James D. Malley - Böcker

This volume brings together the author's work in mathematical statistics as viewed through the lens of Jordan algebras. In particular the three main areas covered in this work are: applications to random quadratic forms (sums of squares); the investigation of algebraic simplifications of maximum likelihood estimation of patterned covariance matrices; and a more wide-ranging mathematical exploration of some of the algebraic problems discussed. The author gives a full and rigorous definition of Jordan algebras and their essential properties and shows how they provide a natural and powerful algebraic tool for statisticians. In particular, the application of these methods to the M-step of the EM algorithm both simplifies this analysis and resolves some practical and important problems. This intertwining of ideas presented by the author will make this an interesting account suitable for researchers addressing these problems in statistics.

This book is for anyone who has biomedical data and needs to identify variables that predict an outcome, for two-group outcomes such as tumor/not-tumor, survival/death, or response from treatment. Statistical learning machines are ideally suited to these types of prediction problems, especially if the variables being studied may not meet the assumptions of traditional techniques. Learning machines come from the world of probability and computer science but are not yet widely used in biomedical research. This introduction brings learning machine techniques to the biomedical world in an accessible way, explaining the underlying principles in nontechnical language and using extensive examples and figures. The authors connect these new methods to familiar techniques by showing how to use the learning machine models to generate smaller, more easily interpretable traditional models. Coverage includes single decision trees, multiple-tree techniques such as Random Forests(TM), neural nets, support vector machines, nearest neighbors and boosting.