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**A Spike Train Probability Model**

**Robert E. Kass and Valérie Ventura**

### Abstract:

Poisson processes are adequate descriptions of spike trains pooled
across large numbers of trials. When probabilities are needed to
describe the behavior of neurons within individual trials, however,
Poisson process models are often inadequate. In principle, an explicit
formula gives the probability density of a single spike train
for a general counting process, but without additional
assumptions the intensity function appearing in that formula can not
be estimated. We propose a simple solution to this problem,
which is to assume that the time at which a neuron fires
is determined probabilistically by,
and only by, two quantities: the
experimental clock time and the time since the last
spike. We show that this model may be used successfully to fit
neuronal data.

*Heidi Sestrich*

*6/22/2000*
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