Refractory Poisson: The Effect of the Refractory Period on Neural Rate Coding

The neuron’s membrane potential build-up allows for refractoriness. In this context, the refractory effect is often the primary reason spike trains are not accurately described by traditional counting distributions. Inspired by this biological phenomenon, this paper introduces a counting distribution that includes a parameter specifying the length of the refractory period in neural spike generation. Specifically, the paper considers a lower bound on the intervals between any two spikes that follow an exponential or Gamma distribution. The proposed distribution is a generalized form of standard counting distributions, such as the Poisson distribution, and is named the refractory Poisson distribution. This study aims to provide estimation methods for the proposed distribution. Additionally, it introduces a novel estimation approach called “one-shot” maximum likelihood estimation. The research also provides guidance on the maximum amount of information that can be reliably transferred through a single neuron due to refractoriness. The optimality conditions for the capacity-achieving distribution in the capacity per unit cost problem are presented, which, to the best of our knowledge, have not been reported in the literature. The proposed counting distribution can be used for numbering any random phenomena where a refractory period exists between occurrences. Additionally, the distribution can be applied in various scenarios. For example, it can replace the Poisson distribution in the Generalized Linear Model as an alternative counting distribution.