Hulin Wu, Jin-Ting Zhang

Nonparametric Regression Methods for Longitudinal Data Analysis: Mixed-Effects Modeling Approaches

ISBN: 0-471-48350-8
Hardcover
400 pages
April 2006

Incorporates mixed-effects modeling techniques for more powerful and efficient methods

This book presents current and effective nonparametric regression techniques for longitudinal data analysis and systematically investigates the incorporation of mixed-effects modeling techniques into various nonparametric regression models. The authors emphasize modeling ideas and inference methodologies, although some theoretical results for the justification of the proposed methods are presented.

With its logical structure and organization, beginning with basic principles, the text develops the foundation needed to master advanced principles and applications. Following a brief overview, data examples from biomedical research studies are presented and point to the need for nonparametric regression analysis approaches. Next, the authors review mixed-effects models and nonparametric regression models, which are the two key building blocks of the proposed modeling techniques.

The core section of the book consists of four chapters dedicated to the major nonparametric regression methods: local polynomial, regression spline, smoothing spline, and penalized spline. The next two chapters extend these modeling techniques to semiparametric and time varying coefficient models for longitudinal data analysis. The final chapter examines discrete longitudinal data modeling and analysis.

Each chapter concludes with a summary that highlights key points and also provides bibliographic notes that point to additional sources for further study. Examples of data analysis from biomedical research are used to illustrate the methodologies contained throughout the book. Technical proofs are presented in separate appendices.

With its focus on solving problems, this is an excellent textbook for upper-level undergraduate and graduate courses in longitudinal data analysis. It is also recommended as a reference for biostatisticians and other theoretical and applied research statisticians with an interest in longitudinal data analysis. Not only do readers gain an understanding of the principles of various nonparametric regression methods, but they also gain a practical understanding of how to use the methods to tackle real-world problems.

Table of Contents

Preface.
Acronyms.
1. Introduction.
2. Parametric Mixed-Effects Models.
3. Nonparametric Regression Smoothers.
4. Local Polynomial Methods.
5. Regression Spline Methods.
6. Smoothing Splines Methods.
7. Penalized Spline Methods.
8. Semiparametric Models.
9. Time-Varying Coefficient Models.
10. Discrete Longitudinal Data.
References.
Index.

George E. P. Box

Improving Almost Anything: Ideas and Essays, Revised Edition

ISBN: 0-471-72755-5
Paperback
598 pages
April 2006

Masterworks in process improvement and quality technology? by George Box and friends

George Box has a unique ability to explain complex ideas simply and eloquently. This revised edition of his masterworks since 1982 clearly demonstrates the range of his wit and intellect. These fascinating readings represent the cornerstones in the theory and application of process improvement, product design, and process control. Readers will gain valuable insights into the fundamentals and philosophy of scientific method using statistics and how it can drive creativity and discovery.

The book is divided into five key parts:

Part A, Some Thoughts on Quality Improvement, concerns the democratization of the scientific method and, in such papers as "When Murphy Speaks?Listen," advises managers to view operation of their processes as ongoing opportunities for improvement.
Part B, Design of Experiments for Process Improvement, illustrates the enormous advantages offered by experimental design in the pursuit of better products and processes.
Part C, Sequential Investigation and Discovery, shows how sequential assembly of designs allows the experimenter to match the difficulty of the problem with the effort needed to solve it.
Part D, Control, describes application of feedback control in the Statistical Process Control (SPC) environment. A simple graphical technique using Box-Jenkins charts is set forth to appropriately adjust processes to target.
Part E, Variance Reduction and Robustness, demonstrates how the existence of more than one source of variation may be used to achieve products robust to the environment in which they must function and emphasizes the importance of error transmission and data transformation in producing robust assemblies.
A Foreword by Dr. J. Stuart Hunter allows readers to gain insight into the workings of a remarkable mind and explains how these ideas can greatly catalyze their efforts in process improvement.

Table of Contents

by Keith B. Oldham,Jerome Spanier

The Fractional Calculus:
Theory and Applications of Differentiation and Integration to Arbitrary Order

ISBN: 0486450015

The product of a collaboration between a mathematician and a chemist, this text is geared toward advanced undergraduates and graduate students. Not only does it explain the theory underlying the properties of the generalized operator, but it also illustrates the wide variety of fields to which these ideas may be applied. Topics include integer order, simple and complex functions, semiderivatives and semiintegrals, and transcendental functions. The text concludes with overviews of applications in the classical calculus and diffusion problems. 1974 ed.

