Gauss Linear Model

The model says that the $(x_n,y_n)\in\mathbb{R}^p\times\mathbb{R}$ are generated as follows:

  • there are no restrictions on the way $x_n$ are generated;
  • given $x_n$, the $y_n$ are generated from $y_n = w\cdot x_n + \xi_n$, where $w\in\mathbb{R}^p$ is a vector of parameters, $\xi_n$ is distributed as $N(0,\sigma^2)$, and $\sigma>0$ is another parameter.

See Section 8.5 of Vovk et al. (2005) and Vovk et al. (2008) for the formulation of this model as an on-line compression model.