2006, Geb.
ISBN: 3-540-20578-0
Erscheinungstermin: September 2006
Uber dieses Buch
The bulk of this volume consists of six sets of notes for
lectures Hilbert gave (often in collaboration with Bernays) on
the foundations of mathematics between 1917 and the early 1930s.
The notes detail the increasing dominance of the metamathematical
perspective in Hilbert’s treatment, i.e., the development of
modern mathematical logic, the evolution of proof theory, and the
parallel emergence of Hilbert's finitist standpoint. The notes
are mostly very polished expositions; e.g., the 1917-18 lectures
are in effect a first draft of Hilbert and Ackermann’s
Grundzuge der theoretischen Logik (1928), reprinted in this
Volume. They are thus essential for understanding the development
of modern mathematical logic leading up to Hilbert and Bernays’s
Grundlagen der Mathematik (1934, 1938). Also included is a
complete version of Bernay’s Habilitationschrift of 1918, only
partially published in 1926.
Inhaltsverzeichnis
Introduction.- Hilbert's Lectures on Principles of Mathematics
from 1917-18.- Hilbert's Lectures on the Logical Calculus from
1920.- Chapter 3: Hilbert's Lectures on Problems of Mathematical
Logic from 1920.- Hilbert's Lectures on Foundations of
Mathematics from 1921-22.- Hilbert's Lectures on Logical
Foundations of Mathematics from 1922-23.- Hilbert's Lectures on
the Infinite from 1924-25.- Hilbert's Typescript on the
Foundations of Thought from c. 1925.- Hilbert's Lecture on
Infinity from 1933.-Miscellanea.- Appendix A: Bernays's
Habilitation Thesis from 1918.- Appendix B: First Edition of
Hilbert and Ackermann, 1928.
Series: Springer Series in Statistics
2005, Approx. 630 p. 176 illus., Hardcover
ISBN: 0-387-25150-2
Due: September 2005
About this book
The book provides a comprehensive treatment of multidimensional
scaling (MDS), a family of statistical techniques for analyzing
the structure of (dis)similarity data. Such data are widespread,
including, for example, intercorrelations of survey items, direct
ratings on the similarity on choice objects, or trade indices for
a set of countries. MDS represents the data as distances among
points in a geometric space of low dimensionality. This map can
help to see patterns in the data that are not obvious from the
data matrices. MDS is also used as a psychological model for
judgments of similarity and preference.
This book may be used as an introduction to MDS for students in
psychology, sociology, and marketing. The prerequisite is an
elementary background in statistics. The book is also well suited
for a variety of advanced courses on MDS topics. All the
mathematics required for more advanced topics is developed
systematically.
This second edition is not only a complete overhaul of its
predecessor, but also adds some 140 pages of new material. Many
chapters are revised or have sections reflecting new insights and
developments in MDS. There are two new chapters, one on
asymmetric models and the other on unfolding. There are also
numerous exercises that help the reader to practice what he or
she has learned, and to delve deeper into the models and its
intricacies. These exercises make it easier to use this edition
in a course. All data sets used in the book can be downloaded
from the web. The appendix on computer programs has also been
updated and enlarged to reflect the state of the art.
Table of contents
Part I. Fundamentals of MDS: The four purposes of
multidimensional scaling. Constructing MDS representations. MDS
models and measures of fit. Three applications of MDS. MDS and
facet theory. How to obtain proximities.- Part II. MDS models and
solving MDS problems. Matrix algebra for MDS. A majorization
algorithm for solving MDS. Metric and non-metric MDS.
Confirmatory MDS. MDS fit measures, their relations, and some
algorithms. Classical scaling. Special solutions, degeneracies,
and local minima; III. Unfolding. Unfolding. Avoiding trivial
solutions in unfolding. Special unfolding models.- Part IV. MDS
geometry as a substantive model. MDS as a psychological model.
Scalar products and Euclidean distances. Euclidean embeddings.-
Part V. MDS and related methods. Procrustes procedures. Three-way
Procrustean models. Three-way MDS models. Modeling asymmetric
data. Methods related to MDS.- Part VI. Appendices.
2005, Approx. 370 p., Softcover
ISBN: 3-7643-7349-0
Due: September 2005
About this textbook
This graduate text provides a careful treatment of the theory and
applications of matrices in the presence of an indefinite inner
product. The theory is a natural extension of the classical
theory of hermitian and unitary matrices in linear algebra.
Applications of the theory to differential equations, difference
equations and systems theory are included.
