State and parameter estimation for a neural model of local field potentials

The study of cortical dynamics during different states such as decision making, sleep and movement, is an important topic in Neuroscience. Modelling efforts aim to relate the neural rhythms present in cortical recordings to the underlying dynamics responsible for their emergence. We present an effort to capture certain features of the neural activity from the cortex of a mouse during natural sleep, obtained through local field potential measurements. Our approach relies on using a discretized Wilson-Cowan Amari neural field model for neural activity, along with a data assimilation method that allows the Bayesian joint estimation of the state and parameters. We demonstrate the feasibility of our approach on synthetic measurements before applying it to a dataset available in literature. Our findings suggest the potential of our approach to characterize the parameters of the external forcing in the neural activity model, while simultaneously inferring a state that aligns with the observed signal.