We recently discussed two recent papers proposing improvements to the commonly used discrete approximation of the log-likelihood for a point process (Paninski, 2004). The likelihood is written as

where are the spike times and is the conditional intensity function (CIF) of the process at time given the preceding spikes. Typically, the integral in this equation cannot be evaluated in closed form. The standard approximation computes the function by binning along a regular lattice with bins size

where is the number of spikes in the th bin. Both papers demonstrate that smarter approximations to the integral are better for point-process statistics than naïvely binning spike train data.

# Evaluating point-process likelihoods

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