Spike-triggered average
The STA provides an estimate of a neuron's linear receptive field.
Mathematically, the STA is the average stimulus preceding a spike.
[1][2][3][4] 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).
[9][10] It can be used to estimate the linear stage of the linear-nonlinear-Poisson (LNP) cascade model.
[4] The approach has also been used to analyze how transcription factor dynamics control gene regulation within individual cells.
[11] Spike-triggered averaging is also commonly referred to as reverse correlation or white-noise analysis.
[12] It is closely related to linear regression, and identical to it in common circumstances.
Then the STA can be written If the stimulus is not white noise, but instead has non-zero correlation across space or time, the standard STA provides a biased estimate of the linear receptive field.
This resolves the spatial dependency issue, however we still assume the stimulus is temporally independent.
The whitened STA is equivalent to linear least-squares regression of the stimulus against the spike train.
This procedure has a simple Bayesian interpretation: ridge regression is equivalent to placing a prior on the STA elements that says they are drawn i.i.d.
from a zero-mean Gaussian prior with covariance proportional to the identity matrix.
The ridge parameter sets the inverse variance of this prior, and is usually fit by cross-validation or empirical Bayes.
For responses generated according to an LNP model, the whitened STA provides an estimate of the subspace spanned by the linear receptive field.
For such cases, maximum likelihood and information-based estimators [5][6][13] have been developed that are both consistent and efficient.
