  How do neuronal populations encode time-dependent stimuli in their population
firing rate? To address this question, I consider the quasi-renewal equation
and the event-based expansion, two theoretical approximations proposed
recently, and test these against peri-stimulus time histograms from L2-3
pyramidal cells in vitro. Parameters are optimized by gradient descent to best
match the firing rate output given the current input. The fitting method can
estimate single-neuron parameters that are normally obtained either with
intracellular recordings or with individual spike trains. I find that
quasi-renewal theory predicts the adapting firing rate with good precision but
not the event-based expansion. Quasi-renewal predictions are equal in quality
with state-of-the-art spike timing prediction methods, and does so without
resorting to the indiviual spike times or the membrane potential responses.
