Someone sent me a question regarding the inverse-Wishart prior distribution for covariance matrix, as it is the default in some software he was using. Inverse-Wishart does not make sense for prior distribution; it has problems because the shape and scale are tangled. See this paper, “Visualizing Distributions of Covariance Matrices,” by Tomoki Tokuda, Ben Goodrich, Iven Van Mechelen, Francis Tuerlinckx and myself. Right now I’d use the LKJ family. In Stan there are lots of options. See also our wiki on prior distributions.
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