Estimating the number of neurons in multi-neuronal spike trains

A common way of studying the relationship between neural activity and behavior is through the analysis of neuronal spike trains that are recorded using one or more electrodes implanted in the brain. Each spike train typically contains spikes generated by multiple neu-rons. A natural question that arises is " what is the number of neu-rons ν generating the spike train? " This article proposes a method-of-moments technique for estimating ν. This technique estimates the noise nonparametrically using data from the silent region of the spike train and it applies to isolated spikes with a possibly small, but non-negligible, presence of overlapping spikes. Conditions are established in which the resulting estimator for ν is shown to be strongly consistent. To gauge its finite sample performance, the technique is applied to simulated spike trains as well as to actual neuronal spike train data. 1. Introduction. In the field of neuroscience, it is generally acknowledged that neurons are the basic units of information processing in the brain. They play this role by generating highly peaked electric action potentials or, more simply, spikes [cf. Brillinger (1988), Dayan and Abbott (2001)]. A sequence of such spikes over time is called a spike train. A typical method of recording spike trains is by inserting electrodes into the brain. In the analysis of a spike train, Brown, Kass and Mitra (2004) note three goals: (i) identify each spike as " signal " (versus pure noise), (ii) determine the number of neurons being recorded, and (iii) assign each spike to the neuron(s) that produced it. (i), (ii) and (iii) are collectively termed spike sorting in the neuroscience literature,