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Bayes linear adjustment for variance matrices

Darren J Wilkinson·Michael Goldstein
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Abstract

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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Darren J Wilkinson, Michael Goldstein. 1995-06-05. Bayes linear adjustment for variance matrices. https://arxiv.org/abs/bayes-an/9506001

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