Average the stimulus history preceding each observed spike, after removing the stimulus mean. With white Gaussian stimulation and a suitable one-filter encoding model, the result is proportional to the relevant linear filter. An even nonlinearity can make the average vanish despite strong stimulus dependence, so averaging alone is not universally sufficient.
For a single linear filter followed by a rate nonlinearity and a Gaussian stimulus-history vector with covariance , Gaussian integration by parts gives . Thus a spike-triggered average estimates , rather than directly, when the stimulus is correlated. Covariance correction, with regularization if necessary, can recover the filter direction. For an even nonlinearity the proportionality factor can vanish; then a one-filter average is insufficient.

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The spike-triggered average (STA) is a method used in computational neuroscience to characterize the relationship between neuronal spike train activity and sensory stimuli. It involves analyzing how specific inputs or stimuli relate to the output of a neuron, particularly the times at which the neuron fires action potentials (or spikes). Here's how it works, step by step: 1. **Data Collection:** A neuron's spiking activity is recorded alongside a sensory stimulus (such as a visual or auditory signal).