Bayesian estimation of latent roots and vectors with special reference to the bivariate normal distribution

This paper discusses from a Bayesian viewpoint some aspects of the estimation of latent roots and vectors of the covariance matrix of the bivariate normal distribution. The joint distribution of (i) the angle of the canonical transformation, and (ii) the ratio of the larger root to the total variance is considered in detail and illustrated by an example. Also discussed is the problem of making inferences about the larger roots, and several simple approximations to the distribution are considered. Finally, a generalization is given of one of the approximation methods to latent roots of higher dimensional covariance matrices.