Parametric inference of neuronal response latency in presence of a background signal

Neurons are commonly characterized by spontaneous generation of action potentials (spikes), which appear without any apparent or controlled stimulation. When a stimulus is applied, the spontaneous firing may prevail and hamper identification of the effect of the stimulus. Therefore, for any rigorous analysis of evoked neuronal activity, the presence of spontaneous firing has to be taken into account. If the background signal is ignored, however small it is compared to the response activity, and however large is the delay, estimation of the response latency will be wrong, and the error will persist even when sample size is increasing. The first question is: what is the response latency to the stimulus? Answering this question becomes even more difficult if the latency is of a complex nature, for example composed of a physically implied deterministic part and a stochastic part. This scenario is considered here, where the response time is a sum of two components; the delay and the relative latency. Parametric estimators for the time delay and the response latency are derived. These estimators are evaluated on simulated data and their properties are discussed. Finally, we show that the mean of the response latency is always satisfactorily estimated, even assuming a wrong distribution for the response latency.