  The computation performed by a neuron can be formulated as a combination of
dimensional reduction in stimulus space and the nonlinearity inherent in a
spiking output. White noise stimulus and reverse correlation (the
spike-triggered average and spike-triggered covariance) are often used in
experimental neuroscience to `ask' neurons which dimensions in stimulus space
they are sensitive to, and to characterize the nonlinearity of the response. In
this paper, we apply reverse correlation to the simplest model neuron with
temporal dynamics--the leaky integrate-and-fire model--and find that even for
this simple case standard techniques do not recover the known neural
computation. To overcome this, we develop novel reverse correlation techniques
by selectively analyzing only `isolated' spikes, and taking explicit account of
the extended silences that precede these isolated spikes. We discuss the
implications of our methods to the characterization of neural adaptation.
Although these methods are developed in the context of the leaky
integrate-and-fire model, our findings are relevant for the analysis of spike
trains from real neurons.
