A point process model for biological events involving activation

The Poisson random process is widely used to describe experiments involving discrete arrival data. However, for creating models of egg-laying behavior in recent neural biology studies on the nematode Caenorhabditis elegans, the authors have found that homogeneous Poisson processes are inadequate to capture the measured temporal patterns. They present here a novel three-state model that effectively represents the measured temporal patterns and that correlates well with the cellular and molecular mechanisms that are known to be responsible for the measured behavior. Although the model involves a combination of two Poisson processes, it is surprisingly tractable. The authors derive closed-form expressions for the probabilistic and statistical properties of the model and present several parameter estimation procedures including a maximum likelihood algorithm. Both simulated and experimental results are illustrated. The experiments with measured data show that the egg-laying patterns fit the three-state model very well. The model also may be applicable in quantifying the link between other neural processes and behavior or in other situations where discrete events occur in clusters.