Coordinate-Free Multivariable Statistics: An Illustrated Geometric Progression from Halmos to Gauss and Bayes (Oxford Statistical Science Series, 2)

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. Topics covered in this book 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.