title: Modeling neural activity with cumulative damage distributions.
abstract: Neurons transmit information as action potentials or spikes. Due to the inherent randomness of the inter-spike intervals (ISIs), probabilistic models are often used for their description. Cumulative damage (CD) distributions are a family of probabilistic models that has been widely considered for describing time-related cumulative processes. This family allows us to consider certain deterministic principles for modeling ISIs from a probabilistic viewpoint and to link its parameters to values with biological interpretation. The CD family includes the Birnbaum-Saunders and inverse Gaussian distributions, which possess distinctive properties and theoretical arguments useful for ISI description. We expand the use of CD distributions to the modeling of neural spiking behavior, mainly by testing the suitability of the Birnbaum-Saunders distribution, which has not been studied in the setting of neural activity. We validate this expansion with original experimental and simulated electrophysiological data.
authors.affiliation: Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Viña del Mar, Chile. victorleivasanchez@gmail.com.|Institute of Statistics, Universidad de Valparaiso, Valparaiso, Chile. victorleivasanchez@gmail.com.
authors.forename: Víctor
authors.initials: V
authors.lastname: Leiva
authors.affiliation: Faculty of Natural and Exact Sciences, Universidad de Playa Ancha, Valparaiso, Chile.
authors.forename: Mauricio
authors.initials: M
authors.lastname: Tejo
authors.affiliation: Centro de Investigación y Modelamiento de Fenómenos Aleatorios - Valparaíso, Faculty of Engineering, Universidad de Valparaíso, Valparaiso, Chile.
authors.forename: Pierre
authors.initials: P
authors.lastname: Guiraud
authors.affiliation: Centro Interdisciplinario de Neurociencia de Valparaíso and Institute of Neuroscience, Universidad de Valparaíso, Valparaiso, Chile.
authors.forename: Oliver
authors.initials: O
authors.lastname: Schmachtenberg
authors.affiliation: Centro Interdisciplinario de Neurociencia de Valparaíso and Institute of Neuroscience, Universidad de Valparaíso, Valparaiso, Chile.
authors.forename: Patricio
authors.initials: P
authors.lastname: Orio
authors.affiliation: Gösta Ekman Laboratory, Department of Psychology, Stockholm University, Stockholm, Sweden.
authors.forename: Fernando
authors.initials: F
authors.lastname: Marmolejo-Ramos
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D003198:Computer Simulation; D005260:Female; D006801:Humans; D008297:Male; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D016011:Normal Distribution
keywords: Birnbaum–Saunders and inverse Gaussian distributions; Integrate-and-fire model; Inter-spike intervals; Maximum likelihood method; Model selection and goodness of fit