Stochastic Models for Multivariate Neural Point Processes: Collective Dynamics and Neural Decoding

Abstract

This chapter reviews a stochastic point process framework for the mod- eling, analysis and decoding of neuronal ensembles. The spiking probability of any neuron in an ensemble is computed recursively via a system of stochastic nonlin- ear equations with delays in discrete time. These equations are expressed in terms of conditional intensity functions, which capture the effects of the neuron’s own spiking history (intrinsic dynamics), ensemble history (collective dynamics), and dependencies on stimuli and behavioral covariates. Four related approaches for the statistical modeling of conditional intensity functions are presented: generalized lin- ear models (GLM), penalized splines, hierarchical Bayesian P-splines, and nonpara- metric function approximation. Decoding of neuronal ensemble spike trains is implemented via stochastic state-space models with point process observations. The framework is illustrated with examples of neural decoding of hand velocities and assessment of collective dynamics in primary motor cortex.