A Bayesian Generative Model of Vestibular Afferent Neuron Spiking

Using an information criterion to evaluate models fitted to spike train data from chinchilla semicircular canal afferent neurons, we found that the superficially complex functional organization of the canal nerve branch can be accurately quantified in an elegant mathematical model with only three free parameters. Spontaneous spike trains are samples from stationary renewal processes whose interval distributions are Exwald distributions, convolutions of Inverse Gaussian and Exponential distributions. We show that a neuronal membrane compartment is a natural computer for calculating parameter likelihoods given samples from a point process with such a distribution, which may facilitate fast, accurate, efficient Bayesian neural computation for estimating the kinematic state of the head. The model suggests that Bayesian neural computation is an aspect of a more general principle that has driven the evolution of nervous system design, the energy efficiency of biological information processing. Significance Statement Nervous systems ought to have evolved to be Bayesian, because Bayesian inference allows statistically optimal evidence-based decisions and actions. A variety of circumstantial evidence suggests that animal nervous systems are indeed capable of Bayesian inference, but it is unclear how they could do this. We have identified a simple, accurate generative model of vestibular semicircular canal afferent neuron spike trains. If the brain is a Bayesian observer and a Bayes-optimal decision maker, then the initial stage of processing vestibular information must be to compute the posterior density of head kinematic state given sense data of this form. The model suggests how neurons could do this. Head kinematic state estimation given point-process inertial data is a well-defined dynamical inference problem whose solution formed a foundation for vertebrate brain evolution. The new model provides a foundation for developing realistic, testable spiking neuron models of dynamical state estimation in the vestibulo-cerebellum, and other parts of the Bayesian brain.