= Poisson spike-train likelihood fitting
{title2=$\ell=\sum_i\log\lambda(t_i)-\int\lambda(t)\,dt$}
For a stimulus-conditioned <Inhomogeneous Poisson process>, the event log-likelihood is the displayed expression. A causal filter expansion $\lambda(t)=\exp[b+\sum_aw_a(s*b_a)(t)]$ can be fitted by <maximum likelihood estimation>, with a smoothness or size penalty and held-out validation. The integral term penalizes predicted spikes that did not occur; fitting only stimulus values at observed spikes omits this essential part.
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