title: Goodness-of-Fit Tests and Nonparametric Adaptive Estimation for Spike Train Analysis.
abstract: 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.
authors.affiliation: CNRS, LJAD, UMR 7351, Université Nice Sophia Antipolis, 06100, Nice, France. reynaudb@unice.fr.
authors.forename: Patricia
authors.initials: P
authors.lastname: Reynaud-Bouret
authors.forename: Vincent
authors.initials: V
authors.lastname: Rivoirard
authors.forename: Franck
authors.initials: F
authors.lastname: Grammont
authors.forename: Christine
authors.initials: C
authors.lastname: Tuleau-Malot
references.citation: Science. 1986 Sep 26;233(4771):1416-9
references.pmid: 3749885
references.citation: Biol Cybern. 1976 May 17;22(4):213-28
references.pmid: 953079
references.citation: J Physiol Paris. 2000 Sep-Dec;94(5-6):569-82
references.pmid: 11165921
references.citation: Science. 1969 May 16;164(3881):828-30
references.pmid: 5767782
references.citation: Biol Cybern. 2003 May;88(5):360-73
references.pmid: 12750898
references.citation: Biophys J. 1984 Sep;46(3):323-30
references.pmid: 6487732
references.citation: J Neurosci Methods. 2009 Jun 30;181(1):119-44
references.pmid: 19473708
references.citation: Annu Rev Neurosci. 2004;27:169-92
references.pmid: 15217330
references.citation: Nature. 2008 Aug 21;454(7207):995-9
references.pmid: 18650810
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Mar;85(3 Pt 1):031916
references.pmid: 22587132
references.citation: Biol Cybern. 1988;59(4-5):265-75
references.pmid: 3196770
references.citation: Neuroreport. 2006 Feb 27;17(3):281-5
references.pmid: 16462598
references.citation: J Neurophysiol. 1989 May;61(5):900-17
references.pmid: 2723733
references.citation: PLoS Comput Biol. 2011 May;7(5):e1002059
references.pmid: 21625580
references.citation: Stat Appl Genet Mol Biol. 2005;4:Article24
references.pmid: 16646842
references.citation: Neural Comput. 2002 Feb;14(2):325-46
references.pmid: 11802915
references.citation: Neural Comput. 2005 Sep;17(9):1927-61
references.pmid: 15992486
references.citation: Biostatistics. 2002 Mar;3(1):1-20
references.pmid: 12933620
references.citation: Biophys J. 1967 Jul;7(4):419-40
references.pmid: 4292792
references.citation: J Comput Neurosci. 2010 Aug;29(1-2):171-182
references.pmid: 19655238
references.citation: Front Comput Neurosci. 2010 Nov 19;4:147
references.pmid: 21151360
references.citation: Neural Comput. 2014 Jul;26(7):1408-54
references.pmid: 24708365
references.citation: BMC Bioinformatics. 2010 Sep 09;11:456
references.pmid: 20828413