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Visualizing Distributions of Covariance Matrices

Since we’ve been discussing prior distributions on covariance matrices, I will recommend this recent article (coauthored with Tomoki Tokuda, Ben Goodrich, Iven Van Mechelen, and Francis Tuerlinckx) on their visualization:

We present some methods for graphing distributions of covariance matrices and demonstrate them 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. Visualizing a distribution of covariance matrices is a step beyond visualizing a single covariance matrix or a single multivariate dataset. Our visualization methods are available through the R package VisCov.

One Comment

  1. Rick Wicklin says:

    That is a nice paper that I hope to study as time allows.

    It is also sometimes useful to plot the distribution of the eigenvalues (or first k eigenvalues) for the covariance matrices (or normalize them to correlation matrices). This can reveal the geometry of the covariance matrices. For an example see http://blogs.sas.com/content/iml/2012/05/16/the-curious-case-of-random-eigenvalues/