Spike-triggered average

The spike-triggered average (STA) is a tool for characterizing the response properties of a neuron using the spikes emitted in response to a time-varying stimulus. The STA provides an estimate of a neuron's linear receptive field. It is a useful technique for the analysis of electrophysiological data.

Mathematically, the STA is the average stimulus preceding a spike. To compute the STA, the stimulus in the time window preceding each spike is extracted, and the resulting (spike-triggered) stimuli are averaged (see diagram). The STA provides an unbiased estimate of a neuron's receptive field only if the stimulus distribution is spherically symmetric (e.g., Gaussian white noise).

The STA has been used to characterize retinal ganglion cells, neurons in the lateral geniculate nucleus and simple cells in the striate cortex (V1) . It can be used to estimate the linear stage of the linear-nonlinear-Poisson (LNP) cascade model.

Spike-triggered averaging is also commonly referred to as “reverse correlation″ or “white-noise analysis”. The STA is well known as the first term in the Volterra kernel or Wiener kernel series expansion. It is closely related to linear regression, and identical to it in common circumstances.

Let ${\displaystyle \mathbf {x_{i}} }$ denote the spatio-temporal stimulus vector preceding the ${\displaystyle i}$'th time bin, and ${\displaystyle y_{i}}$ the spike count in that bin. The stimuli can be assumed to have zero mean (i.e., ${\displaystyle E[\mathbf {x} ]=0}$). If not, it can be transformed to have zero-mean by subtracting the mean stimulus from each vector. The STA is given

...
Wikipedia