title: On the Spike Train Variability Characterized by Variance-to-Mean Power Relationship.
abstract: We propose a statistical method for modeling the non-Poisson variability of spike trains observed in a wide range of brain regions. Central to our approach is the assumption that the variance and the mean of interspike intervals are related by a power function characterized by two parameters: the scale factor and exponent. It is shown that this single assumption allows the variability of spike trains to have an arbitrary scale and various dependencies on the firing rate in the spike count statistics, as well as in the interval statistics, depending on the two parameters of the power function. We also propose a statistical model for spike trains that exhibits the variance-to-mean power relationship. Based on this, a maximum likelihood method is developed for inferring the parameters from rate-modulated spike trains. The proposed method is illustrated on simulated and experimental spike trains.
authors.affiliation: Department of Statistical Modeling, The Institute of Statistical Mathematics, Tokyo 190-8562, Japan; ERATO Sato Live Bio-Forecasting Project, Japan Science and Technology Agency, Kyoto 619-0237, Japan; and Advanced Telecommunications Research Institute International, Kyoto 619-0237, Japan skoyama@ism.ac.jp.
authors.forename: Shinsuke
authors.initials: S
authors.lastname: Koyama
mesh_terms: D000200:Action Potentials; D000818:Animals; D003198:Computer Simulation; D066264:Datasets as Topic; D006110:Grasshoppers; D006309:Hearing / Q000502:physiology; D016013:Likelihood Functions; D008253:Macaca mulatta; D008959:Models, Neurological; D009475:Neurons, Afferent / Q000502:physiology; D013997:Time Factors; D014793:Visual Cortex / Q000502:physiology; D014796:Visual Perception / Q000502:physiology