Coordinate-free Multivariable Statistics

This elementary, self-contained book overcomes the well-known obstacles to full and proper deployment of the geometrical approach to linear statistical method. Topics covered range from the general linear model of Gauss, via Bayes estimation, to the Kalman filter. There are over 60 fully documented figures portraying vector spaces, orthogonal projections, and related items. The basic operations of linear statistical method do not change with the coordinate system. Their treatment is therefore naturally coordinate-free. The book's main novelty lies in its consistent use of separate, dual vector spaces for 'variables' and 'individuals', and of covariance operators as bridges betwen them. The necessary linear algebra for this is included, based on snippets from the famous textbook on vector spaces by P.R. Halmos. A feature of the new approach is its exploitation of a statistically felicitous notation for certain linear and bilinear operators, giving multivariable statistical formulae a simpler 'univariate' look.