Coordinate-Free Multivariable Statistics: An Illustrated Geometric Progression from Halmos to Gauss and Bayes

This detailed study demonstrates proper deployment of the geometrical approach to linear statistical method. Among the topics discussed are the general linear model of Gauss, Bayes estimation and the Kalman filter. With over sixty fully documented figures portraying vector spaces, orthogonal projections, and related items, Stone explains that the basic operations of linear statistical method do not change with the coordinate system; their treatment is therefore naturally coordinate-free. A unique feature of Stone's geometrical approach is his use of a statistically felicitous notation for certain linear and bilinear operators, giving multivariable statistical formulae a simpler, "univariate" look.