# The linear conditional expectation in Hilbert space

@inproceedings{Klebanov2020TheLC, title={The linear conditional expectation in Hilbert space}, author={I. Klebanov and Bjorn Sprungk and T. J. Sullivan}, year={2020} }

The linear conditional expectation (LCE) provides a best linear (or rather, affine) estimate of the conditional expectation and hence plays an important rôle in approximate Bayesian inference, especially the Bayes linear approach. This article establishes the analytical properties of the LCE in an infinite-dimensional Hilbert space context. In addition, working in the space of affine Hilbert–Schmidt operators, we establish a regularisation procedure for this LCE. As an important application, we… CONTINUE READING

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