4.3 Nonlinear Model of Neural Population Dynamics 105 Deadwyler and Hampson, 1995; Pouget et al., 2003; Puchalla et al., 2005). The hippocampus has long been known to be responsible for the for- mation of declarative memories (Squire, 1992; Deadwyler and Hampson, 1995; Deadwyler et al., 1996; Eichenbaum, 1999; Burgess et al., 2002). Damage to it disrupts the propagation of spatio-temporal patterns of activity through hippocampal internal circuitry, resulting in severe anterograde amne- sia. Developing a neural prosthesis for the damaged hippocampus requires restoring this MIMO transformation of spiking activity. In other words, the model needs to predict the output spike trains based on the ongoing input spike trains of the modeled brain region. Our second purpose is to gain a better understanding of the functional organization of the hippocampal neuronal network. This requires the model to provide interpretable representations of the neurons' nonlinear dynamical properties and the functional connectivity between neurons. Model variables should be related to at least the principal biological processes of the system. Because of the duality of our goal, we combined both parametric and nonparametric modeling methods--spiking neuron modeling and Volterra