A spike-train probability model

Poisson processes usually provide adequate descriptions of the irregularity in neuron spike times after pooling the data across large numbers of trial s, as is done in constructing the peristimulus time histogram. When probabi lities are needed to describe the behavior of neurons within individual tri als, however, Poisson process models are often inadequate. In principle, an explicit formula gives the probability density of a single spike train in great generality, but without additional assumptions, the firing-rate inten sity function appearing in that formula cannot be estimated. We propose a s imple solution to this problem, which is to assume that the time at which a neuron fires is determined probabilistically by, and only by, two quantiti es: the experimental clock time and the elapsed Lime since the previous spi ke. We show that this model can be fitted with standard methods and softwar e and that it may used successfully to fit neuronal data.