Parameter shift in linear regression.

The mathematical framework for statistical decision theory is provided by the theory of probability which in turn has its foundations in the theory of measure and integration. In constructing a probability model for an experiment, the first step is a consideration of what are the possible outcomes of the experiment. We assume that all possibilities for the outcomes can be foreseen, and we refer to this collection of outcomes as the sample space H. An arbitrary outcome or point of this space is designated by x. The events to be studied are aggregates of such outcomes, they are represented by subsets of H which belong to the σ-algebra A