Goodness-of-fit tests and nonparametric adaptive estimation for spike train analysis
Tuleau-Malot, Christine; Grammont, Franck; Rivoirard, Vincent; Reynaud-Bouret, Patricia (2014), Goodness-of-fit tests and nonparametric adaptive estimation for spike train analysis, The Journal of Mathematical Neuroscience, 4, 1. http://dx.doi.org/10.1186/2190-8567-4-3
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00789127
Journal nameThe Journal of Mathematical Neuroscience
MetadataShow full item record
Abstract (EN)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 Material The online version of this article (doi:10.1186/2190-8567-4-3) contains supplementary material.
Subjects / Keywordsadaptive estimation; Poisson process; Hawkes process; point processes; spike trains analysis; goodness-of-fit test
Showing items related by title and author.
Lambert, Régis; Tuleau-Malot, Christine; Bessaih, Thomas; Rivoirard, Vincent; Bouret, Yann; Leresche, Nathalie; Reynaud-Bouret, Patricia (2018) Article accepté pour publication ou publié
Doumic, Marie; Hoffmann, Marc; Reynaud-Bouret, Patricia; Rivoirard, Vincent (2012) Article accepté pour publication ou publié