Bayes linear adjustment for variance matrices

Physics – Data Analysis – Statistics and Probability

Scientific paper

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To appear in the Bayesian Statistics 5 conference volume. LaTeX, 11 pages, Chicago BIB-style (included), 2 postscript figures.

Scientific paper

We examine the problem of covariance belief revision using a geometric approach. We exhibit an inner-product space where covariance matrices live naturally --- a space of random real symmetric matrices. The inner-product on this space captures aspects of our beliefs about the relationship between covariance matrices of interest to us, providing a structure rich enough for us to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability specifications.

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