Conditioned Likelihoods Using Bifurcation Continuation in Inverse Modeling of Dynamical Systems

TL;DR

This paper introduces a Bayesian method using bifurcation continuation and rejection sampling to accurately estimate coupling and current parameters in coupled Morris-Lecar neuron models, improving identifiability and reducing bias.

Contribution

It presents the first Bayesian parameter estimation approach for coupled Morris-Lecar neurons employing bifurcation analysis and rejection sampling within MCMC, enhancing estimation accuracy.

Findings

Rejection sampling reduces parameter bias.

Method improves identifiability of coupling strength and applied current.

First Bayesian estimation for coupled Morris-Lecar neurons.

Abstract

The Morris-Lecar (ML) model has applications to neuroscience and cognition. A simple network consisting of a pair of synaptically coupled ML neurons can exhibit a wide variety of deterministic behaviors including asymmetric amplitude state (AAS), equal amplitude state (EAS), and steady state (SS). In addition, in the presence of noise this network can exhibit mixed-mode oscillations (MMO), which represent the system being stochastically driven between these behaviors. In this paper, we develop a method to specifically estimate the parameters representing the coupling strength (gsyn) and the applied current (Iapp) of two reciprocally coupled and biologically similar neurons. This method employs conditioning the likelihood on cumulative power and mean voltage. Conditioning has the potential to improve the identifiability of the estimation problem. Conditioning likelihoods are typically much simpler to model than the explicit joint distribution, which several studies have shown to be difficult or impossible to determine analytically. We adopt a rejection sampling procedure over a closed defined region determined by bifurcation continuation analyses. This rejection sampling procedure is easily embedded within the proposal distribution of a Bayesian Markov chain Monte Carlo (MCMC) scheme and we evaluate its performance. This is the first report of a Bayesian parameter estimation for two reciprocally coupled Morris-Lecar neurons, and we find a proposal utilizing rejection sampling reduces parameter estimate bias relative to naive sampling. Application to stochastically coupled ML neurons is a future goal.