Seymour Geisser

Modes of Parametric Statistical Inference

ISBN: 0-471-66726-9
Hardcover
192 pages
January 2006

A fascinating investigation into the foundations of statistical inference
This publication examines the distinct philosophical foundations of different statistical modes of parametric inference. Unlike many other texts that focus on methodology and applications, this book focuses on a rather unique combination of theoretical and foundational aspects that underlie the field of statistical inference. Readers gain a deeper understanding of the evolution and underlying logic of each mode as well as each mode's strengths and weaknesses.

The book begins with fascinating highlights from the history of statistical inference. Readers are given historical examples of statistical reasoning used to address practical problems that arose throughout the centuries. Next, the book goes on to scrutinize four major modes of statistical inference:

The author provides readers with specific examples and counterexamples of situations and datasets where the modes yield both similar and dissimilar results, including a violation of the likelihood principle in which Bayesian and likelihood methods differ from frequentist methods. Each example is followed by a detailed discussion of why the results may have varied from one mode to another, helping the reader to gain a greater understanding of each mode and how it works. Moreover, the author provides considerable mathematical detail on certain points to highlight key aspects of theoretical development.

The author's writing style and use of examples make the text clear and engaging. This book is fundamental reading for graduate-level students in statistics as well as anyone with an interest in the foundations of statistics and the principles underlying statistical inference, including students in mathematics and the philosophy of science. Readers with a background in theoretical statistics will find the text both accessible and absorbing.

Table of contents

Foreword.
Preface.
1. A Forerunner.
2. Frequentist Analysis.
3. Likelihood.
4. Testing Hypotheses.
5. Unbiased and Invariant Tests.
6. Elements of Bayesianism.
7. Theories of Estimation.
8. Set and Interval Estimation.
References.
Index.

Consul, Prem C., Famoye, Felix

Lagrangian Probability Distributions

2006, XX, 352 p., Hardcover
ISBN: 0-8176-4365-6

About this textbook

Lagrangian expansions can be used to obtain numerous useful probability models, which have been applied to real life situations including, but not limited to: branching processes, queuing processes, stochastic processes, environmental toxicology, diffusion of information, ecology, strikes in industries, sales of new products, and production targets for optimum profits. This book presents a comprehensive, systematic treatment of the class of Lagrangian probability distributions, along with some of its families, their properties, and important applications.

Key features:

* Fills a gap in book literature

* Examines many new Lagrangian probability distributions, their numerous families, general and specific properties, and applications to a variety of different fields

* Presents background mathematical and statistical formulas for easy reference

* Detailed bibliography and index

* Exercises in many chapters

Graduate students and researchers with a good knowledge of standard statistical techniques and an interest in Lagrangian probability distributions will find this work valuable. It may be used as a reference text or in courses and seminars on Distribution Theory and Lagrangian Distributions. Applied scientists and researchers in environmental statistics, reliability, sales management, epidemiology, operations research, optimization in manufacturing and marketing, and infectious disease control will benefit immensely from the various applications in the book.


Written for:

Graduate students and researchers interest in discrete probability distributions; applied scientists and researchers in environmental statistics, reliability, sales management, epidemiology, operations research, optimization in manufacturing and marketing, and infectious disease control

Table of contents

Andrzej Ruszczynski

Nonlinear Optimization

Cloth | 2006 | ISBN: 0-691-11915-5
464 pp. | 6 x 9 | 35 line illus.

Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures.

The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems.

Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.

Andrzej Ruszczynski is Professor of Operations Research at Rutgers University. He is the coauthor of Stochastic Programming and the coeditor of Decision Making under Uncertainty.

Endorsements:

"Nonlinear Optimization will become the standard textbook on its subject, as well as a reference book that everyone will want to own. Not only is it beautiful and elegant, it is also utterly comprehensive and modern, with many realistic and interesting examples."--Robert J. Vanderbei, Princeton University, author of Linear Programming

"This excellent book is the best I have reviewed in the past ten years. Very well written, its three main strengths are its treatment of theory and algorithms on equal terms, its mathematically driven presentation of the material, and its interesting examples and applications."--Ekkehard W. Sachs, Virginia Tech and Universitat Trier

Table of contents

Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.

Fundamentals of Algebraic Graph Transformation

Series: Monographs in Theoretical Computer Science. An EATCS Series
2006, XIV, 388 p. 41 illus., Hardcover
ISBN: 3-540-31187-4

About this book

Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory.

Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool environment. Finally the appendix covers the basics of category theory, signatures and algebras.

The book addresses both research scientists and graduate students in computer science, mathematics and engineering.

