Christensen, R., University of New Mexico, Albuquerque, NM, USA

Advanced Linear Modeling
Multivariate, Time Series, and Spatial Data; Nonparametric Regression & Response Surface Maximization

2nd ed. 2001. Approx. 415 pp. 14 figs. Hardcover
0-387-95296-9

This book introduces several topics related to linear model theory, including: multivariate linear models, discriminant analysis, principal components, factor analysis, time series in both the frequency and time domains, and spatial data analysis. This second edition adds new material on nonparametric regression, response surface maximization, and longitudinal models. The book provides a unified approach to these disparate subjects and serves as a self-contained companion volume to the author's Plane Answers to Complex Questions: The Theory of Linear Models. Ronald Christensen is Professor of Statistics at the University of New Mexico. He is well known for his work on the theory and application of linear models having linear structure.

Contents: Multivariate Linear Models.- Discrimination and Allocation.- Principal Components and Factor Analysis.- Frequencey Analysis of Time Series.- Time Domain Analysis.- Linear Models for Spatial Data: Kriging.- Nonparametric Regression.- Response Surface Maximization.

Series: Springer Texts in Statistics.

Sommer, G., Christian-Albrechts-Universitat zu Kiel, Germany (Ed.)

Geometric Computing with Clifford Algebras
Theoretical Foundations and Applications in Computer Vision and Robotics

2001. XVIII, 551 pp. 89 figs., 16 tabs. Hardcover
3-540-41198-4

This monograph-like anthology introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work shows that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics.

Keywords: Geometric Computing, Clifford Algebras, Algebraic Geometry, Computer Vision ,Signal Processing, Neural Computation, Robotics, Computational Geometry, Algebraic Expressions, Geometric Languages

Contents: Part I. A Unified Algebraic Approach for Classical Geometries: New Algebraic Tools for Classical Geometry, Generalized Homogeneous Coordinates for Computational Geometry, Spherical Conformal Geometry with Geometric Algebra, A Universal Model for Conformal Geometries of Euclidean, Spherical and Double-Hyperbolic Spaces, Geo-MAP Unification, Honing Geometric Algebra for Its Use in the Computer Sciences, Part II. Algebraic Embedding for Signal Theory and Neural Computation: Spatial-Color Clifford Algebras for Invariant Image Recognition, Non-commutative Hypbercomplex Fourier Transforms of Multidimensional Signals, Commutative Hypercomplex Fourier Transforms of Mulitdimensional Signals, Fast Algorithms fo Hypercomplex Fourier Transforms, Local Hypercomplex Signal Representations and Applications, Introduction to Neural Computation in Clifford Algebra, Clifford Algebra Mulitlayer Perceptrons, etc.

Lam, T.Y., University of California, Berkeley, CA, USA

A First Course in Noncommutative Rings, 2nd ed.

2001. XIX, 385 pp. Hardcover
0-387-95183-0

A First Course in Noncommutative Rings, an outgrowth of the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-semester course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semisimple rings, Jacobson's theory of the radical, representation theory of groups and algebras, prime and semiprime rings, local and semilocal rings, perfect and semiperfect rings, etc. By aiming the level of writing at the novice rather than the connoisseur and by stressing th the role of examples and motivation, the author has produced a text that is suitable not only for use in a graduate course, but also for self- study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.

Contents: Wedderburn-Artin Theory.- Jacobson Radical Theory.- Introduction to Representation Theory.- Prime and Primitive Rings.- Introduction to Division Rings.- Local Rings, Semilocal Rings, and Idempotents.- Perfect and Semiperfect Rings.- References.

Series: Graduate Texts in Mathematics. VOL. 131

Chan, K.-S., University of Iowa, Iowa City, IA, USA
Tong, H.H., The London School of Economics, London, UK

Chaos: A Statistical Perspective

2001. Approx. 285 pp. 98 figs. Hardcover
0-387-95280-2

This book discusses dynamical systems that are typically driven by stochastic dynamic noise. It is written by two statisticians essentially for the statistically inclined readers, although readers whose primary interests are in determinate systems will find some of the methodology explained in this book of interest. The statistical approach adopted in this book differs in many ways from the deterministic approach to dynamical systems. Even the very basic notion of initial-value sensitivity requires careful development in the new setting provided. This book covers, in varying depth, many of the contributions made by the statisticians in the past twenty years or so towards our understanding of estimation, the Lyapunov-like index, the nonparametric regression, and many others, many of which are motivated by their dynamical system counterparts but have now acquired a distinct statistical flavour. Kung-Sik Chan is a professor at the University of Iowa, Department of Statistics and Actuarial Science. He is an elected member of the International Statistical Institute. He has served on the editorial boards of the Journal of Business and Economic Statistics and Statistica Sinica. He received a Faculty Scholar Award from the University of Iowa in 1996. Howell Tong holds the Chair of Statistics at the London School of Economics and the University of Hong Kong. He is a foreign member of the Norwegian Academy of Science and Letters, an elected member of the International Statistical Institute and a Council member of its Bernoulli Society, an elected fellow of the Institute of Mathematical Statistics, and an honorary fellow of the Institute of Actuaries (London). He was the Founding Dean of the Graduate School and sometimes the Acting Pro-Vice Chancellor (Research) at the University of Hong Kong. He has served on the editorial boards of several

