Visualizing distributions of covariance matrices

Abstract

Statistical graphics are generally designed for visualizing data, but in this case our primary goal is to understand complex multivariate models that might be used as prior distributions for models with unknown covariance matrices. Visualizing a distribution of covariance matrices is a step beyond visualizing a single covariance matrix or a single multivariate dataset. We take advantage of the symmetries in many standard prior distributions to efficiently and effectively display these highly multivariate distributions using a tableau of low-dimensional displays. We demonstrate our approach for graphing distributions of covariance matrices on several models, including the Wishart, inverse-Wishart, and scaled inverse-Wishart families in different dimensions. Our visualizations follow the principle of decomposing a covariance matrix into scale parameters and correlations, pulling out marginal summaries where possible and using two and three-dimensional plots to reveal multivariate structure. Our visualization methods are available through the R package VisCov.