Maximum Likelihood Estimation for an Ornstein–Uhlenbeck Model for Neural Activity

Abstract

The Ornstein–Uhlenbeck process arises from a leaky stochastic integrate-and-fire model of the membrane potential of a neuron, in which its firing corresponds to the first time the process hits a barrier. We address the problem of estimating the parameters of the underlying process when the available data are the neuron’s successive spikes, or spike train. The first-hitting time density is not tractable, so we use its Laplace transform to determine the identifiable parameters of the model, show that their maximum likelihood estimates are consistent and asymptotically normal, and describe computational methods to obtain the estimates and their standard errors.