A new statistical method for the estimation of the response latency is proposed. When spontaneous discharge is present, the first spike after the stimulus application may be caused by either the stimulus itself, or it may appear due to the prevailing spontaneous activity. Therefore, an appropriate method to deduce the response latency from the time to the first spike after the stimulus is needed. We develop a nonparametric estimator of the response latency based on repeated stimulations. A simulation study is provided to show how the estimator behaves with an increasing number of observations and for different rates of spontaneous and evoked spikes. Our nonparametric approach requires very few assumptions. For comparison, we also consider a parametric model. The proposed probabilistic model can be used for both single and parallel neuronal spike trains. In the case of simultaneously recorded spike trains in several neurons, the estimators of joint distribution and correlations of response latencies are also introduced. Real data from inferior colliculus auditory neurons obtained from a multielectrode probe are studied to demonstrate the statistical estimators of response latencies and their correlations in space.

We study the estimation of statistical moments of interspike intervals based on observation of spike counts in many independent short time windows. This scenario corresponds to the situation in which a target neuron occurs. It receives information from many neurons and has to respond within a short time interval. The precision of the estimation procedures is examined. As the model for neuronal activity, two examples of stationary point processes are considered: renewal process and doubly stochastic Poisson process. Both moment and maximum likelihood estimators are investigated. Not only the mean but also the coefficient of variation is estimated. In accordance with our expectations, numerical studies confirm that the estimation of mean interspike interval is more reliable than the estimation of coefficient of variation. The error of estimation increases with increasing mean interspike interval, which is equivalent to decreasing the size of window (less events are observed in a window) and with decreasing the number of neurons (lower number of windows).