State-space algorithms for estimating spike rate functions.

The accurate characterization of spike firing rates including the determination of when changes in activity occur is a fundamental issue in the analysis of neurophysiological data. Here we describe a state-space model for estimating the spike rate function that provides a maximum likelihood estimate of the spike rate, model goodness-of-fit assessments, as well as confidence intervals for the spike rate function and any other associated quantities of interest. Using simulated spike data, we first compare the performance of the state-space approach with that of Bayesian adaptive regression splines (BARS) and a simple cubic spline smoothing algorithm. We show that the state-space model is computationally efficient and comparable with other spline approaches. Our results suggest both a theoretically sound and practical approach for estimating spike rate functions that is applicable to a wide range of neurophysiological data.