Written for:

Researchers, lecturers, graduate students

Table of contents

Part I: Introduction to Graph Transformation Systems: General Introduction.- Graphs, Typed Graphs, and the Gluing Construction.- Graph Transformation Systems.- Part II: Adhesive High-Level Replacement Categories and Systems: Adhesive High-Level Replacement Categories.- Adhesive High-Level Replacement Systems.- Embedding and Local Confluence.- Constraints and Application Conditions.- Part III: Typed Attributed Graph Transformation Systems: Typed Attributed Graphs.- Typed Attributed Graph Transformation Systems.- Embedding and Local Confluence for Typed AGT Systems.- Adhesive HLR Categories for Typed Attributed Graphs.- Constraints, Application Conditions and Termination for TAGT Systems.- Typed Attributed Graph Transformation with Inheritance.- Part IV: Case Study on Model Transformation, and Tool Support by AGG: Case Study on Model Transformation.- Implementation of Typed Attributed Graph Transformation by AGG.- Appendices: A Short Introduction to Category Theory.- A Short Introduction to Signatures and Algebras.- Detailed Proofs.- References.- Index.

V. I. Krylov
Arthur H. Stroud

Approximate Calculation of Integrals

ISBN: 0486445798
Page Count: 368
Dimensions: 5 3/8 x 8 1/2
A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to the problem of calculation of definite integrals, and the final part of the book explores methods for the calculation of indefinite integrals. 1962 ed.

Table of Contents

Translator's Preface
Part I. Preliminary Information
Chapter 1. Bernoulli Numbers and Bernoulli Polynomials
2. Orthogonal Polynomials
3. Interpolation of Functions
4. Linear Normed Spaces. Linear Operators
Part II. Approximate Calculation of Definite Integrals
5. Quadrature Sums and Problems Related to Them. The Remainder in Approximate Quadrature
6. Interpolatory Quadratures
7. Quadratures of the Highest Algebraic Degree of Precision
8. Quadrature Formulas with Least Estimate of the Remainder
9. Quadrature Formulas Containing Preassigned Nodes
10. Quadrature Formulas with Equal Coefficients
11. Increasing the Precision of Quadrature Formulas
12. Convergence of the Quadrature Process
Part III. Approximate Calculation of Indefinite Integrals
13. Introduction
14. Integration of Functions Given in Tabular Form
15. Calculation of Indefinte Integrals Using a Small Number of Values of the Integrand
16. Methods Which Use Several Previous Values of the Integral
Appendix A. Gaussian Quadrature Formulas for Constant Weight Function
Appendix B. Gaussian-Hermite Quadrature Formulas
Appendix C. Gaussian-Laguerre Quadrature Formulas
Index

Louis Brand

Advanced Calculus: An Introduction to Classical Analysis

ISBN: 0486445488
Page Count: 592
Dimensions: 5 3/8 x 8 1/2

A course in analysis that focuses on the functions of a real variable, this text is geared toward upper-level undergraduate students. It introduces the basic concepts in their simplest setting and illustrates its teachings with numerous examples, practical theorems, and coherent proofs. Starting with the structure of the system of real and complex numbers, it covers the convergence of sequences and series and explores the functions of a real variable and of several variables. Subsequent chapters offer a brief, self-contained introduction to vectors and the important differential invariants, the reversal of order in limiting processes, and Fourier series. 1955 ed.

Table of Contents

1. The Number System
2. Sequences and Series
3. Functions of a Real Variable
4. Functions of Several Variables
5. Vectors
6. The Definite Integral
7. Improper Integrals
8. Line Integrals
9. Multiple Integrals
10. Uniform Convergence
11. Functions of a Complex Variable
12. Fourier Series
Appendixes
Comprehensive Test
Answers to Problems
Index

Hassler Whitney

Geometric Integration Theory

ISBN: 0486445836
Page Count: 400
Dimensions: 5 3/8 x 8 1/2

Geared toward upper-level undergraduates and graduate students, this treatment of geometric integration theory consists of three parts: an introduction to classical theory, a postulational approach to general theory, and a final section on Lebesgue theory. The opening third of the treatment leads to the theory of the Riemann integral and includes a study of smooth manifolds. The second part explores abstract integration theory, some relations between chains and functions, general properties of chains and cochains, and chains and cochains in open sets. The final section surveys Lebesgue theory in terms of flat cochains and differential forms, Lipschitz mappings, and chains and additive set functions. Useful appendixes and indexes conclude the text. 1957 ed.

Table of Contents

Introduction
A. The general problem of integration
B. Some classical topics
C. Indications of general theory
Part I. Classical Theory
1. Grassmann algebra
2. Differential forms
3. Riemann integration theory
4. Smooth manifolds
A. Manifolds in Euclidean space
B. Triangulation of manifolds
C. Cohomology in manifolds
Part II. General Theory
5. Abstract integration theory
6. Some relations between chains and functions
7. General properties of chains and cochains
8. Chains and cochains in open sets
Part III. Lebesgue Theory
9. Flat cochains and differential forms
10. Lipschitz mappings
11. Chains and additive set functions
Appendix I. Vector and linear spaces
Appendix II. Geometric and topological preliminaries
Appendix III. Analytical preliminaries
Index of symbols
Index of terms