# Bayes linear methods

Some kind of approximate Bayes thing

August 17, 2022 — March 28, 2024

Some kind of approximate Bayes method. Utility unclear. Mainstream status: marginal.

From a brief glance, it seems that by assuming “linear beliefs” in some sense, we can construct all necessary posterior updates in terms of covariance matrices and means, without actually stipulating that the prior or likelihood (or anything) is Gaussian.

The results look suspiciously like the standard Gaussian posterior updates, in that the resulting estimator is frequently fancy least squares optimisation and lots of the same machinery is recovered, e.g. Matheron updates can be justified in this framework.

I suspect that I can find mainstream acceptance by simply making explicit Gaussian approximations, and thence avoiding controversy about this slightly esoteric option. But introducing fewer assumptions is always nice?

The best summary is presumably the textbook (Goldstein and Wooff 2007).

- Bayes linear methods
- Bayes Linear Methods I — Adjusting Beliefs: Concepts and Properties
- Bayes Linear Methods II — An example with an introduction to [B/D]
- Bayes Linear Methods III — Analysing Bayes linear influence diagrams and Exchangeability in [B/D]
- [B/D] Reference Manual

## 1 References

*Computational Geosciences*.

*Statistics and Computing*.

*Bayes Linear Statistics: Theory and Methods*. Wiley Series in Probability and Statistics.

*Mathematical Geosciences*.

*Bayes Linear Methodology,” Unpublished Draft*.

*Journal of Statistical Software*.