A method for testing an extended poisson hypothesis of spontaneous quantal transmitter release at neuromuscular junctions

Goodness-of-Fit Tests and Nonparametric Adaptive Estimation for Spike Train Analysis

When dealing with classical spike train analysis, the practitioner often performs goodness-of-fit tests to test whether the observed process is a Poisson process, for instance, or if it obeys another type of probabilistic model (Yana et al. in Biophys. J. 46(3):323-330, 1984; Brown et al. in Neural Comput. 14(2):325-346, 2002; Pouzat and Chaffiol in Technical report, http://arxiv.org/abs/arXiv:0909.2785, 2009). In doing so, there is a fundamental plug-in step, where the parameters of the supposed underlying model are estimated. The aim of this article is to show that plug-in has sometimes very undesirable effects. We propose a new method based on subsampling to deal with those plug-in issues in the case of the Kolmogorov-Smirnov test of uniformity. The method relies on the plug-in of good estimates of the underlying model that have to be consistent with a controlled rate of convergence. Some nonparametric estimates satisfying those constraints in the Poisson or in the Hawkes framework are highlighted. Moreover, they share adaptive properties that are useful from a practical point of view. We show the performance of those methods on simulated data. We also provide a complete analysis with these tools on single unit activity recorded on a monkey during a sensory-motor task.Electronic Supplementary MaterialThe online version of this article (doi:10.1186/2190-8567-4-3) contains supplementary material.

Stationary and non-stationary occurrences of miniature end plate potentials are well described as stationary and non-stationary Poisson processes in the mollusc Navanax inermis

Protractor muscles in the gastropod mollusc Navanax inermis exhibit typical spontaneous miniature end plate potentials with mean amplitude 1.71 +/- 1.19 (standard deviation) mV. The evoked end plate potential is quantized, with a quantum equal to the miniature end plate potential amplitude. When their rate is stationary, occurrence of miniature end plate potentials is a random, Poisson process. When non-stationary, spontaneous miniature end plate potential occurrence is a non-stationary Poisson process, a Poisson process with the mean frequency changing with time. This extends the random Poisson model for miniature end plate potentials to the frequently observed non-stationary occurrence. Reported deviations from a Poisson process can sometimes be accounted for by the non-stationary Poisson process and more complex models, such as clustered release, are not always needed.