Table of Contents

1. Introduction
2. Differentiation and Integrations to Integer Order
3. Fractional Derivatives and Integrals: Definitions and Equivalences
4. Differintegration of Simple Functions
5. General Properties
6. Differintegration of More Complex Functions
7. Semiderivatives and Semiintegrals
8. Techniques in the Fractional Calculus
9. Representation of Transcendental Functions
10. Applications in the Classical Calculus
11. Applications to Diffusion Problems
References
Index

Jan Awrejcewicz Technical University of Lodz, Poland
Vadim A. Krysko Technical University, Sazatov, Russia

Introduction to Asymptotic Methods

Series: Modern Mechanics and Mathematics Volume: 5

ISBN: 1584886773
Publication Date: 5/3/2006
Number of Pages: 272

Explores the fundamental elements of the process of mathematical modelling
Discusses new analytical tools such as the Pad・approximation
Demonstrates the usefulness of asymptotic methods for investigating complex mathematical problems
Illustrates how the application of elongated coordinates and renormalization methods yields highly accurate results
Shows how the application of the methods of renormalization and multiple scales can achieve uniformly suitable solutions

Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important methods of singular perturbations within the scope of application of differential equations. The authors take a challenging and original approach based on the integrated mathematical-analytical treatment of various objects taken from interdisciplinary fields of mechanics, physics, and applied mathematics. This new hybrid approach will lead to results that cannot be obtained by standard theories in the field.

Emphasizing fundamental elements of the mathematical modeling process, the book provides comprehensive coverage of asymptotic approaches, regular and singular perturbations, one-dimensional non-stationary non-linear waves, Pad・approximations, oscillators with negative Duffing type stiffness, and differential equations with discontinuous nonlinearities. The book also offers a method of construction for canonical variables transformation in parametric form along with a number of examples and applications. The book is applications oriented and features results and literature citations that have not been seen in the Western Scientific Community. The authors emphasize the dynamics of the development of perturbation methods and present the development of ideas associated with this wide field of research.

Table of Contents

by Harald J W Muler-Kirsten (University of Kaiserslautern, Germany)

INTRODUCTION TO QUANTUM MECHANICS
Schrodinger Equation and Path Integral

After a consideration of basic quantum mechanics, this introduction aims at a side by side treatment of fundamental applications of the Schrodinger equation on the one hand and the applications of the path integral on the other. Different from traditional texts and using a systematic perturbation method, the solution of Schrodinger equations includes also those with anharmonic oscillator potentials, periodic potentials, screened Coulomb potentials and a typical singular potential, as well as the investigation of the large order behavior of the perturbation series. On the path integral side, after introduction of the basic ideas, the expansion around classical configurations in Euclidean time, such as instantons, is considered, and the method is applied in particular to anharmonic oscillator and periodic potentials. Numerous other aspects are treated on the way, thus providing the reader an instructive overview over diverse quantum mechanical phenomena, e.g. many other potentials, Green's functions, comparison with WKB, calculation of lifetimes and sojourn times, derivation of generating functions, the Coulomb problem in various coordinates, etc. All calculations are given in detail, so that the reader can follow every step.

Contents:

Hamiltonian Mechanics
Mathematical Foundations of Quantum Mechanics
Dirac痴 Ket- and Bra-Formalism
Schr�dinger Equation and Liouville Equation
Quantum Mechanics of the Harmonic Oscillator
Green痴 Functions
Time-Independent Perturbation Theory
The Density Matrix and Polarization Phenomena
Quantum Theory: The General Formalism
The Coulomb Interaction
Quantum Mechanical Tunneling
Linear Potentials
Classical Limit and WKB Method
Power Potentials
Screened Coulomb Potentials
Periodic Potentials
Anharmonic Oscillator Potentials
Singular Potentials
Large Order Behavior of Perturbation Expansions
The Path Integral Formalism
Classical Field Configurations
Path Integrals and Instantons
Path Integrals and Bounces on a Line
Periodic Classical Configurations
Path Integrals and Periodic Classical Configurations
Quantization of Systems with Constraints
The Quantum-Classical Crossover as Phase Transition

Readership: Undergraduate and graduate students in physics; researchers in mathematical physics and particle physics.

828pp Pub. date: Mar 2006
ISBN 981-256-691-0
ISBN 981-256-692-9(pbk)