Towards the Modeling of Neuronal Firing by Gaussian Processes

TL;DR

This paper develops computational methods and algorithms to approximate neuronal firing probability densities using Gaussian process models, enabling simulation of large sample paths when analytical solutions are unavailable.

Contribution

It introduces a novel computational framework for modeling neuronal firing using Gaussian processes, including algorithms for simulating sample paths with complex covariance structures.

Findings

Effective simulation of large sample paths for Gaussian neuronal models.

Approximate estimation of firing probability densities without closed-form solutions.

Parallel algorithms improve computational efficiency for large-scale simulations.

Abstract

This paper focuses on the outline of some computational methods for the approximate solution of the integral equations for the neuronal firing probability density and an algorithm for the generation of sample-paths in order to construct histograms estimating the firing densities. Our results originate from the study of non-Markov stationary Gaussian neuronal models with the aim to determine the neuron's firing probability density function. A parallel algorithm has been implemented in order to simulate large numbers of sample paths of Gaussian processes characterized by damped oscillatory covariances in the presence of time dependent boundaries. The analysis based on the simulation procedure provides an alternative research tool when closed-form results or analytic evaluation of the neuronal firing densities are not available.