Annealed Importance Sampling for Neural Mass Models

Neural Mass Models provide a compact description of the dynamical activity of cell populations in neocortical regions. Moreover, models of regional activity can be connected together into networks, and inferences made about the strength of connections, using M/EEG data and Bayesian inference. To date, however, Bayesian methods have been largely restricted to the Variational Laplace (VL) algorithm which assumes that the posterior distribution is Gaussian and finds model parameters that are only locally optimal. This paper explores the use of Annealed Importance Sampling (AIS) to address these restrictions. We implement AIS using proposals derived from Langevin Monte Carlo (LMC) which uses local gradient and curvature information for efficient exploration of parameter space. In terms of the estimation of Bayes factors, VL and AIS agree about which model is best but report different degrees of belief. Additionally, AIS finds better model parameters and we find evidence of non-Gaussianity in their posterior distribution.Author Summary: The activity of populations of neurons in the human brain can be described using a set of differential equations known as a neural mass model. These models can then be connected to describe activity in multiple brain regions and, by fitting them to human brain imaging data, statistical inferences can be made about changes in macroscopic connectivity among brain regions. For example, the strength of a connection from one region to another may be more strongly engaged in a particular patient population or during a specific cognitive task. Current statistical inference approaches use a Bayesian algorithm based on principles of local optimization and the assumption that uncertainty about model parameters (e.g. connectivity), having seen the data, follows a Gaussian distribution. This paper evaluates current methods against a global Bayesian optimization algorithm and finds that the two approaches (local/global) agree about which model is best, but finds that the global approach produces better parameter estimates.