Maximum likelihood estimations in a nonlinear self-exciting point process model

A nonlinear model generating a self-exciting point process is formulated and identification of the model using maximum likelihood estimations is discussed. Simulations have been performed and parameters are estimated numerically. (Dis)advantages with respect to identification approaches based on correlation densities are outlined. This method may function as a basis to interpret simultaneous recordings of single units in terms of underlying wiring diagrams.