Annealed Importance Sampling for Neural Mass Models.

Area of Science:

• Computational Neuroscience
• Neuroimaging Analysis
• Statistical Modeling

Background:

• Neural Mass Models (NMMs) offer a simplified representation of neocortical population activity.
• Connecting NMMs allows for network analysis, inferring connection strengths from M/EEG data using Bayesian inference.
• Existing Bayesian methods, like Variational Laplace (VL), are limited by Gaussian posterior assumptions and local optimality.

Purpose of the Study:

• To explore Annealed Importance Sampling (AIS) as an alternative to Variational Laplace (VL) for Bayesian inference in NMMs.
• To overcome the limitations of VL, specifically its Gaussian assumption and local parameter optimization.
• To investigate the utility of AIS with Langevin Monte Carlo (LMC) for efficient parameter space exploration.

Main Methods:

• Implementation of Annealed Importance Sampling (AIS) using Langevin Monte Carlo (LMC) proposals.
• LMC utilizes local gradient and curvature information for efficient parameter space exploration.
• Comparison of AIS with the traditional Variational Laplace (VL) method for estimating Bayes factors and model parameters.

Main Results:

• Both VL and AIS agree on the best model but differ in the reported degree of belief.
• AIS identifies superior model parameters compared to VL.
• Evidence of non-Gaussianity in the posterior distribution of model parameters was found using AIS.

Conclusions:

• Annealed Importance Sampling (AIS) offers a more robust approach for Bayesian inference in Neural Mass Models.
• AIS overcomes key limitations of Variational Laplace (VL), including Gaussian assumptions and local optima.
• The findings suggest that AIS provides a more accurate estimation of model parameters and reveals complex, non-Gaussian posterior distributions in brain network analysis.