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The problem of representing and analysing partial aspects of uncertainty is examined using a geometric approach. A Hilbert space of random objects is constructed, where the inner product captures aspects of beliefs about the relationship between the objects. Orthogonal direct sums of the Hilbert space are used to restrict the amount of detail that is required for the prior specification. Using minimal assumptions of temporal consistency, this geometric space is adapted to derive the stochastic relationships between the formal restricted partial belief analysis and the corresponding posterior uncertainty judgements.
Annals of Mathematics and Artificial Intelligence – Springer Journals
Published: Oct 19, 2004
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