Bayesian Modelling and Analysis of Spatio-Temporal Neuronal Networks

This paper illustrates a novel hierarchical dynamic Bayesian network modelling the spiking patterns of neuronal ensembles over time. We introduce, at separate model stages, the parameters characterizing the discrete-time spiking process, the unknown structure of the functional connections among the analysed neurons and its dependence on their spatial arrangement. Estimates for all model parameters and predictions for future spiking states are computed under the Bayesian paradigm via the standard Gibbs sampler using a shrinkage prior. The adequacy of the model is investigated by plotting the residuals and by applying the time-rescaling theorem. We analyse a simulated dataset and a set of experimental multiple spike trains obtained from a culture of neurons in vitro. For the latter data, we find that one neuron plays a pivotal role for the initiation of each cycle of network activity and that the estimated network structure significantly depends on the spatial arrangement of the neurons.