Department of Statistics, UCLA

This article discusses the mathematical and philosophical premises of Gauss’ and Pearson’s methods for advancing science through empirical observation. At the core is the notion that an observation can be decomposed into an ideal part and a random part, and that the relation between the observation and its two parts is known. The premise, named the Gauss-Pearson decomposition, is formalized in an algebraic framework that is as general as possible. Examples illustrate how the decomposition fits naturally into the body of statistical methodology and how it can facilitate understanding of statistical methods.