Modeling Neural Population Coordination via a Block Correlation Matrix

Correlation matrix estimation is challenging. An unstructured correlation matrix is unestimable if p>n. Although extensive methods have been proposed, most of them only emphasize on computation efficiency but few of them provide clear interpretation. Motivated by a neuroscience study and financial market application, we consider a block structure on a correlation matrix to enjoy both interpretability and statistical efficiency. To circumvent intractable normalising constrants calculation resulting from block structure and valid correlation matrix constraints, we propose a novel model based on the canonical representation (Archakov and Hansen, 2020) in a Bayesian framework. I also incorporate a mixture of finite mixtures model (Miller and Harrison, 2018) to allow for estimating unknown block structure. We design a Gibbs sampling scheme where the parameters are updated by conjugacy.