We introduce a novel latent space network model for analyzing multivariate time series of neural spike-train data. The methodology is motivated by an experimental study in mice, where neuronal responses were collected under a sequence of visual discrimination tasks. We adopt a latent variable framework to model the firing rates of aggregated brain areas, while simultaneously inferring the interactions between regions via a hidden network structure. This interaction network is embedded in a geometric latent space, enabling interpretable visualizations and novel model-based summaries. The proposed framework provides an intuitive interpretation of the latent variables, which bear a conceptual connection to node eigen-centrality measures. To capture temporal dependence, we incorporate a nested hidden Markov structure that can flexibly represent non-linear shifts that are induced by the changing of experimental conditions. We further establish theoretical properties of the model by deriving sufficient conditions that prevent degeneracy, thereby guiding our model assumptions. Overall, the proposed methodology provides a unified framework to characterize brain activity, its temporal dynamics, and spillover effects through a hidden latent space network model.
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