Point process adaptive filters for neural data analysis: Theory and applications

Although it is well known that neurons receive, process and transmit signals via sequences of sudden stereotyped electrical events, called action potentials or spikes, many analyses of neural data ignore the highly localized nature of these events. We discuss a point process modeling framework for neural systems to perform inference, assess goodness-of-fit, and estimate a state variable from spiking observations. Under this framework, we develop state space estimation and inference algorithms by constructing state models that describe the stochastic evolution of the signals to estimate, and conditional intensity models that define the probability distribution of observing a particular sequence of spike times for a neuron or ensemble. Posterior densities can then be computed using a recursive Bayesian framework combined with the Chapman- Kolmogorov system of equations for discrete-time analyses or the forward Kolmogorov equation for continuous-time analyses. This allows us to derive a toolbox of estimation algorithms and adaptive filters to address questions of static and dynamic encoding and decoding. We discuss the application of these modeling and estimation methods to the problem of predicting an intended reaching arm movement from simulated neurons in primate primary motor cortex. We show that a Bayesian approximate Gaussian filter is able to maintain accurate estimates of intended arm trajectories.