# Gauss Linear Model

The Gauss statistical model says that the are generated as follows:

- there are no restrictions on the way are generated;
- given , the are generated from , where is a vector of parameters, is distributed as , and is another parameter.

See Section 8.5 of Vovk et al. (2005) and Vovk et al. (2009) for the formulation of this model as an on-line compression model.

The most basic version of this model is where there are no s, and the model is . The summary of is and the Gauss repetitive structure postulates that the distribution of is uniform on the sphere of radius . Borel (1914) noticed that the Gauss statistical model (used by Maxwell as a model in statistical physics) is equivalent to the Gauss repetitive structure (used for a similar purpose by Gibbs). For further historical comments, see Vovk et al. (2005), Section 8.8, and Diaconis and Freedman (1987), Section 6.

**Bibliography**

- Persi Diaconis and David Freedman (1987). A dozen de Finetti-style results in search of a theory.
*Annales de l'Institut Henri Poincare B*23:397-423. - Vladimir Vovk, Alexander Gammerman and Glenn Shafer (2005). Algorithmic learning in a random world. Springer, New York.
- Vladimir Vovk, Ilia Nouretdinov, and Alexander Gammerman (2009). On-line predictive linear regression.
*Annals of Statistics*37:1566-1590.