 (1978; Zbl 0389.62025), in the context of survival analysis. A computational method is also devised to make the maximum likelihood method applicable. An algorithm, derived using the procedure proposed by \textit{A. P. Dempster}, \textit{N. M. Laird} and \textit{D. B. Rubin}, J. R. Stat. Soc., Ser. B 39, 1-38 (1977; Zbl 0364.62022), is proposed for the iterative solution of the likelihood equations. Convergence results for the algorithm as well as a sequence of upper bounds on the log-likelihood values of iterates are shown. The results of the paper are illustrated on simulated experiments.