Contents: 1. Introduction; 2. Deterministic chaos; 3. Chaos and Stochastic Systems; 4. Statistical Analysis I; 5. Statistical Analysis II; 6. Nonlinear Least-Square Prediction; 7. Miscellaneous Topics; References.

Series: Springer Series in Statistics.

Jensen, F.V., University of Aalborg, Denmark

Bayesian Networks and Decision Graphs

2001. XV, 268 pp. 184 figs. Hardcover
0-387-95259-4

Bayesian networks and decision graphs are formal graphical languages for representation and communication of decision scenarios requiring reasoning under uncertainty. Their strengths are two-sided. It is easy for humans to construct and to understand them, and when communicated to a computer, they can easily be compiled. Furthermore, handy algorithms are developed for analyses of the models and for providing responses to a wide range of requests like belief updating, determining optimal strategies, conflict analyses of evidence, most probable explanation, etc. The book emphasizes both the human and the computer side. Part I gives a thorough introduction to Bayesian networks as well as decision trees and infulence diagrams, and through examples and exercises, the reader is instructed in building graphical models from domain knowledge. This part is self-contained and it does not require other background than standard secondary school mathematics. Part II is devoted to the presentation of algorithms and complexity issues. Theis part is also self-contained, but it requires that the reader is familiar with working with texts in the mathematical language. The author also: *Provides a well-founded practical introduction to Bayesian networks, decision trees and influence diagrams *Gives several examples and exercises exploiting the computer systems for Bayesian netowrks and influence diagrams *Gives practical advice on constructiong Bayesian networks and influence diagrams from domain knowledge. *Embeds decision making into the framework of Bayesian networks *Presents in detail the currently most efficient algorithms for probability updating in Bayesian networks *Discusses a wide range of analyes tools and model requests together with algorithms for calculation of responses.

Keywords: Bayesian Networks, Decision Graphs

Contents: Introduction.- Parametric Models.- Semiparametric Models.- Fraility Models.- Cure Rate Models.- Model Comparison.- Joint Models for Longitudinal and Survival Data.- Missing Covariate Data.- Design and Monitoring of Randomized Clinical Trials.- Other Topics.

Series: Statistics for Engineering and Information Science.

Coles, S., University of Bristol, UK

An Introduction to Statistical Modeling of Extreme Values

2001. XIV, 210 pp. 77 figs. Hardcover
1-85233-459-2

Directly oriented towards real practical application, this book develops both the basic theoretical framework of extreme value models and the statistical inferential techniques for using these models in practice. Intended for statisticians and non-statisticians alike, the theoretical treatment is elementary, with heuristics often replacing detailed mathematical proof. Most aspects of extreme modeling techniques are covered, including historical techniques (still widely used) and contemporary techniques based on point process models. A wide range of worked examples, using genuine datasets, illustrate the various modeling procedures and a concluding chapter provides a brief introduction to a number of more advanced topics, including Bayesian inference and spatial extremes. All the computations are carried out using S-PLUS, and the corresponding datasets and functions are available via the Internet for readers to recreate examples for themselves. An essential reference for students and researchers in statistics and disciplines such as engineering, finance and environmental science, this book will also appeal to practitioners looking for practical help in solving real problems. Stuart Coles is Reader in Statistics at the University of Bristol, UK, having previously lectured at the universities of Nottingham and Lancaster. In 1992 he was the first recipient of the Royal Statistical Society's research prize. He has published widely in the statistical literature, principally in the area of extreme value modeling.

Contents: 1. Introduction.- 2. Basics of Statistical Modeling.- 3. Classical Extreme Value Theory and Models.- 4. Threshold Models.- 5. Extremes of Dependent Sequences.- 6. Extremes of Non-Stationary Sequences.- 7. A Point Process Characterization of Extremes.- 8. Multivariate Extremes.- 9. Further Topics.- Appendix A: Computational Aspects.- Index.

Series: Springer Series in Statistics.