A parametric model and Maximum Likelihood estimation of neural rate functions

Accurately recovering stimulus information from measured neural responses is a common task in the analysis and modeling of the central nervous system. Notable variability in action potential timing invoked by similar stimuli suggests stochastic modeling is appropriate. This work presents a Maximum Likelihood estimator for a parametrized rate function under the assumption that spiking follows a inhomogeneous Poisson process. We present a flexible and scalable model, as well as the Cramer-Rao lower bound for a broad class of rate functions. Simulation results are generated and compared to this bound. The proposed estimator yields results close to the lower bounds when the order of the model can be well approximated. Our work shows that such statistical estimation techniques for neural rate functions provide highly accurate results and relatively low computation complexity.