On quadrature methods for refractory point process likelihoods

Parametric models of the conditional intensity of a point process (e.g., generalized linear models) are popular in statistical neuroscience, as they allow us to characterize the variability in neural responses in terms of stimuli and spiking history. Parameter estimation in these models relies heavily on accurate evaluations of the log likelihood and its derivatives. Classical approaches use a discretized time version of the spiking process, and recent work has exploited the existence of a refractory period (during which the conditional intensity is zero following a spike) to obtain more accurate estimates of the likelihood. In this brief letter, we demonstrate that this method can be improved significantly by applying classical quadrature methods directly to the resulting continuous-time integral.