Table of contents
Preface.- Introduction and Outline.- Indefinite Inner Products.-
Orthogonalization and Orthogonal Polynomials.- Classes of Linear
Transformations.- Canonical Forms.- Real H-Selfadjoint Matrices.-
Functions of H-Selfadjoint Matrices.- H-Normal Matrices.- General
Perturbations. Stability of Diagonalizable Matrices.- Definite
Invariant Subspaces.- Differential Equations of First Order.-
Matrix Polynomials.- Differential and Difference Equations of
Higher Order.- Algebraic Riccati Equations.- Appendix: Topics
from Linear Algebra.- Bibliography.- Index.
Series: Springer Series in Statistics
Approx. 420 p., Hardcover
ISBN: 0-387-40266-7
Due: September 2005
About this book
This monograph describes methodology, theory and applications of
the use of polynomial splines in data mining. Over the last
decade or so, the use of such splines has gained considerable
popularity. This monograph will be the first book that discusses
spline methods where both the location of the knots and the
coefficients are optimized. After a preliminary chapter
describing various properties of splines that are needed later
on, the book discusses a number of well known methodologies and
their variations in detail. These methodologies include MARS and
POLYMARS (Chapter 3), POLYCLASS (Chapter 5), Logspline (Chapter 6),
HARE (Chapter 7), Lspec (Chapter 8) and Triogram (Chapter 9). The
last two chapters of the book give a thorough and comprehensive
discussion of the theory behind polynomial spline methodologies.
This monograph is aimed at statistical researchers and graduate
students, as well as applied researchers using nonparametric
statistical methods.
Table of contents
Introduction * Preliminaries * Linear Models * Generalized Linear
Models * Polychotomous Regression and Multiple Classification *
Density Estimation * Survival Analysis * Estimation of the
Spectral Distribution * Multivariate Splines * Alternate
Optimization Methods * Rates of Convergence in Extended Linear
Modeling * Extended Linear Modeling with Free Knot Splines
2005, XXII, 764 p. 49 illus., Hardcover
ISBN: 3-540-40172-5
About this book
This reference work and graduate level textbook considers a wide
range of models and methods for analyzing and forecasting
multiple time series. The models covered include vector
autoregressive, cointegrated, vector autoregressive moving
average, multivariate ARCH and periodic processes as well as
dynamic simultaneous equations and state space models. Least
squares, maximum likelihood, and Bayesian methods are considered
for estimating these models. Different procedures for model
selection and model specification are treated and a wide range of
tests and criteria for model checking are introduced. Causality
analysis, impulse response analysis and innovation accounting are
presented as tools for structural analysis.
The book is accessible to graduate students in business and
economics. In addition, multiple time series courses in other
fields such as statistics and engineering may be based on it.
Applied researchers involved in analyzing multiple time series
may benefit from the book as it provides the background and tools
for their tasks. It bridges the gap to the difficult technical
literature on the topic.
Table of contents
Series: Statistics for Biology and Health
2006, 471 p. 75 illus., Hardcover
ISBN: 0-387-20274-9
Due: September 2005
About this book
In survival analysis there has long been a need for models that
goes beyond the Cox model as the proportional hazards assumption
often fails in practice. This book studies and applies modern
flexible regression models for survival data with a special focus
on extensions of the Cox model and alternative models with the
specific aim of describing time-varying effects of explanatory
variables. One model that receives special attention is Aalen’s
additive hazards model that is particularly well suited for
dealing with time-varying effects. The book covers the use of
residuals and resampling techniques to assess the fit of the
models and also points out how the suggested models can be
utilised for clustered survival data. The authors demonstrate the
practically important aspect of how to do hypothesis testing of
time-varying effects making backwards model selection strategies
possible for the flexible models considered.
The use of the suggested models and methods is illustrated on
real data examples. The methods are available in the R-package
timereg developed by the authors, which is applied throughout the
book with worked examples for the data sets. This gives the
reader a unique chance of obtaining hands-on experience.
This book is well suited for statistical consultants as well as
for those who would like to see more about the theoretical
justification of the suggested procedures. It can be used as a
textbook for a graduate/master course in survival analysis, and
students will appreciate the exercises included after each
chapter. The applied side of the book with many worked examples
accompanied with R-code shows in detail how one can analyse real
data and at the same time gives a deeper understanding of the
underlying theory.
Table of contents
Introduction.- Probabilistic background.- Estimation for filtered
counting process data.- Nonparametric procedures for survival
data.- Additive hazards models.- Multiplicative hazards models.-
Multiplicative-additive hazards models.- Accelerated failure time
and transformation models.- Clustered failure time data.-
Competing risks model.- Marked point process models.